TSTP Solution File: NUM925+5 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 17:35:29 EDT 2024
% Result : Theorem 0.42s 0.70s
% Output : Proof 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : NUM925+5 : TPTP v8.2.0. Released v5.3.0.
% 0.03/0.16 % Command : do_cvc5 %s %d
% 0.16/0.39 % Computer : n024.cluster.edu
% 0.16/0.39 % Model : x86_64 x86_64
% 0.16/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39 % Memory : 8042.1875MB
% 0.16/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39 % CPULimit : 300
% 0.16/0.39 % WCLimit : 300
% 0.16/0.39 % DateTime : Tue May 28 01:54:24 EDT 2024
% 0.16/0.40 % CPUTime :
% 0.39/0.58 %----Proving TF0_NAR, FOF, or CNF
% 0.42/0.70 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.42/0.70 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.NwafCFT6y3/cvc5---1.0.5_23974.smt2
% 0.42/0.70 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.NwafCFT6y3/cvc5---1.0.5_23974.smt2
% 0.42/0.70 (assume a0 (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (= (tptp.ti X_a (tptp.one_one X_a)) (tptp.one_one X_a)))))
% 0.42/0.70 (assume a1 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1) B_2) (tptp.plus_plus X_a B_1 B_2)))))
% 0.42/0.70 (assume a2 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.plus_plus X_a B_1 (tptp.ti X_a B_2)) (tptp.plus_plus X_a B_1 B_2)))))
% 0.42/0.70 (assume a3 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2)))))
% 0.42/0.70 (assume a4 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.plus_plus X_a (tptp.ti X_a B_1) B_2) (tptp.plus_plus X_a B_1 B_2)))))
% 0.42/0.70 (assume a5 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.plus_plus X_a B_1 (tptp.ti X_a B_2)) (tptp.plus_plus X_a B_1 B_2)))))
% 0.42/0.70 (assume a6 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2)))))
% 0.42/0.70 (assume a7 (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (= (tptp.ti X_a (tptp.zero_zero X_a)) (tptp.zero_zero X_a)))))
% 0.42/0.70 (assume a8 (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a (tptp.zero_zero X_a)) (tptp.zero_zero X_a)))))
% 0.42/0.70 (assume a9 (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (= (tptp.ti X_a (tptp.zero_zero X_a)) (tptp.zero_zero X_a)))))
% 0.42/0.70 (assume a10 (forall ((X_a $$unsorted)) (= (tptp.ti X_a (tptp.undefined X_a)) (tptp.undefined X_a))))
% 0.42/0.70 (assume a11 (forall ((B_1 $$unsorted)) (= (tptp.bit0 (tptp.ti tptp.int B_1)) (tptp.bit0 B_1))))
% 0.42/0.70 (assume a12 (forall ((B_1 $$unsorted)) (= (tptp.ti tptp.int (tptp.bit0 B_1)) (tptp.bit0 B_1))))
% 0.42/0.70 (assume a13 (forall ((B_1 $$unsorted)) (= (tptp.bit1 (tptp.ti tptp.int B_1)) (tptp.bit1 B_1))))
% 0.42/0.70 (assume a14 (forall ((B_1 $$unsorted)) (= (tptp.ti tptp.int (tptp.bit1 B_1)) (tptp.bit1 B_1))))
% 0.42/0.70 (assume a15 (= (tptp.ti tptp.int tptp.pls) tptp.pls))
% 0.42/0.70 (assume a16 (forall ((B_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.number X_a) (= (tptp.number_number_of X_a (tptp.ti tptp.int B_1)) (tptp.number_number_of X_a B_1)))))
% 0.42/0.70 (assume a17 (forall ((B_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.number X_a) (= (tptp.ti X_a (tptp.number_number_of X_a B_1)) (tptp.number_number_of X_a B_1)))))
% 0.42/0.70 (assume a18 (forall ((B_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.semiring_1_of_nat X_a (tptp.ti tptp.nat B_1)) (tptp.semiring_1_of_nat X_a B_1)))))
% 0.42/0.70 (assume a19 (forall ((B_1 $$unsorted) (X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.ti X_a (tptp.semiring_1_of_nat X_a B_1)) (tptp.semiring_1_of_nat X_a B_1)))))
% 0.42/0.70 (assume a20 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (= (tptp.ord_less X_a (tptp.ti X_a B_1) B_2) (tptp.ord_less X_a B_1 B_2)))))
% 0.42/0.70 (assume a21 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (= (tptp.ord_less X_a B_1 (tptp.ti X_a B_2)) (tptp.ord_less X_a B_1 B_2)))))
% 0.42/0.70 (assume a22 (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.ord_less tptp.nat (tptp.ti tptp.nat B_1) B_2) (tptp.ord_less tptp.nat B_1 B_2))))
% 0.42/0.70 (assume a23 (forall ((B_1 $$unsorted) (B_2 $$unsorted)) (= (tptp.ord_less tptp.nat B_1 (tptp.ti tptp.nat B_2)) (tptp.ord_less tptp.nat B_1 B_2))))
% 0.42/0.70 (assume a24 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (= (tptp.power_power X_a (tptp.ti X_a B_1) B_2) (tptp.power_power X_a B_1 B_2)))))
% 0.42/0.70 (assume a25 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (= (tptp.power_power X_a B_1 (tptp.ti tptp.nat B_2)) (tptp.power_power X_a B_1 B_2)))))
% 0.42/0.70 (assume a26 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (= (tptp.ti X_a (tptp.power_power X_a B_1 B_2)) (tptp.power_power X_a B_1 B_2)))))
% 0.42/0.70 (assume a27 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (= (tptp.power_power X_a (tptp.ti X_a B_1) B_2) (tptp.power_power X_a B_1 B_2)))))
% 0.42/0.70 (assume a28 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (= (tptp.power_power X_a B_1 (tptp.ti tptp.nat B_2)) (tptp.power_power X_a B_1 B_2)))))
% 0.42/0.70 (assume a29 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (= (tptp.ti X_a (tptp.power_power X_a B_1 B_2)) (tptp.power_power X_a B_1 B_2)))))
% 0.42/0.70 (assume a30 (= (tptp.ti tptp.nat tptp.n) tptp.n))
% 0.42/0.70 (assume a31 (= (tptp.ti tptp.int tptp.t) tptp.t))
% 0.42/0.70 (assume a32 (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))
% 0.42/0.70 (assume a33 (tptp.ord_less tptp.int (tptp.one_one tptp.int) tptp.t))
% 0.42/0.70 (assume a34 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (= (tptp.plus_plus X_a (tptp.power_power X_a Xa (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.power_power X_a Ya (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (tptp.zero_zero X_a)) (and (= (tptp.ti X_a Xa) (tptp.zero_zero X_a)) (= (tptp.ti X_a Ya) (tptp.zero_zero X_a))))))))
% 0.42/0.70 (assume a35 (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a (tptp.one_one X_a) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.one_one X_a)))))
% 0.42/0.70 (assume a36 (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.power_power X_a (tptp.zero_zero X_a) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)))))
% 0.42/0.70 (assume a37 (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))))
% 0.42/0.70 (assume a38 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (= (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int (tptp.bit1 tptp.pls) W)))))))
% 0.42/0.70 (assume a39 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V (tptp.bit1 tptp.pls))))))))
% 0.42/0.70 (assume a40 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))))))
% 0.42/0.70 (assume a41 (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.plus_plus X_a (tptp.one_one X_a) (tptp.one_one X_a)) (tptp.number_number_of X_a (tptp.bit0 (tptp.bit1 tptp.pls)))))))
% 0.42/0.70 (assume a42 (forall ((X $$unsorted)) (= (tptp.power_power tptp.int (tptp.power_power tptp.int X (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.power_power tptp.int X (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit0 (tptp.bit1 tptp.pls))))))))
% 0.42/0.70 (assume a43 (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((W $$unsorted)) (and (=> (= (tptp.number_number_of tptp.nat W) (tptp.zero_zero tptp.nat)) (= (tptp.power_power X_a (tptp.zero_zero X_a) (tptp.number_number_of tptp.nat W)) (tptp.one_one X_a))) (=> (not (= (tptp.number_number_of tptp.nat W) (tptp.zero_zero tptp.nat))) (= (tptp.power_power X_a (tptp.zero_zero X_a) (tptp.number_number_of tptp.nat W)) (tptp.zero_zero X_a))))))))
% 0.42/0.70 (assume a44 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.one_one X_a) (tptp.number_number_of X_a (tptp.bit1 tptp.pls))))))
% 0.42/0.70 (assume a45 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.number_number_of X_a (tptp.bit1 tptp.pls)) (tptp.one_one X_a)))))
% 0.42/0.70 (assume a46 (tptp.ord_less tptp.nat (tptp.zero_zero tptp.nat) tptp.n))
% 0.42/0.70 (assume a47 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.ord_less tptp.int X Y) (= X Y) (tptp.ord_less tptp.int Y X))))
% 0.42/0.70 (assume a48 (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.number_number_of tptp.int K_1) (tptp.number_number_of tptp.int L_1)) (tptp.ord_less tptp.int K_1 L_1))))
% 0.42/0.70 (assume a49 (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.number_number_of tptp.int V) (tptp.number_number_of tptp.int W)) (tptp.number_number_of tptp.int (tptp.plus_plus tptp.int V W)))))
% 0.42/0.70 (assume a50 (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (tptp.ord_less X_a (tptp.number_number_of X_a Xa) (tptp.number_number_of X_a Ya)) (tptp.ord_less tptp.int Xa Ya))))))
% 0.42/0.70 (assume a51 (= (tptp.zero_zero tptp.int) (tptp.number_number_of tptp.int tptp.pls)))
% 0.42/0.70 (assume a52 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.power_power tptp.int (tptp.semiring_1_of_nat tptp.int M) N) (tptp.semiring_1_of_nat tptp.int (tptp.power_power tptp.nat M N)))))
% 0.42/0.70 (assume a53 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.semiring_1_of_nat tptp.int (tptp.power_power tptp.nat M N)) (tptp.power_power tptp.int (tptp.semiring_1_of_nat tptp.int M) N))))
% 0.42/0.70 (assume a54 (forall ((M $$unsorted) (N $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.semiring_1_of_nat tptp.int M) (tptp.plus_plus tptp.int (tptp.semiring_1_of_nat tptp.int N) Z)) (tptp.plus_plus tptp.int (tptp.semiring_1_of_nat tptp.int (tptp.plus_plus tptp.nat M N)) Z))))
% 0.42/0.70 (assume a55 (forall ((M $$unsorted) (N $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.semiring_1_of_nat tptp.int M) (tptp.semiring_1_of_nat tptp.int N)) (tptp.semiring_1_of_nat tptp.int (tptp.plus_plus tptp.nat M N)))))
% 0.42/0.70 (assume a56 (= (tptp.semiring_1_of_nat tptp.int (tptp.one_one tptp.nat)) (tptp.one_one tptp.int)))
% 0.42/0.70 (assume a57 (= (tptp.number_number_of tptp.nat tptp.pls) (tptp.zero_zero tptp.nat)))
% 0.42/0.70 (assume a58 (= (tptp.zero_zero tptp.nat) (tptp.number_number_of tptp.nat tptp.pls)))
% 0.42/0.70 (assume a59 (forall ((Na $$unsorted)) (= (= (tptp.semiring_1_of_nat tptp.int Na) (tptp.zero_zero tptp.int)) (= Na (tptp.zero_zero tptp.nat)))))
% 0.42/0.70 (assume a60 (= (tptp.semiring_1_of_nat tptp.int (tptp.zero_zero tptp.nat)) (tptp.zero_zero tptp.int)))
% 0.42/0.70 (assume a61 (= (tptp.plus_plus tptp.nat (tptp.one_one tptp.nat) (tptp.one_one tptp.nat)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))
% 0.42/0.70 (assume a62 (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K1) (tptp.bit1 K2)) (tptp.ord_less tptp.int K1 K2))))
% 0.42/0.70 (assume a63 (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K_1) (tptp.bit1 L_1)) (tptp.ord_less tptp.int K_1 L_1))))
% 0.42/0.70 (assume a64 (not (tptp.ord_less tptp.int tptp.pls tptp.pls)))
% 0.42/0.70 (assume a65 (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K1) (tptp.bit0 K2)) (tptp.ord_less tptp.int K1 K2))))
% 0.42/0.70 (assume a66 (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K_1) (tptp.bit0 L_1)) (tptp.ord_less tptp.int K_1 L_1))))
% 0.42/0.70 (assume a67 (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.ord_less tptp.int I J) (tptp.ord_less tptp.int (tptp.plus_plus tptp.int I K) (tptp.plus_plus tptp.int J K)))))
% 0.42/0.70 (assume a68 (forall ((V_1 $$unsorted) (V $$unsorted)) (and (=> (tptp.ord_less tptp.int V tptp.pls) (= (tptp.plus_plus tptp.nat (tptp.number_number_of tptp.nat V) (tptp.number_number_of tptp.nat V_1)) (tptp.number_number_of tptp.nat V_1))) (=> (not (tptp.ord_less tptp.int V tptp.pls)) (and (=> (tptp.ord_less tptp.int V_1 tptp.pls) (= (tptp.plus_plus tptp.nat (tptp.number_number_of tptp.nat V) (tptp.number_number_of tptp.nat V_1)) (tptp.number_number_of tptp.nat V))) (=> (not (tptp.ord_less tptp.int V_1 tptp.pls)) (= (tptp.plus_plus tptp.nat (tptp.number_number_of tptp.nat V) (tptp.number_number_of tptp.nat V_1)) (tptp.number_number_of tptp.nat (tptp.plus_plus tptp.int V V_1)))))))))
% 0.42/0.70 (assume a69 (= (tptp.one_one tptp.int) (tptp.number_number_of tptp.int (tptp.bit1 tptp.pls))))
% 0.42/0.70 (assume a70 (= (tptp.number_number_of tptp.nat (tptp.bit1 tptp.pls)) (tptp.one_one tptp.nat)))
% 0.42/0.70 (assume a71 (= (tptp.one_one tptp.nat) (tptp.number_number_of tptp.nat (tptp.bit1 tptp.pls))))
% 0.42/0.70 (assume a72 (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (= (tptp.number_number_of X_a Xa) (tptp.number_number_of X_a Ya)) (= Xa Ya))))))
% 0.42/0.70 (assume a73 (forall ((X_a $$unsorted)) (=> (tptp.number X_a) (forall ((Wa $$unsorted) (Xa $$unsorted)) (= (= (tptp.number_number_of X_a Wa) (tptp.ti X_a Xa)) (= (tptp.ti X_a Xa) (tptp.number_number_of X_a Wa)))))))
% 0.42/0.70 (assume a74 (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (= (tptp.bit1 K_1) (tptp.bit1 L_1)) (= K_1 L_1))))
% 0.42/0.70 (assume a75 (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (= (tptp.bit0 K_1) (tptp.bit0 L_1)) (= K_1 L_1))))
% 0.42/0.70 (assume a76 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (= (tptp.ord_less X_a (tptp.plus_plus X_a A_2 A_2) (tptp.zero_zero X_a)) (tptp.ord_less X_a A_2 (tptp.zero_zero X_a)))))))
% 0.42/0.70 (assume a77 (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int Z1 Z2) Z3) (tptp.plus_plus tptp.int Z1 (tptp.plus_plus tptp.int Z2 Z3)))))
% 0.42/0.70 (assume a78 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus tptp.int X (tptp.plus_plus tptp.int Y Z)) (tptp.plus_plus tptp.int Y (tptp.plus_plus tptp.int X Z)))))
% 0.42/0.70 (assume a79 (forall ((Z $$unsorted) (W $$unsorted)) (= (tptp.plus_plus tptp.int Z W) (tptp.plus_plus tptp.int W Z))))
% 0.42/0.70 (assume a80 (forall ((Ma $$unsorted) (Na $$unsorted)) (= (= (tptp.semiring_1_of_nat tptp.int Ma) (tptp.semiring_1_of_nat tptp.int Na)) (= Ma Na))))
% 0.42/0.70 (assume a81 (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted)) (= (tptp.ord_less X_a (tptp.number_number_of X_a Xa) (tptp.zero_zero X_a)) (tptp.ord_less tptp.int Xa tptp.pls))))))
% 0.42/0.70 (assume a82 (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Ya $$unsorted)) (= (tptp.ord_less X_a (tptp.zero_zero X_a) (tptp.number_number_of X_a Ya)) (tptp.ord_less tptp.int tptp.pls Ya))))))
% 0.42/0.70 (assume a83 (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K_1) tptp.pls) (tptp.ord_less tptp.int K_1 tptp.pls))))
% 0.42/0.70 (assume a84 (forall ((K1 $$unsorted) (K2 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K1) (tptp.bit0 K2)) (tptp.ord_less tptp.int K1 K2))))
% 0.42/0.70 (assume a85 (forall ((K_1 $$unsorted) (L_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 K_1) (tptp.bit0 L_1)) (tptp.ord_less tptp.int K_1 L_1))))
% 0.42/0.70 (assume a86 (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 K_1) tptp.pls) (tptp.ord_less tptp.int K_1 tptp.pls))))
% 0.42/0.70 (assume a87 (forall ((K_1 $$unsorted)) (= (tptp.ord_less tptp.int tptp.pls (tptp.bit0 K_1)) (tptp.ord_less tptp.int tptp.pls K_1))))
% 0.42/0.70 (assume a88 (forall ((Wa $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit1 Wa) (tptp.zero_zero tptp.int)) (tptp.ord_less tptp.int Wa (tptp.zero_zero tptp.int)))))
% 0.42/0.70 (assume a89 (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))
% 0.42/0.70 (assume a90 (forall ((Wa $$unsorted)) (= (tptp.ord_less tptp.int (tptp.bit0 Wa) (tptp.zero_zero tptp.int)) (tptp.ord_less tptp.int Wa (tptp.zero_zero tptp.int)))))
% 0.42/0.70 (assume a91 (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.one_one tptp.int)))
% 0.42/0.70 (assume a92 (forall ((Wa $$unsorted) (Z_1 $$unsorted)) (= (tptp.ord_less tptp.int Wa (tptp.plus_plus tptp.int Z_1 (tptp.one_one tptp.int))) (or (tptp.ord_less tptp.int Wa Z_1) (= Wa Z_1)))))
% 0.42/0.70 (assume a93 (forall ((K $$unsorted)) (not (tptp.ord_less tptp.int (tptp.semiring_1_of_nat tptp.int K) (tptp.zero_zero tptp.int)))))
% 0.42/0.70 (assume a94 (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Xa $$unsorted)) (= (tptp.ord_less X_a (tptp.number_number_of X_a Xa) (tptp.one_one X_a)) (tptp.ord_less tptp.int Xa (tptp.bit1 tptp.pls)))))))
% 0.42/0.70 (assume a95 (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Ya $$unsorted)) (= (tptp.ord_less X_a (tptp.one_one X_a) (tptp.number_number_of X_a Ya)) (tptp.ord_less tptp.int (tptp.bit1 tptp.pls) Ya))))))
% 0.42/0.70 (assume a96 (forall ((Z_1 $$unsorted)) (= (tptp.ord_less tptp.int (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z_1) Z_1) (tptp.zero_zero tptp.int)) (tptp.ord_less tptp.int Z_1 (tptp.zero_zero tptp.int)))))
% 0.42/0.70 (assume a97 (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.plus_plus X_a A_2 A_2) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))))
% 0.42/0.70 (assume a98 (forall ((K $$unsorted)) (not (= (tptp.bit1 K) tptp.pls))))
% 0.42/0.70 (assume a99 (forall ((L $$unsorted)) (not (= tptp.pls (tptp.bit1 L)))))
% 0.42/0.70 (assume a100 (forall ((K $$unsorted) (L $$unsorted)) (not (= (tptp.bit1 K) (tptp.bit0 L)))))
% 0.42/0.70 (assume a101 (forall ((K $$unsorted) (L $$unsorted)) (not (= (tptp.bit0 K) (tptp.bit1 L)))))
% 0.42/0.70 (assume a102 (forall ((K_1 $$unsorted)) (= (= (tptp.bit0 K_1) tptp.pls) (= K_1 tptp.pls))))
% 0.42/0.70 (assume a103 (forall ((L_1 $$unsorted)) (= (= tptp.pls (tptp.bit0 L_1)) (= tptp.pls L_1))))
% 0.42/0.70 (assume a104 (= (tptp.bit0 tptp.pls) tptp.pls))
% 0.42/0.70 (assume a105 (= tptp.pls (tptp.zero_zero tptp.int)))
% 0.42/0.70 (assume a106 (not (= (tptp.zero_zero tptp.int) (tptp.one_one tptp.int))))
% 0.42/0.70 (assume a107 (forall ((K $$unsorted)) (= (tptp.plus_plus tptp.int K tptp.pls) K)))
% 0.42/0.70 (assume a108 (forall ((K $$unsorted)) (= (tptp.plus_plus tptp.int tptp.pls K) K)))
% 0.42/0.70 (assume a109 (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit0 K) (tptp.bit0 L)) (tptp.bit0 (tptp.plus_plus tptp.int K L)))))
% 0.42/0.70 (assume a110 (forall ((K $$unsorted)) (= (tptp.bit0 K) (tptp.plus_plus tptp.int K K))))
% 0.42/0.70 (assume a111 (forall ((Z $$unsorted)) (= (tptp.plus_plus tptp.int Z (tptp.zero_zero tptp.int)) Z)))
% 0.42/0.70 (assume a112 (forall ((Z $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.zero_zero tptp.int) Z) Z)))
% 0.42/0.70 (assume a113 (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.number_number_of X_a tptp.pls) (tptp.zero_zero X_a)))))
% 0.42/0.70 (assume a114 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.number_number_of X_a tptp.pls) (tptp.zero_zero X_a)))))
% 0.42/0.70 (assume a115 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.zero_zero X_a) (tptp.number_number_of X_a tptp.pls)))))
% 0.42/0.70 (assume a116 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a tptp.pls) A_1) (tptp.ti X_a A_1))))))
% 0.42/0.70 (assume a117 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.plus_plus X_a A_1 (tptp.number_number_of X_a tptp.pls)) (tptp.ti X_a A_1))))))
% 0.42/0.70 (assume a118 (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_2 $$unsorted) (Wa $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat Wa)) (tptp.zero_zero X_a)) (and (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)) (not (= (tptp.number_number_of tptp.nat Wa) (tptp.zero_zero tptp.nat)))))))))
% 0.42/0.70 (assume a119 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.plus_plus X_a (tptp.number_number_of X_a W) Z)) (tptp.plus_plus X_a (tptp.number_number_of X_a (tptp.plus_plus tptp.int V W)) Z))))))
% 0.42/0.70 (assume a120 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a W)) (tptp.number_number_of X_a (tptp.plus_plus tptp.int V W)))))))
% 0.42/0.70 (assume a121 (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (= (tptp.number_number_of X_a (tptp.plus_plus tptp.int V W)) (tptp.plus_plus X_a (tptp.number_number_of X_a V) (tptp.number_number_of X_a W)))))))
% 0.42/0.70 (assume a122 (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit1 K) (tptp.bit0 L)) (tptp.bit1 (tptp.plus_plus tptp.int K L)))))
% 0.42/0.70 (assume a123 (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.plus_plus tptp.int (tptp.bit0 K) (tptp.bit1 L)) (tptp.bit1 (tptp.plus_plus tptp.int K L)))))
% 0.42/0.70 (assume a124 (forall ((K $$unsorted)) (= (tptp.bit1 K) (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) K) K))))
% 0.42/0.70 (assume a125 (forall ((Z $$unsorted)) (not (= (tptp.plus_plus tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) Z) Z) (tptp.zero_zero tptp.int)))))
% 0.42/0.70 (assume a126 (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((N $$unsorted)) (= (tptp.number_number_of X_a (tptp.semiring_1_of_nat tptp.int N)) (tptp.semiring_1_of_nat X_a N))))))
% 0.42/0.70 (assume a127 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (= (tptp.ord_less X_a (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (not (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))))))))
% 0.42/0.70 (assume a128 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (not (tptp.ord_less X_a (tptp.power_power X_a A_1 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)))))))
% 0.42/0.70 (assume a129 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Xa $$unsorted) (Ya $$unsorted)) (= (tptp.ord_less X_a (tptp.zero_zero X_a) (tptp.plus_plus X_a (tptp.power_power X_a Xa (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.power_power X_a Ya (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (or (not (= (tptp.ti X_a Xa) (tptp.zero_zero X_a))) (not (= (tptp.ti X_a Ya) (tptp.zero_zero X_a)))))))))
% 0.42/0.70 (assume a130 (tptp.linord219039673up_add tptp.int))
% 0.42/0.70 (assume a131 (tptp.ring_11004092258visors tptp.int))
% 0.42/0.70 (assume a132 (tptp.no_zero_divisors tptp.int))
% 0.42/0.70 (assume a133 (tptp.linordered_idom tptp.int))
% 0.42/0.70 (assume a134 (tptp.number_semiring tptp.int))
% 0.42/0.70 (assume a135 (tptp.zero_neq_one tptp.int))
% 0.42/0.70 (assume a136 (tptp.semiring_1 tptp.int))
% 0.42/0.70 (assume a137 (tptp.semiring_0 tptp.int))
% 0.42/0.70 (assume a138 (tptp.mult_zero tptp.int))
% 0.42/0.70 (assume a139 (tptp.ring_char_0 tptp.int))
% 0.42/0.70 (assume a140 (tptp.number_ring tptp.int))
% 0.42/0.70 (assume a141 (tptp.power tptp.int))
% 0.42/0.70 (assume a142 (tptp.number tptp.int))
% 0.42/0.70 (assume a143 (tptp.no_zero_divisors tptp.nat))
% 0.42/0.70 (assume a144 (tptp.number_semiring tptp.nat))
% 0.42/0.70 (assume a145 (tptp.zero_neq_one tptp.nat))
% 0.42/0.70 (assume a146 (tptp.semiring_1 tptp.nat))
% 0.42/0.70 (assume a147 (tptp.semiring_0 tptp.nat))
% 0.42/0.70 (assume a148 (tptp.mult_zero tptp.nat))
% 0.42/0.70 (assume a149 (tptp.power tptp.nat))
% 0.42/0.70 (assume a150 (tptp.number tptp.nat))
% 0.42/0.70 (assume a151 (forall ((T $$unsorted) (A $$unsorted)) (= (tptp.ti T (tptp.ti T A)) (tptp.ti T A))))
% 0.42/0.70 (assume a152 (not (not (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int)))))
% 0.42/0.70 (assume a153 true)
% 0.42/0.70 (step t1 (cl (not (= (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) (not (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule equiv_pos2)
% 0.42/0.70 (step t2 (cl (= (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule refl)
% 0.42/0.70 (step t3 (cl (= (= (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) true) (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))) :rule equiv_simplify)
% 0.42/0.70 (step t4 (cl (not (= (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) true)) (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) :rule equiv1 :premises (t3))
% 0.42/0.70 (step t5 (cl (= (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))))) :rule all_simplify)
% 0.42/0.70 (step t6 (cl (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) :rule refl)
% 0.42/0.70 (step t7 (cl (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) :rule all_simplify)
% 0.42/0.70 (step t8 (cl (= (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))) (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))) :rule cong :premises (t6 t7))
% 0.42/0.70 (step t9 (cl (= (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) true)) :rule all_simplify)
% 0.42/0.70 (step t10 (cl (= (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))) true)) :rule trans :premises (t8 t9))
% 0.42/0.70 (step t11 (cl (= (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) true)) :rule trans :premises (t5 t10))
% 0.42/0.70 (step t12 (cl (= (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) :rule resolution :premises (t4 t11))
% 0.42/0.70 (step t13 (cl (= (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= tptp.pls (tptp.zero_zero tptp.int))))) :rule refl)
% 0.42/0.70 (step t14 (cl (= (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule refl)
% 0.42/0.70 (step t15 (cl (= (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule refl)
% 0.42/0.70 (step t16 (cl (= (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule cong :premises (t2 t12 t13 t14 t15))
% 0.42/0.70 (step t17 (cl (not (= (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) (not (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule equiv_pos2)
% 0.42/0.70 (step t18 (cl (= (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule refl)
% 0.42/0.70 (step t19 (cl (= (= (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule equiv_simplify)
% 0.42/0.70 (step t20 (cl (= (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) (not (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule equiv2 :premises (t19))
% 0.42/0.70 (step t21 (cl (not (not (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule not_not)
% 0.42/0.70 (step t22 (cl (= (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule resolution :premises (t20 t21))
% 0.42/0.70 (step t23 (cl (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule implies_neg1)
% 0.42/0.70 (anchor :step t24)
% 0.42/0.70 (assume t24.a0 (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))
% 0.42/0.70 (assume t24.a1 (= tptp.pls (tptp.zero_zero tptp.int)))
% 0.42/0.70 (assume t24.a2 (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))
% 0.42/0.70 (assume t24.a3 (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))
% 0.42/0.70 (assume t24.a4 (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))
% 0.42/0.70 (step t24.t1 (cl (not (= (= true false) false)) (not (= true false)) false) :rule equiv_pos2)
% 0.42/0.70 (step t24.t2 (cl (= (= true false) false)) :rule all_simplify)
% 0.42/0.70 (step t24.t3 (cl (= (= (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) true) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule equiv_simplify)
% 0.42/0.70 (step t24.t4 (cl (= (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) true) (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule equiv2 :premises (t24.t3))
% 0.42/0.70 (step t24.t5 (cl (= (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) true)) :rule resolution :premises (t24.t4 t24.a4))
% 0.42/0.70 (step t24.t6 (cl (= true (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule symm :premises (t24.t5))
% 0.42/0.70 (step t24.t7 (cl (= tptp.int tptp.int)) :rule refl)
% 0.42/0.70 (step t24.t8 (cl (= (tptp.zero_zero tptp.int) tptp.pls)) :rule symm :premises (t24.a1))
% 0.42/0.70 (step t24.t9 (cl (= (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) :rule symm :premises (t24.a3))
% 0.42/0.70 (step t24.t10 (cl (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule symm :premises (t24.t9))
% 0.42/0.70 (step t24.t11 (cl (= (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (tptp.zero_zero tptp.int))) :rule symm :premises (t24.a2))
% 0.42/0.70 (step t24.t12 (cl (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.zero_zero tptp.int))) :rule trans :premises (t24.t10 t24.t11))
% 0.42/0.70 (step t24.t13 (cl (= (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) :rule cong :premises (t24.t7 t24.t8 t24.t12))
% 0.42/0.70 (step t24.t14 (cl (= (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) false) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))) :rule equiv_simplify)
% 0.42/0.70 (step t24.t15 (cl (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) false) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))) :rule equiv2 :premises (t24.t14))
% 0.42/0.70 (step t24.t16 (cl (not (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) :rule not_not)
% 0.42/0.70 (step t24.t17 (cl (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) false) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) :rule resolution :premises (t24.t15 t24.t16))
% 0.42/0.70 (step t24.t18 (cl (= (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) false)) :rule resolution :premises (t24.t17 t24.a0))
% 0.42/0.70 (step t24.t19 (cl (= true false)) :rule trans :premises (t24.t6 t24.t13 t24.t18))
% 0.42/0.70 (step t24.t20 (cl false) :rule resolution :premises (t24.t1 t24.t2 t24.t19))
% 0.42/0.70 (step t24 (cl (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) :rule subproof :discharge (t24.a0 t24.a1 t24.a2 t24.a3 t24.a4))
% 0.42/0.70 (step t25 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) :rule and_pos)
% 0.42/0.70 (step t26 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (= tptp.pls (tptp.zero_zero tptp.int))) :rule and_pos)
% 0.42/0.70 (step t27 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule and_pos)
% 0.42/0.70 (step t28 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule and_pos)
% 0.42/0.70 (step t29 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) :rule and_pos)
% 0.42/0.70 (step t30 (cl false (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule resolution :premises (t24 t25 t26 t27 t28 t29))
% 0.42/0.71 (step t31 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) false) :rule reordering :premises (t30))
% 0.42/0.71 (step t32 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) false) :rule contraction :premises (t31))
% 0.42/0.71 (step t33 (cl (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) false) :rule resolution :premises (t23 t32))
% 0.42/0.71 (step t34 (cl (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) (not false)) :rule implies_neg2)
% 0.42/0.71 (step t35 (cl (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false)) :rule resolution :premises (t33 t34))
% 0.42/0.71 (step t36 (cl (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false)) :rule contraction :premises (t35))
% 0.42/0.71 (step t37 (cl (= (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule implies_simplify)
% 0.42/0.71 (step t38 (cl (not (=> (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false)) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule equiv1 :premises (t37))
% 0.42/0.71 (step t39 (cl (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule resolution :premises (t36 t38))
% 0.42/0.71 (step t40 (cl (= (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) false)) :rule resolution :premises (t22 t39))
% 0.42/0.71 (step t41 (cl (= (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) false))) :rule cong :premises (t18 t40))
% 0.42/0.71 (step t42 (cl (= (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) false) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule all_simplify)
% 0.42/0.71 (step t43 (cl (= (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule trans :premises (t41 t42))
% 0.42/0.71 (step t44 (cl (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule implies_neg1)
% 0.42/0.71 (anchor :step t45)
% 0.42/0.71 (assume t45.a0 (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))
% 0.42/0.71 (assume t45.a1 (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))))
% 0.42/0.71 (assume t45.a2 (= tptp.pls (tptp.zero_zero tptp.int)))
% 0.42/0.71 (assume t45.a3 (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))
% 0.42/0.71 (assume t45.a4 (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))
% 0.42/0.71 (step t45.t1 (cl (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule and_neg)
% 0.42/0.71 (step t45.t2 (cl (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule resolution :premises (t45.t1 t45.a1 t45.a2 t45.a4 t45.a3 t45.a0))
% 0.42/0.71 (step t45 (cl (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule subproof :discharge (t45.a0 t45.a1 t45.a2 t45.a3 t45.a4))
% 0.42/0.71 (step t46 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) :rule and_pos)
% 0.42/0.71 (step t47 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) :rule and_pos)
% 0.42/0.71 (step t48 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (= tptp.pls (tptp.zero_zero tptp.int))) :rule and_pos)
% 0.42/0.71 (step t49 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule and_pos)
% 0.42/0.71 (step t50 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule and_pos)
% 0.42/0.71 (step t51 (cl (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t45 t46 t47 t48 t49 t50))
% 0.42/0.71 (step t52 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule reordering :premises (t51))
% 0.42/0.71 (step t53 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule contraction :premises (t52))
% 0.42/0.71 (step t54 (cl (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule resolution :premises (t44 t53))
% 0.42/0.71 (step t55 (cl (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule implies_neg2)
% 0.42/0.71 (step t56 (cl (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule resolution :premises (t54 t55))
% 0.42/0.71 (step t57 (cl (=> (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (and (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule contraction :premises (t56))
% 0.42/0.71 (step t58 (cl (not (and (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))) (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int))) (= tptp.pls (tptp.zero_zero tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t17 t43 t57))
% 0.42/0.71 (step t59 (cl (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule not_and :premises (t58))
% 0.42/0.71 (step t60 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule or_neg)
% 0.42/0.71 (step t61 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))))) :rule or_neg)
% 0.42/0.71 (step t62 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (not (= tptp.pls (tptp.zero_zero tptp.int))))) :rule or_neg)
% 0.42/0.71 (step t63 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule or_neg)
% 0.42/0.71 (step t64 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule or_neg)
% 0.42/0.71 (step t65 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t59 t60 t61 t62 t63 t64))
% 0.42/0.71 (step t66 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (not (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule contraction :premises (t65))
% 0.42/0.71 (step t67 (cl (or (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t1 t16 t66))
% 0.42/0.71 (step t68 (cl (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule or :premises (t67))
% 0.42/0.71 (step t69 (cl (tptp.ord_less tptp.int tptp.pls (tptp.zero_zero tptp.int)) (not (tptp.ord_less tptp.int (tptp.zero_zero tptp.int) (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (= tptp.pls (tptp.zero_zero tptp.int))) (not (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule reordering :premises (t68))
% 0.42/0.71 (step t70 (cl (not (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule equiv_pos2)
% 0.42/0.71 (step t71 (cl (not (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule reordering :premises (t70))
% 0.42/0.71 (step t72 (cl (not (= (not (not (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int)))) (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) (not (not (not (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int))))) (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) :rule equiv_pos2)
% 0.42/0.71 (step t73 (cl (= (not (not (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int)))) (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int)))) :rule all_simplify)
% 0.42/0.71 (step t74 (cl (= (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int)) (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) :rule all_simplify)
% 0.42/0.71 (step t75 (cl (= (not (not (= (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int)))) (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) :rule trans :premises (t73 t74))
% 0.42/0.71 (step t76 (cl (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))))) :rule resolution :premises (t72 t75 a152))
% 0.42/0.71 (step t77 (cl (not (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule or_pos)
% 0.42/0.71 (step t78 (cl (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) (not (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule reordering :premises (t77))
% 0.42/0.71 (step t79 (cl (=> (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038)))))) :rule implies_neg1)
% 0.42/0.71 (anchor :step t80)
% 0.42/0.71 (assume t80.a0 (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))))
% 0.42/0.71 (step t80.t1 (cl (or (not (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038)))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule forall_inst :args ((:= X_a tptp.int) (:= BOUND_VARIABLE_2038 (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))
% 0.42/0.71 (step t80.t2 (cl (not (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038)))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule or :premises (t80.t1))
% 0.42/0.71 (step t80.t3 (cl (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t80.t2 t80.a0))
% 0.42/0.71 (step t80 (cl (not (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038)))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule subproof :discharge (t80.a0))
% 0.42/0.71 (step t81 (cl (=> (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t79 t80))
% 0.42/0.71 (step t82 (cl (=> (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) (not (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule implies_neg2)
% 0.42/0.71 (step t83 (cl (=> (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) (=> (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule resolution :premises (t81 t82))
% 0.42/0.71 (step t84 (cl (=> (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))))) :rule contraction :premises (t83))
% 0.42/0.71 (step t85 (cl (not (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038)))))) (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule implies :premises (t84))
% 0.42/0.71 (step t86 (cl (not (= (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))))) (not (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038)))))) :rule equiv_pos2)
% 0.42/0.71 (anchor :step t87 :args ((X_a $$unsorted) (:= X_a X_a)))
% 0.42/0.71 (step t87.t1 (cl (= X_a X_a)) :rule refl)
% 0.42/0.71 (step t87.t2 (cl (= (tptp.ring_11004092258visors X_a) (tptp.ring_11004092258visors X_a))) :rule refl)
% 0.42/0.71 (anchor :step t87.t3 :args ((A_2 $$unsorted) (:= A_2 A_2)))
% 0.42/0.71 (step t87.t3.t1 (cl (= A_2 A_2)) :rule refl)
% 0.42/0.71 (step t87.t3.t2 (cl (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))))) :rule all_simplify)
% 0.42/0.71 (step t87.t3.t3 (cl (= (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2)))) :rule all_simplify)
% 0.42/0.71 (step t87.t3.t4 (cl (= (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2))))) :rule cong :premises (t87.t3.t2 t87.t3.t3))
% 0.42/0.71 (step t87.t3 (cl (= (forall ((A_2 $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2)))))) :rule bind)
% 0.42/0.71 (step t87.t4 (cl (= (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))))) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2))))))) :rule cong :premises (t87.t2 t87.t3))
% 0.42/0.71 (step t87 (cl (= (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2)))))))) :rule bind)
% 0.42/0.71 (step t88 (cl (= (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2)))))) (forall ((X_a $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2)))))))) :rule all_simplify)
% 0.42/0.71 (step t89 (cl (= (forall ((X_a $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2)))))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))))) :rule all_simplify)
% 0.42/0.71 (step t90 (cl (= (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a A_2)))))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))))) :rule trans :premises (t88 t89))
% 0.42/0.71 (step t91 (cl (= (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.power_power X_a A_2 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls)))) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038))))))) :rule trans :premises (t87 t90))
% 0.42/0.71 (step t92 (cl (forall ((X_a $$unsorted) (BOUND_VARIABLE_2038 $$unsorted)) (or (not (tptp.ring_11004092258visors X_a)) (= (= (tptp.zero_zero X_a) (tptp.power_power X_a BOUND_VARIABLE_2038 (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero X_a) (tptp.ti X_a BOUND_VARIABLE_2038)))))) :rule resolution :premises (t86 t91 a37))
% 0.42/0.71 (step t93 (cl (or (not (tptp.ring_11004092258visors tptp.int)) (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t85 t92))
% 0.42/0.71 (step t94 (cl (= (= (tptp.zero_zero tptp.int) (tptp.power_power tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.number_number_of tptp.nat (tptp.bit0 (tptp.bit1 tptp.pls))))) (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule resolution :premises (t78 a131 t93))
% 0.42/0.71 (step t95 (cl (= (tptp.zero_zero tptp.int) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule resolution :premises (t71 t76 t94))
% 0.42/0.71 (step t96 (cl (not (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule or_pos)
% 0.42/0.71 (step t97 (cl (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))) (not (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule reordering :premises (t96))
% 0.42/0.71 (step t98 (cl (=> (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) :rule implies_neg1)
% 0.42/0.71 (anchor :step t99)
% 0.42/0.71 (assume t99.a0 (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))))
% 0.42/0.71 (step t99.t1 (cl (or (not (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule forall_inst :args ((:= B_1 (tptp.one_one tptp.int)) (:= B_2 (tptp.semiring_1_of_nat tptp.int tptp.n)) (:= X_a tptp.int)))
% 0.42/0.71 (step t99.t2 (cl (not (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule or :premises (t99.t1))
% 0.42/0.71 (step t99.t3 (cl (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule resolution :premises (t99.t2 t99.a0))
% 0.42/0.71 (step t99 (cl (not (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule subproof :discharge (t99.a0))
% 0.42/0.71 (step t100 (cl (=> (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule resolution :premises (t98 t99))
% 0.42/0.71 (step t101 (cl (=> (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (not (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule implies_neg2)
% 0.42/0.71 (step t102 (cl (=> (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) (=> (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule resolution :premises (t100 t101))
% 0.42/0.71 (step t103 (cl (=> (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))))) :rule contraction :premises (t102))
% 0.42/0.71 (step t104 (cl (not (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule implies :premises (t103))
% 0.42/0.71 (step t105 (cl (not (= (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))))) (not (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2))))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) :rule equiv_pos2)
% 0.42/0.71 (anchor :step t106 :args ((B_1 $$unsorted) (:= B_1 B_1) (B_2 $$unsorted) (:= B_2 B_2) (X_a $$unsorted) (:= X_a X_a)))
% 0.42/0.71 (step t106.t1 (cl (= B_1 B_1)) :rule refl)
% 0.42/0.71 (step t106.t2 (cl (= B_2 B_2)) :rule refl)
% 0.42/0.71 (step t106.t3 (cl (= X_a X_a)) :rule refl)
% 0.42/0.71 (step t106.t4 (cl (= (tptp.linord219039673up_add X_a) (tptp.linord219039673up_add X_a))) :rule refl)
% 0.42/0.71 (step t106.t5 (cl (= (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) :rule all_simplify)
% 0.42/0.71 (step t106.t6 (cl (= (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2))) (=> (tptp.linord219039673up_add X_a) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) :rule cong :premises (t106.t4 t106.t5))
% 0.42/0.71 (step t106 (cl (= (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))))) :rule bind)
% 0.42/0.71 (step t107 (cl (= (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))))) :rule all_simplify)
% 0.42/0.71 (step t108 (cl (= (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (= (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)) (tptp.plus_plus X_a B_1 B_2)))) (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2))))))) :rule trans :premises (t106 t107))
% 0.42/0.71 (step t109 (cl (forall ((B_1 $$unsorted) (B_2 $$unsorted) (X_a $$unsorted)) (or (not (tptp.linord219039673up_add X_a)) (= (tptp.plus_plus X_a B_1 B_2) (tptp.ti X_a (tptp.plus_plus X_a B_1 B_2)))))) :rule resolution :premises (t105 t108 a3))
% 0.42/0.71 (step t110 (cl (or (not (tptp.linord219039673up_add tptp.int)) (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)))))) :rule resolution :premises (t104 t109))
% 0.42/0.71 (step t111 (cl (= (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n)) (tptp.ti tptp.int (tptp.plus_plus tptp.int (tptp.one_one tptp.int) (tptp.semiring_1_of_nat tptp.int tptp.n))))) :rule resolution :premises (t97 a130 t110))
% 0.42/0.71 (step t112 (cl) :rule resolution :premises (t69 t95 t111 a105 a89 a32))
% 0.42/0.71
% 0.42/0.71 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.NwafCFT6y3/cvc5---1.0.5_23974.smt2
% 0.42/0.71 % cvc5---1.0.5 exiting
% 0.42/0.71 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------