TSTP Solution File: RNG024-6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG024-6 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n002.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 17:41:27 EDT 2024
% Result : Unsatisfiable 0.27s 0.59s
% Output : Proof 0.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : RNG024-6 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.18 % Command : do_cvc5 %s %d
% 0.19/0.41 % Computer : n002.cluster.edu
% 0.19/0.41 % Model : x86_64 x86_64
% 0.19/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.41 % Memory : 8042.1875MB
% 0.19/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.41 % CPULimit : 300
% 0.19/0.41 % WCLimit : 300
% 0.19/0.41 % DateTime : Sat May 25 21:20:09 EDT 2024
% 0.19/0.41 % CPUTime :
% 0.27/0.56 %----Proving TF0_NAR, FOF, or CNF
% 0.27/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.27/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.X8Vkjryn2K/cvc5---1.0.5_4262.smt2
% 0.27/0.59 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.X8Vkjryn2K/cvc5---1.0.5_4262.smt2
% 0.27/0.60 (assume a0 (forall ((X $$unsorted)) (= (tptp.add tptp.additive_identity X) X)))
% 0.27/0.60 (assume a1 (forall ((X $$unsorted)) (= (tptp.add X tptp.additive_identity) X)))
% 0.27/0.60 (assume a2 (forall ((X $$unsorted)) (= (tptp.multiply tptp.additive_identity X) tptp.additive_identity)))
% 0.27/0.60 (assume a3 (forall ((X $$unsorted)) (= (tptp.multiply X tptp.additive_identity) tptp.additive_identity)))
% 0.27/0.60 (assume a4 (forall ((X $$unsorted)) (= (tptp.add (tptp.additive_inverse X) X) tptp.additive_identity)))
% 0.27/0.60 (assume a5 (forall ((X $$unsorted)) (= (tptp.add X (tptp.additive_inverse X)) tptp.additive_identity)))
% 0.27/0.60 (assume a6 (forall ((X $$unsorted)) (= (tptp.additive_inverse (tptp.additive_inverse X)) X)))
% 0.27/0.60 (assume a7 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.add Y Z)) (tptp.add (tptp.multiply X Y) (tptp.multiply X Z)))))
% 0.27/0.60 (assume a8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.add X Y) Z) (tptp.add (tptp.multiply X Z) (tptp.multiply Y Z)))))
% 0.27/0.60 (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))))
% 0.27/0.60 (assume a10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.add X (tptp.add Y Z)) (tptp.add (tptp.add X Y) Z))))
% 0.27/0.60 (assume a11 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))))
% 0.27/0.60 (assume a12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X X) Y) (tptp.multiply X (tptp.multiply X Y)))))
% 0.27/0.60 (assume a13 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))))
% 0.27/0.60 (assume a14 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.commutator X Y) (tptp.add (tptp.multiply Y X) (tptp.additive_inverse (tptp.multiply X Y))))))
% 0.27/0.60 (assume a15 (not (= (tptp.associator tptp.x tptp.y tptp.y) tptp.additive_identity)))
% 0.27/0.60 (step t1 (cl (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (not (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (not (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule and_neg)
% 0.27/0.60 (step t2 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule implies_neg1)
% 0.27/0.60 (anchor :step t3)
% 0.27/0.60 (assume t3.a0 (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))
% 0.27/0.60 (assume t3.a1 (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))
% 0.27/0.60 (assume t3.a2 (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))))
% 0.27/0.60 (assume t3.a3 (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))
% 0.27/0.60 (step t3.t1 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule implies_neg1)
% 0.27/0.60 (anchor :step t3.t2)
% 0.27/0.60 (assume t3.t2.a0 (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))
% 0.27/0.60 (assume t3.t2.a1 (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))))
% 0.27/0.60 (assume t3.t2.a2 (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))
% 0.27/0.60 (assume t3.t2.a3 (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))
% 0.27/0.60 (step t3.t2.t1 (cl (= (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) tptp.additive_identity)) :rule symm :premises (t3.t2.a3))
% 0.27/0.60 (step t3.t2.t2 (cl (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule symm :premises (t3.t2.t1))
% 0.27/0.60 (step t3.t2.t3 (cl (= (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule refl)
% 0.27/0.60 (step t3.t2.t4 (cl (= (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) :rule symm :premises (t3.t2.a2))
% 0.27/0.60 (step t3.t2.t5 (cl (= (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule cong :premises (t3.t2.t3 t3.t2.t4))
% 0.27/0.60 (step t3.t2.t6 (cl (= (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule symm :premises (t3.t2.a1))
% 0.27/0.60 (step t3.t2.t7 (cl (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.associator tptp.x tptp.y tptp.y))) :rule symm :premises (t3.t2.a0))
% 0.27/0.60 (step t3.t2.t8 (cl (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule trans :premises (t3.t2.t2 t3.t2.t5 t3.t2.t6 t3.t2.t7))
% 0.27/0.60 (step t3.t2 (cl (not (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (not (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (not (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule subproof :discharge (t3.t2.a0 t3.t2.a1 t3.t2.a2 t3.t2.a3))
% 0.27/0.60 (step t3.t3 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule and_pos)
% 0.27/0.60 (step t3.t4 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule and_pos)
% 0.27/0.60 (step t3.t5 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule and_pos)
% 0.27/0.60 (step t3.t6 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule and_pos)
% 0.27/0.60 (step t3.t7 (cl (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))) :rule resolution :premises (t3.t2 t3.t3 t3.t4 t3.t5 t3.t6))
% 0.27/0.60 (step t3.t8 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule reordering :premises (t3.t7))
% 0.27/0.60 (step t3.t9 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule contraction :premises (t3.t8))
% 0.27/0.60 (step t3.t10 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule resolution :premises (t3.t1 t3.t9))
% 0.27/0.60 (step t3.t11 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (not (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)))) :rule implies_neg2)
% 0.27/0.60 (step t3.t12 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)))) :rule resolution :premises (t3.t10 t3.t11))
% 0.27/0.60 (step t3.t13 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)))) :rule contraction :premises (t3.t12))
% 0.27/0.60 (step t3.t14 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule implies :premises (t3.t13))
% 0.27/0.60 (step t3.t15 (cl (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (not (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (not (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule and_neg)
% 0.27/0.60 (step t3.t16 (cl (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule resolution :premises (t3.t15 t3.a0 t3.a2 t3.a3 t3.a1))
% 0.27/0.60 (step t3.t17 (cl (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule resolution :premises (t3.t14 t3.t16))
% 0.27/0.60 (step t3 (cl (not (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (not (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3))
% 0.27/0.60 (step t4 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule and_pos)
% 0.27/0.60 (step t5 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule and_pos)
% 0.27/0.60 (step t6 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule and_pos)
% 0.27/0.60 (step t7 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule and_pos)
% 0.27/0.60 (step t8 (cl (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule resolution :premises (t3 t4 t5 t6 t7))
% 0.27/0.60 (step t9 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule reordering :premises (t8))
% 0.27/0.60 (step t10 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule contraction :premises (t9))
% 0.27/0.60 (step t11 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule resolution :premises (t2 t10))
% 0.27/0.60 (step t12 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (not (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)))) :rule implies_neg2)
% 0.27/0.60 (step t13 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)))) :rule resolution :premises (t11 t12))
% 0.27/0.60 (step t14 (cl (=> (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)))) :rule contraction :premises (t13))
% 0.27/0.60 (step t15 (cl (not (and (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule implies :premises (t14))
% 0.27/0.60 (step t16 (cl (not (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (not (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y))) :rule resolution :premises (t1 t15))
% 0.27/0.60 (step t17 (cl (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)) (not (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (not (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule reordering :premises (t16))
% 0.27/0.60 (step t18 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y))))) :rule implies_neg1)
% 0.27/0.60 (anchor :step t19)
% 0.27/0.60 (assume t19.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))))
% 0.27/0.60 (step t19.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y))))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.y)))
% 0.27/0.60 (step t19.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y))))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule or :premises (t19.t1))
% 0.27/0.60 (step t19.t3 (cl (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule resolution :premises (t19.t2 t19.a0))
% 0.27/0.60 (step t19 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y))))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule subproof :discharge (t19.a0))
% 0.27/0.60 (step t20 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule resolution :premises (t18 t19))
% 0.27/0.60 (step t21 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (not (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule implies_neg2)
% 0.27/0.60 (step t22 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule resolution :premises (t20 t21))
% 0.27/0.60 (step t23 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y)))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule contraction :premises (t22))
% 0.27/0.60 (step t24 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Y) (tptp.multiply X (tptp.multiply Y Y))))) (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule implies :premises (t23))
% 0.27/0.60 (step t25 (cl (= (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) :rule resolution :premises (t24 a11))
% 0.27/0.60 (step t26 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X)))) :rule implies_neg1)
% 0.27/0.60 (anchor :step t27)
% 0.27/0.60 (assume t27.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))))
% 0.27/0.60 (step t27.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)) (:= Y (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))
% 0.27/0.60 (step t27.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule or :premises (t27.t1))
% 0.27/0.60 (step t27.t3 (cl (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule resolution :premises (t27.t2 t27.a0))
% 0.27/0.60 (step t27 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule subproof :discharge (t27.a0))
% 0.27/0.60 (step t28 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule resolution :premises (t26 t27))
% 0.27/0.60 (step t29 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (not (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))))) :rule implies_neg2)
% 0.27/0.60 (step t30 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))))) :rule resolution :premises (t28 t29))
% 0.27/0.60 (step t31 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y))))) :rule contraction :premises (t30))
% 0.27/0.60 (step t32 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.add X Y) (tptp.add Y X)))) (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule implies :premises (t31))
% 0.27/0.60 (step t33 (cl (= (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))) (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y)))) :rule resolution :premises (t32 a9))
% 0.27/0.60 (step t34 (cl (=> (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) :rule implies_neg1)
% 0.27/0.60 (anchor :step t35)
% 0.27/0.60 (assume t35.a0 (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))))
% 0.27/0.60 (step t35.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule forall_inst :args ((:= X (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))
% 0.27/0.60 (step t35.t2 (cl (not (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule or :premises (t35.t1))
% 0.27/0.60 (step t35.t3 (cl (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule resolution :premises (t35.t2 t35.a0))
% 0.27/0.60 (step t35 (cl (not (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule subproof :discharge (t35.a0))
% 0.27/0.60 (step t36 (cl (=> (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule resolution :premises (t34 t35))
% 0.27/0.60 (step t37 (cl (=> (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (not (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule implies_neg2)
% 0.27/0.60 (step t38 (cl (=> (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) (=> (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule resolution :premises (t36 t37))
% 0.27/0.60 (step t39 (cl (=> (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule contraction :premises (t38))
% 0.27/0.60 (step t40 (cl (not (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule implies :premises (t39))
% 0.27/0.60 (step t41 (cl (not (= (forall ((X $$unsorted)) (= (tptp.add (tptp.additive_inverse X) X) tptp.additive_identity)) (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))))) (not (forall ((X $$unsorted)) (= (tptp.add (tptp.additive_inverse X) X) tptp.additive_identity))) (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) :rule equiv_pos2)
% 0.27/0.60 (anchor :step t42 :args ((X $$unsorted) (:= X X)))
% 0.27/0.60 (step t42.t1 (cl (= X X)) :rule refl)
% 0.27/0.60 (step t42.t2 (cl (= (= (tptp.add (tptp.additive_inverse X) X) tptp.additive_identity) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) :rule all_simplify)
% 0.27/0.60 (step t42 (cl (= (forall ((X $$unsorted)) (= (tptp.add (tptp.additive_inverse X) X) tptp.additive_identity)) (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X))))) :rule bind)
% 0.27/0.60 (step t43 (cl (forall ((X $$unsorted)) (= tptp.additive_identity (tptp.add (tptp.additive_inverse X) X)))) :rule resolution :premises (t41 t42 a4))
% 0.27/0.60 (step t44 (cl (= tptp.additive_identity (tptp.add (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))) (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))) :rule resolution :premises (t40 t43))
% 0.27/0.60 (step t45 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z))))))) :rule implies_neg1)
% 0.27/0.60 (anchor :step t46)
% 0.27/0.60 (assume t46.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))))
% 0.27/0.60 (step t46.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z))))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))) :rule forall_inst :args ((:= X tptp.x) (:= Y tptp.y) (:= Z tptp.y)))
% 0.27/0.60 (step t46.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z))))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule or :premises (t46.t1))
% 0.27/0.60 (step t46.t3 (cl (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule resolution :premises (t46.t2 t46.a0))
% 0.27/0.60 (step t46 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z))))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule subproof :discharge (t46.a0))
% 0.27/0.60 (step t47 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule resolution :premises (t45 t46))
% 0.27/0.60 (step t48 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (not (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))) :rule implies_neg2)
% 0.27/0.60 (step t49 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))) :rule resolution :premises (t47 t48))
% 0.27/0.60 (step t50 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z)))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y))))))) :rule contraction :premises (t49))
% 0.27/0.60 (step t51 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.associator X Y Z) (tptp.add (tptp.multiply (tptp.multiply X Y) Z) (tptp.additive_inverse (tptp.multiply X (tptp.multiply Y Z))))))) (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule implies :premises (t50))
% 0.27/0.60 (step t52 (cl (= (tptp.associator tptp.x tptp.y tptp.y) (tptp.add (tptp.multiply (tptp.multiply tptp.x tptp.y) tptp.y) (tptp.additive_inverse (tptp.multiply tptp.x (tptp.multiply tptp.y tptp.y)))))) :rule resolution :premises (t51 a13))
% 0.27/0.60 (step t53 (cl (not (= tptp.additive_identity (tptp.associator tptp.x tptp.y tptp.y)))) :rule not_symm :premises (a15))
% 0.27/0.60 (step t54 (cl) :rule resolution :premises (t17 t25 t33 t44 t52 t53))
% 0.27/0.60
% 0.27/0.60 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.X8Vkjryn2K/cvc5---1.0.5_4262.smt2
% 0.27/0.60 % cvc5---1.0.5 exiting
% 0.27/0.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------