TSTP Solution File: KLE041+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Sat Sep 17 17:23:58 EDT 2022
% Result : Theorem 14.56s 9.76s
% Output : Proof 14.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 07:57:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 14.56/9.76 % SZS status Theorem
% 14.56/9.76 % SZS output start Proof
% 14.56/9.76 tff(star_type, type, (
% 14.56/9.76 star: $i > $i)).
% 14.56/9.76 tff(tptp_fun_X1_0_type, type, (
% 14.56/9.76 tptp_fun_X1_0: $i)).
% 14.56/9.76 tff(addition_type, type, (
% 14.56/9.76 addition: ( $i * $i ) > $i)).
% 14.56/9.76 tff(one_type, type, (
% 14.56/9.76 one: $i)).
% 14.56/9.76 tff(multiplication_type, type, (
% 14.56/9.76 multiplication: ( $i * $i ) > $i)).
% 14.56/9.76 tff(tptp_fun_X0_1_type, type, (
% 14.56/9.76 tptp_fun_X0_1: $i)).
% 14.56/9.76 tff(leq_type, type, (
% 14.56/9.76 leq: ( $i * $i ) > $o)).
% 14.56/9.76 tff(1,plain,
% 14.56/9.76 (^[A: $i, B: $i] : refl((leq(A, B) <=> (addition(A, B) = B)) <=> (leq(A, B) <=> (addition(A, B) = B)))),
% 14.56/9.76 inference(bind,[status(th)],[])).
% 14.56/9.76 tff(2,plain,
% 14.56/9.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.56/9.76 inference(quant_intro,[status(thm)],[1])).
% 14.56/9.76 tff(3,plain,
% 14.56/9.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B)) <=> ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.56/9.76 inference(rewrite,[status(thm)],[])).
% 14.56/9.76 tff(4,axiom,(![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','order')).
% 14.56/9.76 tff(5,plain,
% 14.56/9.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[4, 3])).
% 14.56/9.76 tff(6,plain,(
% 14.56/9.76 ![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.56/9.76 inference(skolemize,[status(sab)],[5])).
% 14.56/9.76 tff(7,plain,
% 14.56/9.76 (![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[6, 2])).
% 14.56/9.76 tff(8,plain,
% 14.56/9.76 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))),
% 14.56/9.76 inference(quant_inst,[status(thm)],[])).
% 14.56/9.76 tff(9,plain,
% 14.56/9.76 (leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0))),
% 14.56/9.76 inference(unit_resolution,[status(thm)],[8, 7])).
% 14.56/9.76 tff(10,plain,
% 14.56/9.76 (^[A: $i] : refl((multiplication(one, A) = A) <=> (multiplication(one, A) = A))),
% 14.56/9.76 inference(bind,[status(th)],[])).
% 14.56/9.76 tff(11,plain,
% 14.56/9.76 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 14.56/9.76 inference(quant_intro,[status(thm)],[10])).
% 14.56/9.76 tff(12,plain,
% 14.56/9.76 (![A: $i] : (multiplication(one, A) = A) <=> ![A: $i] : (multiplication(one, A) = A)),
% 14.56/9.76 inference(rewrite,[status(thm)],[])).
% 14.56/9.76 tff(13,axiom,(![A: $i] : (multiplication(one, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','multiplicative_left_identity')).
% 14.56/9.76 tff(14,plain,
% 14.56/9.76 (![A: $i] : (multiplication(one, A) = A)),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[13, 12])).
% 14.56/9.76 tff(15,plain,(
% 14.56/9.76 ![A: $i] : (multiplication(one, A) = A)),
% 14.56/9.76 inference(skolemize,[status(sab)],[14])).
% 14.56/9.76 tff(16,plain,
% 14.56/9.76 (![A: $i] : (multiplication(one, A) = A)),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[15, 11])).
% 14.56/9.76 tff(17,plain,
% 14.56/9.76 ((~![A: $i] : (multiplication(one, A) = A)) | (multiplication(one, star(X0!1)) = star(X0!1))),
% 14.56/9.76 inference(quant_inst,[status(thm)],[])).
% 14.56/9.76 tff(18,plain,
% 14.56/9.76 (multiplication(one, star(X0!1)) = star(X0!1)),
% 14.56/9.76 inference(unit_resolution,[status(thm)],[17, 16])).
% 14.56/9.76 tff(19,plain,
% 14.56/9.76 (leq(multiplication(one, star(X0!1)), star(X1!0)) <=> leq(star(X0!1), star(X1!0))),
% 14.56/9.76 inference(monotonicity,[status(thm)],[18])).
% 14.56/9.76 tff(20,plain,
% 14.56/9.76 (leq(star(X0!1), star(X1!0)) <=> leq(multiplication(one, star(X0!1)), star(X1!0))),
% 14.56/9.76 inference(symmetry,[status(thm)],[19])).
% 14.56/9.76 tff(21,plain,
% 14.56/9.76 ((~leq(star(X0!1), star(X1!0))) <=> (~leq(multiplication(one, star(X0!1)), star(X1!0)))),
% 14.56/9.76 inference(monotonicity,[status(thm)],[20])).
% 14.56/9.76 tff(22,plain,
% 14.56/9.76 ((~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))) <=> (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1))))),
% 14.56/9.76 inference(rewrite,[status(thm)],[])).
% 14.56/9.76 tff(23,plain,
% 14.56/9.76 ((~![X0: $i, X1: $i] : (leq(X0, X1) => leq(star(X0), star(X1)))) <=> (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1))))),
% 14.56/9.76 inference(rewrite,[status(thm)],[])).
% 14.56/9.76 tff(24,axiom,(~![X0: $i, X1: $i] : (leq(X0, X1) => leq(star(X0), star(X1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 14.56/9.76 tff(25,plain,
% 14.56/9.76 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[24, 23])).
% 14.56/9.76 tff(26,plain,
% 14.56/9.76 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[25, 22])).
% 14.56/9.76 tff(27,plain,
% 14.56/9.76 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[26, 22])).
% 14.56/9.76 tff(28,plain,
% 14.56/9.76 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[27, 22])).
% 14.56/9.76 tff(29,plain,
% 14.56/9.76 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[28, 22])).
% 14.56/9.76 tff(30,plain,
% 14.56/9.76 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[29, 22])).
% 14.56/9.76 tff(31,plain,
% 14.56/9.76 (~![X0: $i, X1: $i] : ((~leq(X0, X1)) | leq(star(X0), star(X1)))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[30, 22])).
% 14.56/9.76 tff(32,plain,(
% 14.56/9.76 ~((~leq(X0!1, X1!0)) | leq(star(X0!1), star(X1!0)))),
% 14.56/9.76 inference(skolemize,[status(sab)],[31])).
% 14.56/9.76 tff(33,plain,
% 14.56/9.76 (~leq(star(X0!1), star(X1!0))),
% 14.56/9.76 inference(or_elim,[status(thm)],[32])).
% 14.56/9.76 tff(34,plain,
% 14.56/9.76 (~leq(multiplication(one, star(X0!1)), star(X1!0))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[33, 21])).
% 14.56/9.76 tff(35,plain,
% 14.56/9.76 (^[A: $i, B: $i, C: $i] : refl(((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 14.56/9.76 inference(bind,[status(th)],[])).
% 14.56/9.76 tff(36,plain,
% 14.56/9.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 14.56/9.76 inference(quant_intro,[status(thm)],[35])).
% 14.56/9.76 tff(37,plain,
% 14.56/9.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 14.56/9.76 inference(rewrite,[status(thm)],[])).
% 14.56/9.76 tff(38,plain,
% 14.56/9.76 (^[A: $i, B: $i, C: $i] : rewrite((leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A)))),
% 14.56/9.76 inference(bind,[status(th)],[])).
% 14.56/9.76 tff(39,plain,
% 14.56/9.76 (![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A)) <=> ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 14.56/9.76 inference(quant_intro,[status(thm)],[38])).
% 14.56/9.76 tff(40,axiom,(![A: $i, B: $i, C: $i] : (leq(addition(multiplication(A, B), C), A) => leq(multiplication(C, star(B)), A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_induction_right')).
% 14.56/9.76 tff(41,plain,
% 14.56/9.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[40, 39])).
% 14.56/9.76 tff(42,plain,
% 14.56/9.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[41, 37])).
% 14.56/9.76 tff(43,plain,(
% 14.56/9.76 ![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 14.56/9.76 inference(skolemize,[status(sab)],[42])).
% 14.56/9.76 tff(44,plain,
% 14.56/9.76 (![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))),
% 14.56/9.76 inference(modus_ponens,[status(thm)],[43, 36])).
% 14.56/9.76 tff(45,plain,
% 14.56/9.76 (((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0)))) <=> ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0)))),
% 14.56/9.77 inference(rewrite,[status(thm)],[])).
% 14.56/9.77 tff(46,plain,
% 14.56/9.77 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | ((~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0)))),
% 14.56/9.77 inference(quant_inst,[status(thm)],[])).
% 14.56/9.77 tff(47,plain,
% 14.56/9.77 ((~![A: $i, B: $i, C: $i] : ((~leq(addition(multiplication(A, B), C), A)) | leq(multiplication(C, star(B)), A))) | (~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0))),
% 14.56/9.77 inference(modus_ponens,[status(thm)],[46, 45])).
% 14.56/9.77 tff(48,plain,
% 14.56/9.77 ((~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))) | leq(multiplication(one, star(X0!1)), star(X1!0))),
% 14.56/9.77 inference(unit_resolution,[status(thm)],[47, 44])).
% 14.56/9.77 tff(49,plain,
% 14.56/9.77 (~leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))),
% 14.56/9.77 inference(unit_resolution,[status(thm)],[48, 34])).
% 14.56/9.77 tff(50,plain,
% 14.56/9.77 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)))),
% 14.56/9.77 inference(quant_inst,[status(thm)],[])).
% 14.56/9.77 tff(51,plain,
% 14.56/9.77 (leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0))),
% 14.56/9.77 inference(unit_resolution,[status(thm)],[50, 7])).
% 14.56/9.77 tff(52,plain,
% 14.56/9.77 (^[A: $i] : refl(leq(addition(one, multiplication(star(A), A)), star(A)) <=> leq(addition(one, multiplication(star(A), A)), star(A)))),
% 14.56/9.77 inference(bind,[status(th)],[])).
% 14.56/9.77 tff(53,plain,
% 14.56/9.77 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 14.56/9.77 inference(quant_intro,[status(thm)],[52])).
% 14.56/9.77 tff(54,plain,
% 14.56/9.77 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A)) <=> ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 14.56/9.77 inference(rewrite,[status(thm)],[])).
% 14.56/9.77 tff(55,axiom,(![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','star_unfold_left')).
% 14.56/9.77 tff(56,plain,
% 14.56/9.77 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 14.56/9.77 inference(modus_ponens,[status(thm)],[55, 54])).
% 14.56/9.77 tff(57,plain,(
% 14.56/9.77 ![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 14.56/9.77 inference(skolemize,[status(sab)],[56])).
% 14.56/9.77 tff(58,plain,
% 14.56/9.77 (![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))),
% 14.56/9.77 inference(modus_ponens,[status(thm)],[57, 53])).
% 14.56/9.77 tff(59,plain,
% 14.56/9.77 ((~![A: $i] : leq(addition(one, multiplication(star(A), A)), star(A))) | leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 14.56/9.77 inference(quant_inst,[status(thm)],[])).
% 14.56/9.77 tff(60,plain,
% 14.56/9.77 (leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 14.56/9.77 inference(unit_resolution,[status(thm)],[59, 58])).
% 14.56/9.77 tff(61,plain,
% 14.56/9.77 ((~(leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)))) | (~leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))) | (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0))),
% 14.56/9.77 inference(tautology,[status(thm)],[])).
% 14.56/9.77 tff(62,plain,
% 14.56/9.77 ((~(leq(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) <=> (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)))) | (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0))),
% 14.56/9.77 inference(unit_resolution,[status(thm)],[61, 60])).
% 14.56/9.77 tff(63,plain,
% 14.56/9.77 (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = star(X1!0)),
% 14.56/9.77 inference(unit_resolution,[status(thm)],[62, 51])).
% 14.56/9.77 tff(64,plain,
% 14.56/9.77 ((~![A: $i, B: $i] : (leq(A, B) <=> (addition(A, B) = B))) | (leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(65,plain,
% 14.71/9.77 (leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0)),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[64, 7])).
% 14.71/9.77 tff(66,plain,
% 14.71/9.77 (leq(X0!1, X1!0)),
% 14.71/9.77 inference(or_elim,[status(thm)],[32])).
% 14.71/9.77 tff(67,plain,
% 14.71/9.77 ((~(leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0))) | (~leq(X0!1, X1!0)) | (addition(X0!1, X1!0) = X1!0)),
% 14.71/9.77 inference(tautology,[status(thm)],[])).
% 14.71/9.77 tff(68,plain,
% 14.71/9.77 ((~(leq(X0!1, X1!0) <=> (addition(X0!1, X1!0) = X1!0))) | (addition(X0!1, X1!0) = X1!0)),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[67, 66])).
% 14.71/9.77 tff(69,plain,
% 14.71/9.77 (addition(X0!1, X1!0) = X1!0),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[68, 65])).
% 14.71/9.77 tff(70,plain,
% 14.71/9.77 (X1!0 = addition(X0!1, X1!0)),
% 14.71/9.77 inference(symmetry,[status(thm)],[69])).
% 14.71/9.77 tff(71,plain,
% 14.71/9.77 (multiplication(star(X1!0), X1!0) = multiplication(star(X1!0), addition(X0!1, X1!0))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[70])).
% 14.71/9.77 tff(72,plain,
% 14.71/9.77 (multiplication(star(X1!0), addition(X0!1, X1!0)) = multiplication(star(X1!0), X1!0)),
% 14.71/9.77 inference(symmetry,[status(thm)],[71])).
% 14.71/9.77 tff(73,plain,
% 14.71/9.77 (^[A: $i, B: $i, C: $i] : refl((multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))))),
% 14.71/9.77 inference(bind,[status(th)],[])).
% 14.71/9.77 tff(74,plain,
% 14.71/9.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.71/9.77 inference(quant_intro,[status(thm)],[73])).
% 14.71/9.77 tff(75,plain,
% 14.71/9.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C))) <=> ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.71/9.77 inference(rewrite,[status(thm)],[])).
% 14.71/9.77 tff(76,axiom,(![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','right_distributivity')).
% 14.71/9.77 tff(77,plain,
% 14.71/9.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[76, 75])).
% 14.71/9.77 tff(78,plain,(
% 14.71/9.77 ![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.71/9.77 inference(skolemize,[status(sab)],[77])).
% 14.71/9.77 tff(79,plain,
% 14.71/9.77 (![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[78, 74])).
% 14.71/9.77 tff(80,plain,
% 14.71/9.77 ((~![A: $i, B: $i, C: $i] : (multiplication(A, addition(B, C)) = addition(multiplication(A, B), multiplication(A, C)))) | (multiplication(star(X1!0), addition(X0!1, X1!0)) = addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(81,plain,
% 14.71/9.77 (multiplication(star(X1!0), addition(X0!1, X1!0)) = addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[80, 79])).
% 14.71/9.77 tff(82,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)) = multiplication(star(X1!0), addition(X0!1, X1!0))),
% 14.71/9.77 inference(symmetry,[status(thm)],[81])).
% 14.71/9.77 tff(83,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)) = multiplication(star(X1!0), X1!0)),
% 14.71/9.77 inference(transitivity,[status(thm)],[82, 72])).
% 14.71/9.77 tff(84,plain,
% 14.71/9.77 (addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))) = addition(one, multiplication(star(X1!0), X1!0))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[83])).
% 14.71/9.77 tff(85,plain,
% 14.71/9.77 (addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0)) = addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[84])).
% 14.71/9.77 tff(86,plain,
% 14.71/9.77 (^[C: $i, B: $i, A: $i] : refl((addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> (addition(A, addition(B, C)) = addition(addition(A, B), C)))),
% 14.71/9.77 inference(bind,[status(th)],[])).
% 14.71/9.77 tff(87,plain,
% 14.71/9.77 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.71/9.77 inference(quant_intro,[status(thm)],[86])).
% 14.71/9.77 tff(88,plain,
% 14.71/9.77 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C)) <=> ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.71/9.77 inference(rewrite,[status(thm)],[])).
% 14.71/9.77 tff(89,axiom,(![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_associativity')).
% 14.71/9.77 tff(90,plain,
% 14.71/9.77 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[89, 88])).
% 14.71/9.77 tff(91,plain,(
% 14.71/9.77 ![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.71/9.77 inference(skolemize,[status(sab)],[90])).
% 14.71/9.77 tff(92,plain,
% 14.71/9.77 (![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[91, 87])).
% 14.71/9.77 tff(93,plain,
% 14.71/9.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))) = addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0)))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(94,plain,
% 14.71/9.77 (addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))) = addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0))),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[93, 92])).
% 14.71/9.77 tff(95,plain,
% 14.71/9.77 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 14.71/9.77 inference(bind,[status(th)],[])).
% 14.71/9.77 tff(96,plain,
% 14.71/9.77 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 14.71/9.77 inference(quant_intro,[status(thm)],[95])).
% 14.71/9.77 tff(97,plain,
% 14.71/9.77 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 14.71/9.77 inference(rewrite,[status(thm)],[])).
% 14.71/9.77 tff(98,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_idempotence')).
% 14.71/9.77 tff(99,plain,
% 14.71/9.77 (![A: $i] : (addition(A, A) = A)),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[98, 97])).
% 14.71/9.77 tff(100,plain,(
% 14.71/9.77 ![A: $i] : (addition(A, A) = A)),
% 14.71/9.77 inference(skolemize,[status(sab)],[99])).
% 14.71/9.77 tff(101,plain,
% 14.71/9.77 (![A: $i] : (addition(A, A) = A)),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[100, 96])).
% 14.71/9.77 tff(102,plain,
% 14.71/9.77 ((~![A: $i] : (addition(A, A) = A)) | (addition(one, one) = one)),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(103,plain,
% 14.71/9.77 (addition(one, one) = one),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[102, 101])).
% 14.71/9.77 tff(104,plain,
% 14.71/9.77 (addition(addition(one, one), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))) = addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[103])).
% 14.71/9.77 tff(105,plain,
% 14.71/9.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(one, addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))) = addition(addition(one, one), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(106,plain,
% 14.71/9.77 (addition(one, addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))) = addition(addition(one, one), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[105, 92])).
% 14.71/9.77 tff(107,plain,
% 14.71/9.77 (addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0)) = addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 14.71/9.77 inference(symmetry,[status(thm)],[94])).
% 14.71/9.77 tff(108,plain,
% 14.71/9.77 (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = addition(addition(one, addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), star(X1!0))),
% 14.71/9.77 inference(symmetry,[status(thm)],[85])).
% 14.71/9.77 tff(109,plain,
% 14.71/9.77 (star(X1!0) = addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 14.71/9.77 inference(symmetry,[status(thm)],[63])).
% 14.71/9.77 tff(110,plain,
% 14.71/9.77 (star(X1!0) = addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0)))),
% 14.71/9.77 inference(transitivity,[status(thm)],[109, 108, 107])).
% 14.71/9.77 tff(111,plain,
% 14.71/9.77 (addition(one, star(X1!0)) = addition(one, addition(one, addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), star(X1!0))))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[110])).
% 14.71/9.77 tff(112,plain,
% 14.71/9.77 (^[A: $i, B: $i] : refl((addition(A, B) = addition(B, A)) <=> (addition(A, B) = addition(B, A)))),
% 14.71/9.77 inference(bind,[status(th)],[])).
% 14.71/9.77 tff(113,plain,
% 14.71/9.77 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.71/9.77 inference(quant_intro,[status(thm)],[112])).
% 14.71/9.77 tff(114,plain,
% 14.71/9.77 (![A: $i, B: $i] : (addition(A, B) = addition(B, A)) <=> ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.71/9.77 inference(rewrite,[status(thm)],[])).
% 14.71/9.77 tff(115,axiom,(![A: $i, B: $i] : (addition(A, B) = addition(B, A))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE002+0.ax','additive_commutativity')).
% 14.71/9.77 tff(116,plain,
% 14.71/9.77 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[115, 114])).
% 14.71/9.77 tff(117,plain,(
% 14.71/9.77 ![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.71/9.77 inference(skolemize,[status(sab)],[116])).
% 14.71/9.77 tff(118,plain,
% 14.71/9.77 (![A: $i, B: $i] : (addition(A, B) = addition(B, A))),
% 14.71/9.77 inference(modus_ponens,[status(thm)],[117, 113])).
% 14.71/9.77 tff(119,plain,
% 14.71/9.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, star(X1!0)) = addition(star(X1!0), one))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(120,plain,
% 14.71/9.77 (addition(one, star(X1!0)) = addition(star(X1!0), one)),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[119, 118])).
% 14.71/9.77 tff(121,plain,
% 14.71/9.77 (addition(star(X1!0), one) = addition(one, star(X1!0))),
% 14.71/9.77 inference(symmetry,[status(thm)],[120])).
% 14.71/9.77 tff(122,plain,
% 14.71/9.77 ((~![A: $i, B: $i] : (addition(A, B) = addition(B, A))) | (addition(one, multiplication(star(X1!0), X1!0)) = addition(multiplication(star(X1!0), X1!0), one))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(123,plain,
% 14.71/9.77 (addition(one, multiplication(star(X1!0), X1!0)) = addition(multiplication(star(X1!0), X1!0), one)),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[122, 118])).
% 14.71/9.77 tff(124,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X1!0), one) = addition(one, multiplication(star(X1!0), X1!0))),
% 14.71/9.77 inference(symmetry,[status(thm)],[123])).
% 14.71/9.77 tff(125,plain,
% 14.71/9.77 (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one) = addition(multiplication(star(X1!0), X1!0), one)),
% 14.71/9.77 inference(monotonicity,[status(thm)],[83])).
% 14.71/9.77 tff(126,plain,
% 14.71/9.77 (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one) = addition(one, multiplication(star(X1!0), X1!0))),
% 14.71/9.77 inference(transitivity,[status(thm)],[125, 124])).
% 14.71/9.77 tff(127,plain,
% 14.71/9.77 (addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0)) = addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[126])).
% 14.71/9.77 tff(128,plain,
% 14.71/9.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0))) = addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0)))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(129,plain,
% 14.71/9.77 (addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0))) = addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0))),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[128, 92])).
% 14.71/9.77 tff(130,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))) = addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[83])).
% 14.71/9.77 tff(131,plain,
% 14.71/9.77 (addition(addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), addition(one, star(X1!0))) = addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[130])).
% 14.71/9.77 tff(132,plain,
% 14.71/9.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X1!0), X0!1), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))) = addition(addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), addition(one, star(X1!0))))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(133,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))) = addition(addition(multiplication(star(X1!0), X0!1), addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0))), addition(one, star(X1!0)))),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[132, 92])).
% 14.71/9.77 tff(134,plain,
% 14.71/9.77 (addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0)) = addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))),
% 14.71/9.77 inference(symmetry,[status(thm)],[129])).
% 14.71/9.77 tff(135,plain,
% 14.71/9.77 (addition(addition(one, multiplication(star(X1!0), X1!0)), star(X1!0)) = addition(addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), one), star(X1!0))),
% 14.71/9.77 inference(symmetry,[status(thm)],[127])).
% 14.71/9.77 tff(136,plain,
% 14.71/9.77 (star(X1!0) = addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0)))),
% 14.71/9.77 inference(transitivity,[status(thm)],[109, 135, 134])).
% 14.71/9.77 tff(137,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), star(X1!0)) = addition(multiplication(star(X1!0), X0!1), addition(addition(multiplication(star(X1!0), X0!1), multiplication(star(X1!0), X1!0)), addition(one, star(X1!0))))),
% 14.71/9.77 inference(monotonicity,[status(thm)],[136])).
% 14.71/9.77 tff(138,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), star(X1!0)) = star(X1!0)),
% 14.71/9.77 inference(transitivity,[status(thm)],[137, 133, 131, 129, 127, 63])).
% 14.71/9.77 tff(139,plain,
% 14.71/9.77 (addition(addition(multiplication(star(X1!0), X0!1), star(X1!0)), one) = addition(star(X1!0), one)),
% 14.71/9.77 inference(monotonicity,[status(thm)],[138])).
% 14.71/9.77 tff(140,plain,
% 14.71/9.77 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X1!0), X0!1), addition(star(X1!0), one)) = addition(addition(multiplication(star(X1!0), X0!1), star(X1!0)), one))),
% 14.71/9.77 inference(quant_inst,[status(thm)],[])).
% 14.71/9.77 tff(141,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), addition(star(X1!0), one)) = addition(addition(multiplication(star(X1!0), X0!1), star(X1!0)), one)),
% 14.71/9.77 inference(unit_resolution,[status(thm)],[140, 92])).
% 14.71/9.77 tff(142,plain,
% 14.71/9.77 (addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0))) = addition(multiplication(star(X1!0), X0!1), addition(star(X1!0), one))),
% 14.74/9.79 inference(monotonicity,[status(thm)],[120])).
% 14.74/9.79 tff(143,plain,
% 14.74/9.79 ((~![C: $i, B: $i, A: $i] : (addition(A, addition(B, C)) = addition(addition(A, B), C))) | (addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0))) = addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)))),
% 14.74/9.79 inference(quant_inst,[status(thm)],[])).
% 14.74/9.79 tff(144,plain,
% 14.74/9.79 (addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0))) = addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))),
% 14.74/9.79 inference(unit_resolution,[status(thm)],[143, 92])).
% 14.74/9.79 tff(145,plain,
% 14.74/9.79 (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = addition(multiplication(star(X1!0), X0!1), addition(one, star(X1!0)))),
% 14.74/9.79 inference(symmetry,[status(thm)],[144])).
% 14.74/9.79 tff(146,plain,
% 14.74/9.79 (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)),
% 14.74/9.79 inference(transitivity,[status(thm)],[145, 142, 141, 139, 121, 111, 106, 104, 94, 85, 63])).
% 14.74/9.79 tff(147,plain,
% 14.74/9.79 ((~(leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))) | leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) | (~(addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))),
% 14.74/9.79 inference(tautology,[status(thm)],[])).
% 14.74/9.79 tff(148,plain,
% 14.74/9.79 ((~(leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) <=> (addition(addition(multiplication(star(X1!0), X0!1), one), star(X1!0)) = star(X1!0)))) | leq(addition(multiplication(star(X1!0), X0!1), one), star(X1!0))),
% 14.74/9.79 inference(unit_resolution,[status(thm)],[147, 146])).
% 14.74/9.79 tff(149,plain,
% 14.74/9.79 ($false),
% 14.74/9.79 inference(unit_resolution,[status(thm)],[148, 49, 9])).
% 14.74/9.79 % SZS output end Proof
%------------------------------------------------------------------------------