TSTP Solution File: KLE129+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:24:15 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE129+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 08:42:19 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% 0.13/0.40 tff(forward_diamond_type, type, (
% 0.13/0.40 forward_diamond: ( $i * $i ) > $i)).
% 0.13/0.40 tff(domain_type, type, (
% 0.13/0.40 domain: $i > $i)).
% 0.13/0.40 tff(multiplication_type, type, (
% 0.13/0.40 multiplication: ( $i * $i ) > $i)).
% 0.13/0.40 tff(divergence_type, type, (
% 0.13/0.40 divergence: $i > $i)).
% 0.13/0.40 tff(tptp_fun_X0_0_type, type, (
% 0.13/0.40 tptp_fun_X0_0: $i)).
% 0.13/0.40 tff(addition_type, type, (
% 0.13/0.40 addition: ( $i * $i ) > $i)).
% 0.13/0.40 tff(zero_type, type, (
% 0.13/0.40 zero: $i)).
% 0.13/0.40 tff(1,plain,
% 0.13/0.40 (^[X0: $i] : refl((forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> (forward_diamond(X0, divergence(X0)) = divergence(X0)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(2,plain,
% 0.13/0.40 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.40 tff(3,plain,
% 0.13/0.40 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0)) <=> ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(4,axiom,(![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+7.ax','divergence1')).
% 0.13/0.40 tff(5,plain,
% 0.13/0.40 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.13/0.40 tff(6,plain,(
% 0.13/0.40 ![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.13/0.40 inference(skolemize,[status(sab)],[5])).
% 0.13/0.40 tff(7,plain,
% 0.13/0.40 (![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.13/0.40 tff(8,plain,
% 0.13/0.40 ((~![X0: $i] : (forward_diamond(X0, divergence(X0)) = divergence(X0))) | (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(9,plain,
% 0.13/0.40 (forward_diamond(X0!0, divergence(X0!0)) = divergence(X0!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.13/0.40 tff(10,plain,
% 0.13/0.40 (^[X0: $i, X1: $i] : refl((forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(11,plain,
% 0.13/0.40 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[10])).
% 0.13/0.40 tff(12,plain,
% 0.13/0.40 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1)))) <=> ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(13,axiom,(![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax','forward_diamond')).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.13/0.40 tff(15,plain,(
% 0.13/0.40 ![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[14])).
% 0.13/0.40 tff(16,plain,
% 0.13/0.40 (![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 ((~![X0: $i, X1: $i] : (forward_diamond(X0, X1) = domain(multiplication(X0, domain(X1))))) | (forward_diamond(X0!0, divergence(X0!0)) = domain(multiplication(X0!0, domain(divergence(X0!0)))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (forward_diamond(X0!0, divergence(X0!0)) = domain(multiplication(X0!0, domain(divergence(X0!0))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.40 tff(19,plain,
% 0.13/0.40 (domain(multiplication(X0!0, domain(divergence(X0!0)))) = forward_diamond(X0!0, divergence(X0!0))),
% 0.13/0.40 inference(symmetry,[status(thm)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (domain(multiplication(X0!0, domain(divergence(X0!0)))) = divergence(X0!0)),
% 0.13/0.40 inference(transitivity,[status(thm)],[19, 9])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))) = forward_diamond(X0!0, divergence(X0!0))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 (forward_diamond(X0!0, divergence(X0!0)) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))),
% 0.13/0.40 inference(symmetry,[status(thm)],[21])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (divergence(X0!0) = forward_diamond(X0!0, divergence(X0!0))),
% 0.13/0.40 inference(symmetry,[status(thm)],[9])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (^[A: $i] : refl((addition(A, A) = A) <=> (addition(A, A) = A))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.13/0.40 inference(quant_intro,[status(thm)],[24])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 (![A: $i] : (addition(A, A) = A) <=> ![A: $i] : (addition(A, A) = A)),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(27,axiom,(![A: $i] : (addition(A, A) = A)), file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax','additive_idempotence')).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (![A: $i] : (addition(A, A) = A)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.13/0.40 tff(29,plain,(
% 0.13/0.40 ![A: $i] : (addition(A, A) = A)),
% 0.13/0.40 inference(skolemize,[status(sab)],[28])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 (![A: $i] : (addition(A, A) = A)),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 ((~![A: $i] : (addition(A, A) = A)) | (addition(divergence(X0!0), divergence(X0!0)) = divergence(X0!0))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (addition(divergence(X0!0), divergence(X0!0)) = divergence(X0!0)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))) = divergence(X0!0)),
% 0.13/0.40 inference(transitivity,[status(thm)],[21, 9])).
% 0.13/0.40 tff(34,plain,
% 0.13/0.40 (addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = addition(divergence(X0!0), divergence(X0!0))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20, 33])).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))),
% 0.13/0.40 inference(transitivity,[status(thm)],[34, 32, 23, 22])).
% 0.13/0.40 tff(36,plain,
% 0.13/0.40 ((domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero) <=> (divergence(X0!0) = zero)),
% 0.13/0.40 inference(monotonicity,[status(thm)],[20])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 ((divergence(X0!0) = zero) <=> (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.13/0.40 inference(symmetry,[status(thm)],[36])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~(divergence(X0!0) = zero)) <=> (~(domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[37])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 ((![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) & (~(divergence(X0!0) = zero))) <=> (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) & (~(divergence(X0!0) = zero)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 ((~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((~![X0: $i] : (![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)) => (divergence(X0) = zero))) <=> (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(42,axiom,(~![X0: $i] : (![X1: $i] : ((addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1))) => (domain(X1) = zero)) => (divergence(X0) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','goals')).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[46, 40])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (~![X0: $i] : ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0, domain(X1))) = forward_diamond(X0, domain(X1)))) | (domain(X1) = zero))) | (divergence(X0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[48, 40])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) & (~(divergence(X0!0) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[49, 39])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (~(divergence(X0!0) = zero)),
% 0.19/0.41 inference(and_elim,[status(thm)],[50])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (~(domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[51, 38])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[X1: $i] : refl(((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) <=> ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero)) <=> ![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,plain,
% 0.19/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))),
% 0.19/0.41 inference(and_elim,[status(thm)],[50])).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | ((~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))) <=> ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | (~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(58,plain,
% 0.19/0.41 ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | ((~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 ((~![X1: $i] : ((~(addition(domain(X1), forward_diamond(X0!0, domain(X1))) = forward_diamond(X0!0, domain(X1)))) | (domain(X1) = zero))) | (~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 ((~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))) | (domain(multiplication(X0!0, domain(divergence(X0!0)))) = zero)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (~(addition(domain(multiplication(X0!0, domain(divergence(X0!0)))), forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0)))))) = forward_diamond(X0!0, domain(multiplication(X0!0, domain(divergence(X0!0))))))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[60, 52])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[61, 35])).
% 0.19/0.41 % SZS output end Proof
%------------------------------------------------------------------------------