%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : KLE044-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:52:16 PM UTC 2026
% Result : Unsatisfiable 41.97s 6.32s
% Output : CNFRefutation 41.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 135 ( 135 unt; 10 def)
% Number of atoms : 299 ( 134 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 11 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 169 ( 0 sgn 169 !; 0 ?; 124 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq3(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
fof(f4,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f5,axiom,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f7,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f9,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f10,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f11,axiom,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f12,axiom,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f17,axiom,
! [X0,X1] : ifeq2(leq(X0,X1),true,addition(X0,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).
fof(f18,axiom,
! [X0,X1] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f19,plain,
! [X0,X1] : true = ifeq3(addition(X0,X1),X1,leq(X0,X1),true),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
fof(f21,plain,
! [X0] : true = leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
fof(f23,plain,
! [X0] : true = leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X2,X0,X1] : ifeq(leq(addition(multiplication(X0,X1),X2),X1),true,leq(multiplication(star(X0),X2),X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
fof(f25,plain,
! [X2,X0,X1] : true = ifeq(leq(addition(multiplication(X0,X1),X2),X1),true,leq(multiplication(star(X0),X2),X1),true),
inference(reorient_equations,[],[f24]) ).
fof(f26,axiom,
! [X2,X0,X1] : ifeq(leq(addition(multiplication(X0,X1),X2),X0),true,leq(multiplication(X2,star(X1)),X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
fof(f27,plain,
! [X2,X0,X1] : true = ifeq(leq(addition(multiplication(X0,X1),X2),X0),true,leq(multiplication(X2,star(X1)),X0),true),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq3(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_79,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(cnf_transformation,[],[f12]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] : ifeq2(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(cnf_transformation,[],[f17]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(cnf_transformation,[],[f19]) ).
tcf(c_86,plain,
! [X0: $i] : leq(addition(one,multiplication(X0,star(X0))),star(X0)) = true,
inference(cnf_transformation,[],[f21]) ).
tcf(c_87,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)) = true,
inference(cnf_transformation,[],[f23]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(leq(addition(multiplication(X0,X1),X2),X1),true,leq(multiplication(star(X0),X2),X1),true) = true,
inference(cnf_transformation,[],[f25]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(leq(addition(multiplication(X0,X1),X2),X0),true,leq(multiplication(X2,star(X1)),X0),true) = true,
inference(cnf_transformation,[],[f27]) ).
tcf(c_90,negated_conjecture,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
inference(cnf_transformation,[],[f28]) ).
tcf(c_163,definition,
iPr_def_10 = addition(one,sK2_goals_X0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_164,definition,
iPr_def_11 = star(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_165,definition,
iPr_def_12 = star(sK2_goals_X0),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_166,definition,
iPr_def_13 = leq(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_167,definition,
iPr_def_14 = star(sK1_goals_X0),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_168,definition,
iPr_def_15 = addition(one,sK1_goals_X0),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_169,definition,
iPr_def_16 = star(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_170,definition,
iPr_def_17 = leq(iPr_def_14,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_171,definition,
iPr_def_18 = tuple(iPr_def_13,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_172,definition,
iPr_def_19 = tuple(true,true),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_173,negated_conjecture,
iPr_def_18 != iPr_def_19,
inference(demodulation,[status(thm)],[c_90,c_172,c_168,c_169,c_167,c_170,c_165,c_163,c_164,c_166,c_171]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(leq(addition(multiplication(X0,X1),X2),X0),true,leq(multiplication(X2,star(X1)),X0),true) = true,
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(leq(addition(multiplication(X0,X1),X2),X1),true,leq(multiplication(star(X0),X2),X1),true) = true,
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_176,plain,
! [X0: $i] : leq(addition(one,multiplication(star(X0),X0)),star(X0)) = true,
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_177,plain,
! [X0: $i] : leq(addition(one,multiplication(X0,star(X0))),star(X0)) = true,
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] : ifeq3(addition(X0,X1),X1,leq(X0,X1),true) = true,
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] : ifeq2(leq(X0,X1),true,addition(X0,X1),X1) = X1,
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X2,X1)) = multiplication(addition(X0,X2),X1),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i,X2: $i] : addition(multiplication(X0,X1),multiplication(X0,X2)) = multiplication(X0,addition(X1,X2)),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_184,plain,
! [X0: $i] : multiplication(one,X0) = X0,
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_185,plain,
! [X0: $i] : multiplication(X0,one) = X0,
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_187,plain,
! [X0: $i] : addition(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] : addition(addition(X0,X1),X2) = addition(X0,addition(X1,X2)),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] : addition(X0,X1) = addition(X1,X0),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq3(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[status(thm)],[c_189,c_190]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] : ifeq(leq(addition(multiplication(sK1_goals_X0,X0),X1),X0),true,leq(multiplication(iPr_def_14,X1),X0),true) = true,
inference(superposition,[status(thm)],[c_167,c_175]) ).
tcf(c_350,plain,
leq(addition(one,multiplication(iPr_def_12,sK2_goals_X0)),iPr_def_12) = true,
inference(superposition,[status(thm)],[c_165,c_176]) ).
tcf(c_361,plain,
leq(addition(one,multiplication(iPr_def_15,iPr_def_16)),iPr_def_16) = true,
inference(superposition,[status(thm)],[c_169,c_177]) ).
tcf(c_379,plain,
! [X0: $i] : ifeq2(true,true,addition(addition(one,multiplication(star(X0),X0)),star(X0)),star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_176,c_179]) ).
tcf(c_382,plain,
ifeq2(true,true,addition(addition(one,multiplication(iPr_def_12,sK2_goals_X0)),iPr_def_12),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_350,c_179]) ).
tcf(c_391,plain,
addition(iPr_def_12,addition(one,multiplication(iPr_def_12,sK2_goals_X0))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_382,c_192,c_190,c_189,c_336]) ).
tcf(c_392,plain,
! [X0: $i] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(demodulation,[status(thm)],[c_379,c_192,c_190,c_189]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] : ifeq(leq(addition(multiplication(X0,X1),one),X0),true,leq(star(X1),X0),true) = true,
inference(superposition,[status(thm)],[c_184,c_174]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i] : ifeq(leq(addition(one,multiplication(X0,X1)),X0),true,leq(star(X1),X0),true) = true,
inference(demodulation,[status(thm)],[c_403,c_190]) ).
tcf(c_411,plain,
! [X0: $i] : ifeq3(X0,X0,leq(X0,X0),true) = true,
inference(superposition,[status(thm)],[c_187,c_178]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] : ifeq(leq(multiplication(X0,X1),X1),true,leq(multiplication(star(X0),multiplication(X0,X1)),X1),true) = true,
inference(superposition,[status(thm)],[c_187,c_175]) ).
tcf(c_414,plain,
! [X0: $i] : leq(X0,X0) = true,
inference(demodulation,[status(thm)],[c_411,c_193]) ).
tcf(c_437,plain,
ifeq2(true,true,addition(addition(one,multiplication(iPr_def_15,iPr_def_16)),iPr_def_16),iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_361,c_179]) ).
tcf(c_440,plain,
addition(iPr_def_16,addition(one,multiplication(iPr_def_15,iPr_def_16))) = iPr_def_16,
inference(demodulation,[status(thm)],[c_437,c_192,c_190,c_189,c_336]) ).
tcf(c_456,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(one,X1),X0),
inference(superposition,[status(thm)],[c_184,c_182]) ).
tcf(c_460,plain,
! [X0: $i,X1: $i] : addition(multiplication(X0,X1),X1) = multiplication(addition(X0,one),X1),
inference(superposition,[status(thm)],[c_184,c_182]) ).
tcf(c_468,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X1,X0)) = multiplication(addition(X1,one),X0),
inference(demodulation,[status(thm)],[c_460,c_190]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(superposition,[status(thm)],[c_185,c_183]) ).
tcf(c_481,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq3(multiplication(X0,addition(X1,X2)),multiplication(X0,X2),leq(multiplication(X0,X1),multiplication(X0,X2)),true) = true,
inference(superposition,[status(thm)],[c_183,c_178]) ).
tcf(c_530,plain,
! [X0: $i,X1: $i] : ifeq2(leq(X0,X1),true,addition(X1,X0),X1) = X1,
inference(superposition,[status(thm)],[c_190,c_179]) ).
tcf(c_578,plain,
! [X0: $i,X1: $i] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(superposition,[status(thm)],[c_187,c_189]) ).
tcf(c_829,plain,
! [X0: $i,X1: $i] : ifeq(leq(multiplication(addition(sK1_goals_X0,X0),X1),X1),true,leq(multiplication(iPr_def_14,multiplication(X0,X1)),X1),true) = true,
inference(superposition,[status(thm)],[c_182,c_343]) ).
tcf(c_1370,plain,
addition(one,iPr_def_15) = iPr_def_15,
inference(superposition,[status(thm)],[c_168,c_578]) ).
tcf(c_1376,plain,
! [X0: $i] : addition(one,star(X0)) = star(X0),
inference(superposition,[status(thm)],[c_392,c_578]) ).
tcf(c_1400,plain,
addition(iPr_def_15,one) = iPr_def_15,
inference(demodulation,[status(thm)],[c_1370,c_190]) ).
tcf(c_1513,plain,
addition(one,iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_165,c_1376]) ).
tcf(c_1514,plain,
addition(one,iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_167,c_1376]) ).
tcf(c_1516,plain,
addition(one,iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_169,c_1376]) ).
tcf(c_1526,plain,
addition(iPr_def_16,one) = iPr_def_16,
inference(demodulation,[status(thm)],[c_1516,c_190]) ).
tcf(c_1528,plain,
addition(iPr_def_14,one) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1514,c_190]) ).
tcf(c_1529,plain,
addition(iPr_def_12,one) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1513,c_190]) ).
tcf(c_1539,plain,
! [X0: $i] : addition(iPr_def_16,addition(one,X0)) = addition(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_1526,c_189]) ).
tcf(c_1547,plain,
addition(iPr_def_16,multiplication(iPr_def_15,iPr_def_16)) = iPr_def_16,
inference(demodulation,[status(thm)],[c_440,c_1539]) ).
tcf(c_1593,plain,
! [X0: $i] : addition(iPr_def_12,addition(one,X0)) = addition(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1529,c_189]) ).
tcf(c_1600,plain,
addition(iPr_def_12,multiplication(iPr_def_12,sK2_goals_X0)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_391,c_1593]) ).
tcf(c_1671,plain,
! [X0: $i] : addition(X0,multiplication(sK1_goals_X0,X0)) = multiplication(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_168,c_456]) ).
tcf(c_2109,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_15,X0)) = multiplication(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_1400,c_468]) ).
tcf(c_2111,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_16,X0)) = multiplication(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_1526,c_468]) ).
tcf(c_2113,plain,
! [X0: $i] : addition(X0,multiplication(iPr_def_14,X0)) = multiplication(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_1528,c_468]) ).
tcf(c_2201,plain,
multiplication(iPr_def_15,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_1547,c_2109]) ).
tcf(c_2360,plain,
! [X0: $i] : addition(X0,multiplication(X0,sK2_goals_X0)) = multiplication(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_163,c_472]) ).
tcf(c_2465,plain,
multiplication(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1600,c_2360]) ).
tcf(c_2671,plain,
! [X0: $i,X1: $i] : ifeq3(multiplication(X0,star(X1)),multiplication(X0,star(X1)),leq(multiplication(X0,one),multiplication(X0,star(X1))),true) = true,
inference(superposition,[status(thm)],[c_1376,c_481]) ).
tcf(c_2718,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(X0,star(X1))) = true,
inference(demodulation,[status(thm)],[c_2671,c_193,c_185]) ).
tcf(c_2921,plain,
ifeq(leq(iPr_def_16,iPr_def_16),true,leq(multiplication(star(iPr_def_15),iPr_def_16),iPr_def_16),true) = true,
inference(superposition,[status(thm)],[c_2201,c_412]) ).
tcf(c_2942,plain,
leq(multiplication(iPr_def_16,iPr_def_16),iPr_def_16) = true,
inference(demodulation,[status(thm)],[c_2921,c_191,c_169,c_414]) ).
tcf(c_3009,plain,
ifeq(leq(addition(one,iPr_def_12),iPr_def_12),true,leq(star(iPr_def_10),iPr_def_12),true) = true,
inference(superposition,[status(thm)],[c_2465,c_404]) ).
tcf(c_3028,plain,
true = iPr_def_13,
inference(demodulation,[status(thm)],[c_3009,c_191,c_190,c_164,c_166,c_414,c_1529]) ).
tcf(c_3176,plain,
! [X0: $i] : leq(X0,X0) = iPr_def_13,
inference(demodulation,[status(thm)],[c_414,c_3028]) ).
tcf(c_3197,plain,
tuple(iPr_def_13,iPr_def_13) = iPr_def_19,
inference(demodulation,[status(thm)],[c_172,c_3028]) ).
tcf(c_3527,plain,
leq(multiplication(iPr_def_16,iPr_def_16),iPr_def_16) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_2942,c_3028]) ).
tcf(c_3945,plain,
! [X0: $i,X1: $i] : ifeq2(leq(X0,X1),iPr_def_13,addition(X1,X0),X1) = X1,
inference(light_normalisation,[status(thm)],[c_530,c_3028]) ).
tcf(c_3958,plain,
ifeq2(iPr_def_13,iPr_def_13,addition(iPr_def_16,multiplication(iPr_def_16,iPr_def_16)),iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_3527,c_3945]) ).
tcf(c_3991,plain,
multiplication(iPr_def_16,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_3958,c_192,c_2111]) ).
tcf(c_5174,plain,
! [X0: $i] : addition(multiplication(X0,iPr_def_16),iPr_def_16) = multiplication(addition(X0,iPr_def_16),iPr_def_16),
inference(superposition,[status(thm)],[c_3991,c_182]) ).
tcf(c_5178,plain,
! [X0: $i] : addition(iPr_def_16,multiplication(X0,iPr_def_16)) = multiplication(addition(X0,iPr_def_16),iPr_def_16),
inference(demodulation,[status(thm)],[c_5174,c_190]) ).
tcf(c_9109,plain,
! [X0: $i,X1: $i] : leq(X0,multiplication(X0,star(X1))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_2718,c_3028]) ).
tcf(c_9116,plain,
! [X0: $i] : leq(X0,multiplication(X0,iPr_def_16)) = iPr_def_13,
inference(superposition,[status(thm)],[c_169,c_9109]) ).
tcf(c_11488,plain,
! [X0: $i,X1: $i] : ifeq(leq(multiplication(addition(sK1_goals_X0,X0),X1),X1),iPr_def_13,leq(multiplication(iPr_def_14,multiplication(X0,X1)),X1),iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_829,c_3028]) ).
tcf(c_11515,plain,
ifeq(leq(multiplication(addition(sK1_goals_X0,iPr_def_16),iPr_def_16),iPr_def_16),iPr_def_13,leq(multiplication(iPr_def_14,iPr_def_16),iPr_def_16),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_3991,c_11488]) ).
tcf(c_11519,plain,
leq(multiplication(iPr_def_14,iPr_def_16),iPr_def_16) = iPr_def_13,
inference(demodulation,[status(thm)],[c_11515,c_191,c_1671,c_2201,c_3176,c_5178]) ).
tcf(c_11701,plain,
ifeq2(iPr_def_13,iPr_def_13,addition(iPr_def_16,multiplication(iPr_def_14,iPr_def_16)),iPr_def_16) = iPr_def_16,
inference(superposition,[status(thm)],[c_11519,c_3945]) ).
tcf(c_11705,plain,
multiplication(iPr_def_14,iPr_def_16) = iPr_def_16,
inference(demodulation,[status(thm)],[c_11701,c_192,c_2113]) ).
tcf(c_13150,plain,
leq(iPr_def_14,iPr_def_16) = iPr_def_13,
inference(superposition,[status(thm)],[c_11705,c_9116]) ).
tcf(c_13177,plain,
iPr_def_13 = iPr_def_17,
inference(demodulation,[status(thm)],[c_170,c_13150]) ).
tcf(c_13183,plain,
tuple(iPr_def_13,iPr_def_13) = iPr_def_18,
inference(demodulation,[status(thm)],[c_171,c_13177]) ).
tcf(c_13184,plain,
iPr_def_18 = iPr_def_19,
inference(demodulation,[status(thm)],[c_3197,c_13183]) ).
tcf(c_13185,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13184,c_173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE044-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 18:40:46 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running UEQ theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 41.97/6.32 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 41.97/6.32 % SZS status Started for theBenchmark.p
% 41.97/6.32 % SZS status Unsatisfiable for theBenchmark.p
% 41.97/6.32
% 41.97/6.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 41.97/6.32
% 41.97/6.32 % ------ iProver source info
% 41.97/6.32
% 41.97/6.32 % git: date: 2026-07-19 20:42:38 +0200
% 41.97/6.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 41.97/6.32 % git: non_committed_changes: false
% 41.97/6.32
% 41.97/6.32 % ------ Parsing...% successful
% 41.97/6.32
% 41.97/6.32
% 41.97/6.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 41.97/6.32
% 41.97/6.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 41.97/6.32
% 41.97/6.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 41.97/6.32
% 41.97/6.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 41.97/6.32 % ------ Proving...
% 41.97/6.32 % ------ Problem Properties
% 41.97/6.32
% 41.97/6.32 %
% 41.97/6.32 % clauses 31
% 41.97/6.32 % conjectures 1
% 41.97/6.32 % EPR 1
% 41.97/6.32 % Horn 31
% 41.97/6.32 % unary 31
% 41.97/6.32 % binary 0
% 41.97/6.32 % lits 31
% 41.97/6.32 % lits eq 31
% 41.97/6.32 % fd_pure 0
% 41.97/6.32 % fd_pseudo 0
% 41.97/6.32 % fd_cond 0
% 41.97/6.32 % fd_pseudo_cond 0
% 41.97/6.32 % AC symbols 1
% 41.97/6.32
% 41.97/6.32 % ------ Input Options Time Limit: Unbounded
% 41.97/6.32
% 41.97/6.32
% 41.97/6.32 % ------
% 41.97/6.32 % Current options:
% 41.97/6.32 % ------
% 41.97/6.32
% 41.97/6.32
% 41.97/6.32 %
% 41.97/6.32
% 41.97/6.32 % ------ Proving...
% 41.97/6.32 %
% 41.97/6.32
% 41.97/6.32 % SZS status Unsatisfiable for theBenchmark.p
% 41.97/6.32
% 41.97/6.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 41.97/6.33
% 41.97/6.33
%------------------------------------------------------------------------------