%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 01:00:10 PM UTC 2026
% Result : Unsatisfiable 8.44s 1.72s
% Output : CNFRefutation 8.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 19
% Syntax : Number of formulae : 149 ( 149 unt; 4 def)
% Number of atoms : 298 ( 148 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 : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 151 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
fof(f6,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
fof(f8,axiom,
! [X0] : add(inverse(X0),X0) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse2) ).
fof(f9,plain,
! [X0] : multiplicative_identity = add(inverse(X0),X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
fof(f11,axiom,
! [X0] : multiply(inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse2) ).
fof(f12,plain,
! [X0] : additive_identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
fof(f14,axiom,
! [X0] : multiply(multiplicative_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
fof(f15,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
fof(f16,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
fof(f17,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_71,plain,
! [X0: $i] : add(inverse(X0),X0) = multiplicative_identity,
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[],[f12]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[],[f13]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
tcf(c_76,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f15]) ).
tcf(c_77,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_78,negated_conjecture,
add(add(a,b),c) != add(a,add(b,c)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_126,definition,
iPr_def_10 = add(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_127,definition,
iPr_def_11 = add(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_128,definition,
iPr_def_12 = add(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_129,definition,
iPr_def_13 = add(a,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_130,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_78,c_128,c_129,c_126,c_127]) ).
tcf(c_131,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_132,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_133,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_134,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_135,plain,
! [X0: $i] : multiply(inverse(X0),X0) = additive_identity,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_136,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_137,plain,
! [X0: $i] : add(inverse(X0),X0) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_138,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_208,plain,
inverse(multiplicative_identity) = additive_identity,
inference(superposition,[status(thm)],[c_133,c_136]) ).
tcf(c_210,plain,
inverse(additive_identity) = multiplicative_identity,
inference(superposition,[status(thm)],[c_131,c_138]) ).
tcf(c_232,plain,
add(c,b) = iPr_def_12,
inference(superposition,[status(thm)],[c_144,c_128]) ).
tcf(c_235,plain,
add(iPr_def_12,a) = iPr_def_13,
inference(superposition,[status(thm)],[c_144,c_129]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[status(thm)],[c_134,c_139]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(superposition,[status(thm)],[c_136,c_139]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),inverse(X0)) = add(additive_identity,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_136,c_140]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
inference(superposition,[status(thm)],[c_133,c_140]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X0),X1) = multiply(X0,add(X1,X1)),
inference(superposition,[status(thm)],[c_140,c_139]) ).
tcf(c_296,plain,
! [X0: $i] : add(b,multiply(c,X0)) = multiply(iPr_def_12,add(b,X0)),
inference(superposition,[status(thm)],[c_128,c_141]) ).
tcf(c_297,plain,
! [X0: $i] : add(a,multiply(b,X0)) = multiply(iPr_def_10,add(a,X0)),
inference(superposition,[status(thm)],[c_126,c_141]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_138,c_141]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_132,c_141]) ).
tcf(c_305,plain,
! [X0: $i] : add(iPr_def_10,multiply(c,X0)) = multiply(iPr_def_11,add(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_127,c_141]) ).
tcf(c_306,plain,
! [X0: $i] : add(a,multiply(iPr_def_12,X0)) = multiply(iPr_def_13,add(a,X0)),
inference(superposition,[status(thm)],[c_129,c_141]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(superposition,[status(thm)],[c_138,c_141]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),inverse(X0)) = multiply(multiplicative_identity,add(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_138,c_142]) ).
tcf(c_350,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),c) = multiply(iPr_def_11,add(X0,c)),
inference(superposition,[status(thm)],[c_127,c_142]) ).
tcf(c_361,plain,
! [X0: $i] : add(multiply(X0,iPr_def_10),c) = multiply(add(X0,c),iPr_def_11),
inference(superposition,[status(thm)],[c_127,c_142]) ).
tcf(c_362,plain,
! [X0: $i] : add(multiply(X0,a),iPr_def_12) = multiply(add(X0,iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_129,c_142]) ).
tcf(c_416,plain,
! [X0: $i] : add(iPr_def_12,multiply(X0,a)) = multiply(iPr_def_13,add(X0,iPr_def_12)),
inference(demodulation,[status(thm)],[c_362,c_144,c_143]) ).
tcf(c_417,plain,
! [X0: $i] : add(c,multiply(X0,iPr_def_10)) = multiply(iPr_def_11,add(X0,c)),
inference(demodulation,[status(thm)],[c_361,c_144,c_143]) ).
tcf(c_422,plain,
! [X0: $i] : add(c,multiply(iPr_def_10,X0)) = multiply(iPr_def_11,add(X0,c)),
inference(demodulation,[status(thm)],[c_350,c_144]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(demodulation,[status(thm)],[c_313,c_134]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_302,c_133]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_245,c_132]) ).
tcf(c_437,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X0,X1)) = add(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c_347,c_144,c_133]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),add(X0,X1)) = multiply(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c_267,c_143,c_131]) ).
tcf(c_560,plain,
! [X0: $i] : add(X0,X0) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_136,c_432]) ).
tcf(c_575,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_134,c_433]) ).
tcf(c_577,plain,
! [X0: $i] : add(multiplicative_identity,multiply(additive_identity,X0)) = add(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_208,c_433]) ).
tcf(c_590,plain,
! [X0: $i] : multiply(additive_identity,add(X0,multiplicative_identity)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_210,c_434]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[status(thm)],[c_143,c_241]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(add(multiplicative_identity,X1),X0),
inference(superposition,[status(thm)],[c_143,c_269]) ).
tcf(c_711,plain,
multiply(add(multiplicative_identity,c),b) = multiply(iPr_def_12,add(b,b)),
inference(superposition,[status(thm)],[c_296,c_269]) ).
tcf(c_726,plain,
multiply(add(multiplicative_identity,b),a) = multiply(iPr_def_10,add(a,a)),
inference(superposition,[status(thm)],[c_297,c_269]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_144,c_303]) ).
tcf(c_811,plain,
multiply(add(multiplicative_identity,c),iPr_def_10) = multiply(iPr_def_11,add(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_305,c_269]) ).
tcf(c_814,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_560,c_132]) ).
tcf(c_816,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_575,c_138]) ).
tcf(c_829,plain,
! [X0: $i] : multiply(additive_identity,X0) = multiply(additive_identity,multiplicative_identity),
inference(demodulation,[status(thm)],[c_590,c_816]) ).
tcf(c_830,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_829,c_134]) ).
tcf(c_831,plain,
! [X0: $i] : add(multiplicative_identity,X0) = add(multiplicative_identity,additive_identity),
inference(demodulation,[status(thm)],[c_577,c_830]) ).
tcf(c_832,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_831,c_132]) ).
tcf(c_847,plain,
multiply(multiplicative_identity,iPr_def_10) = multiply(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_811,c_814,c_832]) ).
tcf(c_848,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_847,c_143,c_133]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_730,c_830]) ).
tcf(c_857,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_856,c_132]) ).
tcf(c_858,plain,
multiply(multiplicative_identity,a) = multiply(iPr_def_10,a),
inference(demodulation,[status(thm)],[c_726,c_814,c_832]) ).
tcf(c_859,plain,
multiply(iPr_def_10,a) = a,
inference(demodulation,[status(thm)],[c_858,c_133]) ).
tcf(c_861,plain,
multiply(multiplicative_identity,b) = multiply(iPr_def_12,b),
inference(demodulation,[status(thm)],[c_711,c_814,c_832]) ).
tcf(c_862,plain,
multiply(iPr_def_12,b) = b,
inference(demodulation,[status(thm)],[c_861,c_133]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(multiplicative_identity,X0),
inference(demodulation,[status(thm)],[c_640,c_832]) ).
tcf(c_873,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_872,c_133]) ).
tcf(c_875,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_619,c_832]) ).
tcf(c_876,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_875,c_134]) ).
tcf(c_1596,plain,
multiply(add(multiplicative_identity,iPr_def_10),iPr_def_11) = add(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_848,c_269]) ).
tcf(c_1600,plain,
! [X0: $i] : add(a,multiply(X0,a)) = multiply(add(iPr_def_10,X0),a),
inference(superposition,[status(thm)],[c_859,c_140]) ).
tcf(c_1678,plain,
multiply(c,iPr_def_12) = c,
inference(superposition,[status(thm)],[c_128,c_857]) ).
tcf(c_1679,plain,
multiply(b,iPr_def_10) = b,
inference(superposition,[status(thm)],[c_126,c_857]) ).
tcf(c_1688,plain,
multiply(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_129,c_857]) ).
tcf(c_1720,plain,
multiply(iPr_def_10,b) = b,
inference(demodulation,[status(thm)],[c_1679,c_143]) ).
tcf(c_1721,plain,
multiply(iPr_def_12,c) = c,
inference(demodulation,[status(thm)],[c_1678,c_143]) ).
tcf(c_1725,plain,
add(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1596,c_144,c_143,c_134,c_832]) ).
tcf(c_1739,plain,
! [X0: $i] : multiply(a,add(iPr_def_10,X0)) = a,
inference(demodulation,[status(thm)],[c_1600,c_143,c_876]) ).
tcf(c_1887,plain,
multiply(iPr_def_13,add(a,b)) = add(a,b),
inference(superposition,[status(thm)],[c_862,c_306]) ).
tcf(c_1991,plain,
add(iPr_def_12,c) = iPr_def_12,
inference(superposition,[status(thm)],[c_1721,c_873]) ).
tcf(c_2107,plain,
! [X0: $i] : multiply(iPr_def_11,add(add(X0,X0),c)) = add(c,multiply(X0,add(iPr_def_10,iPr_def_10))),
inference(superposition,[status(thm)],[c_277,c_417]) ).
tcf(c_2194,plain,
multiply(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1887,c_143,c_126]) ).
tcf(c_2233,plain,
! [X0: $i] : multiply(iPr_def_11,add(X0,c)) = multiply(iPr_def_11,add(c,X0)),
inference(demodulation,[status(thm)],[c_2107,c_144,c_417,c_814]) ).
tcf(c_2673,plain,
multiply(iPr_def_11,add(b,c)) = add(c,b),
inference(superposition,[status(thm)],[c_1720,c_422]) ).
tcf(c_2741,plain,
multiply(iPr_def_11,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2673,c_232,c_2233]) ).
tcf(c_2932,plain,
add(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_2741,c_873]) ).
tcf(c_2958,plain,
multiply(a,iPr_def_11) = a,
inference(superposition,[status(thm)],[c_1725,c_1739]) ).
tcf(c_3159,plain,
multiply(iPr_def_11,a) = a,
inference(demodulation,[status(thm)],[c_2958,c_143]) ).
tcf(c_3383,plain,
multiply(iPr_def_13,add(iPr_def_11,iPr_def_12)) = add(iPr_def_12,a),
inference(superposition,[status(thm)],[c_3159,c_416]) ).
tcf(c_3478,plain,
add(inverse(iPr_def_12),iPr_def_12) = add(iPr_def_13,inverse(iPr_def_12)),
inference(superposition,[status(thm)],[c_1688,c_437]) ).
tcf(c_3489,plain,
add(inverse(iPr_def_10),iPr_def_10) = add(iPr_def_13,inverse(iPr_def_10)),
inference(superposition,[status(thm)],[c_2194,c_437]) ).
tcf(c_3595,plain,
add(iPr_def_13,inverse(iPr_def_10)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_3489,c_137]) ).
tcf(c_3596,plain,
add(iPr_def_13,inverse(iPr_def_12)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_3478,c_137]) ).
tcf(c_3607,plain,
multiply(iPr_def_11,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3383,c_143,c_235,c_2932]) ).
tcf(c_3760,plain,
! [X0: $i] : add(iPr_def_13,multiply(iPr_def_11,X0)) = multiply(iPr_def_11,add(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_3607,c_139]) ).
tcf(c_3856,plain,
! [X0: $i] : add(iPr_def_13,multiply(inverse(iPr_def_10),X0)) = multiply(multiplicative_identity,add(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_3595,c_141]) ).
tcf(c_3864,plain,
! [X0: $i] : add(iPr_def_13,multiply(inverse(iPr_def_12),X0)) = multiply(multiplicative_identity,add(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_3596,c_141]) ).
tcf(c_3911,plain,
multiply(inverse(iPr_def_10),iPr_def_11) = multiply(c,inverse(iPr_def_10)),
inference(superposition,[status(thm)],[c_127,c_439]) ).
tcf(c_3950,plain,
multiply(inverse(iPr_def_12),iPr_def_12) = multiply(c,inverse(iPr_def_12)),
inference(superposition,[status(thm)],[c_1991,c_439]) ).
tcf(c_3982,plain,
multiply(c,inverse(iPr_def_12)) = additive_identity,
inference(demodulation,[status(thm)],[c_3950,c_135]) ).
tcf(c_3988,plain,
multiply(c,inverse(iPr_def_10)) = multiply(iPr_def_11,inverse(iPr_def_10)),
inference(demodulation,[status(thm)],[c_3911,c_143]) ).
tcf(c_4020,plain,
! [X0: $i] : add(iPr_def_13,multiply(inverse(iPr_def_12),X0)) = add(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_3864,c_133]) ).
tcf(c_4022,plain,
! [X0: $i] : add(iPr_def_13,multiply(inverse(iPr_def_10),X0)) = add(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_3856,c_133]) ).
tcf(c_4337,plain,
! [X0: $i] : add(iPr_def_13,multiply(X0,inverse(iPr_def_12))) = add(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_143,c_4020]) ).
tcf(c_4364,plain,
! [X0: $i] : add(iPr_def_13,multiply(X0,inverse(iPr_def_10))) = add(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_143,c_4022]) ).
tcf(c_5207,plain,
add(iPr_def_13,c) = add(iPr_def_13,additive_identity),
inference(superposition,[status(thm)],[c_3982,c_4337]) ).
tcf(c_5231,plain,
add(iPr_def_13,multiply(iPr_def_11,inverse(iPr_def_10))) = add(iPr_def_13,c),
inference(superposition,[status(thm)],[c_3988,c_4364]) ).
tcf(c_5247,plain,
add(iPr_def_13,c) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5207,c_132]) ).
tcf(c_5248,plain,
add(iPr_def_13,multiply(iPr_def_11,inverse(iPr_def_10))) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5231,c_5247]) ).
tcf(c_5249,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_5248,c_134,c_3595,c_3760]) ).
tcf(c_5250,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5249,c_130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 06:31:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running UEQ theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 8.44/1.72 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.44/1.72 % SZS status Started for theBenchmark.p
% 8.44/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 8.44/1.72
% 8.44/1.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.44/1.72
% 8.44/1.72 % ------ iProver source info
% 8.44/1.72
% 8.44/1.72 % git: date: 2026-07-19 20:42:38 +0200
% 8.44/1.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.44/1.72 % git: non_committed_changes: false
% 8.44/1.72
% 8.44/1.72 % ------ Parsing...% successful
% 8.44/1.72
% 8.44/1.72
% 8.44/1.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.44/1.72
% 8.44/1.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.44/1.72
% 8.44/1.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.44/1.72
% 8.44/1.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.44/1.72 % ------ Proving...
% 8.44/1.72 % ------ Problem Properties
% 8.44/1.72
% 8.44/1.72 %
% 8.44/1.72 % clauses 19
% 8.44/1.72 % conjectures 1
% 8.44/1.72 % EPR 1
% 8.44/1.72 % Horn 19
% 8.44/1.72 % unary 19
% 8.44/1.72 % binary 0
% 8.44/1.72 % lits 19
% 8.44/1.72 % lits eq 19
% 8.44/1.72 % fd_pure 0
% 8.44/1.72 % fd_pseudo 0
% 8.44/1.72 % fd_cond 0
% 8.44/1.72 % fd_pseudo_cond 0
% 8.44/1.72 % AC symbols 0
% 8.44/1.72
% 8.44/1.72 % ------ Input Options Time Limit: Unbounded
% 8.44/1.72
% 8.44/1.72
% 8.44/1.72 % ------
% 8.44/1.72 % Current options:
% 8.44/1.72 % ------
% 8.44/1.72
% 8.44/1.72
% 8.44/1.72 %
% 8.44/1.72
% 8.44/1.72 % ------ Proving...
% 8.44/1.72 %
% 8.44/1.72
% 8.44/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 8.44/1.72
% 8.44/1.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.44/1.72
% 8.44/1.72
%------------------------------------------------------------------------------