%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO015-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 01:00:14 PM UTC 2026
% Result : Unsatisfiable 9.34s 2.18s
% Output : CNFRefutation 9.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 149 ( 149 unt; 5 def)
% Number of atoms : 265 ( 148 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 161 ( 0 sgn 161 !; 0 ?; 139 :)
% 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(f10,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
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,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f18,axiom,
add(inverse(a),inverse(b)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_plus_b_inverse_is_d) ).
fof(f19,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
fof(f20,plain,
d != inverse(c),
inference(reorient_equations,[],[f19]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,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_69,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_70,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_71,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_72,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_76,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[],[f13]) ).
tcf(c_77,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
tcf(c_78,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f15]) ).
tcf(c_79,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[],[f16]) ).
tcf(c_80,plain,
multiply(a,b) = c,
inference(cnf_transformation,[],[f17]) ).
tcf(c_81,plain,
add(inverse(a),inverse(b)) = d,
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
inverse(c) != d,
inference(cnf_transformation,[],[f20]) ).
tcf(c_135,definition,
iPr_def_10 = inverse(c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_136,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_137,definition,
iPr_def_12 = inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_138,definition,
iPr_def_13 = add(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_139,definition,
iPr_def_14 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_140,negated_conjecture,
iPr_def_10 != d,
inference(demodulation,[status(thm)],[c_82,c_135]) ).
tcf(c_141,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_142,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_143,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_144,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_146,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_148,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_155,plain,
iPr_def_13 = d,
inference(demodulation,[status(thm)],[c_81,c_137,c_136,c_138]) ).
tcf(c_156,plain,
iPr_def_14 = c,
inference(demodulation,[status(thm)],[c_80,c_139]) ).
tcf(c_232,plain,
inverse(iPr_def_14) = iPr_def_10,
inference(demodulation,[status(thm)],[c_135,c_156]) ).
tcf(c_233,plain,
iPr_def_10 != iPr_def_13,
inference(demodulation,[status(thm)],[c_140,c_155]) ).
tcf(c_237,plain,
multiply(a,iPr_def_11) = additive_identity,
inference(superposition,[status(thm)],[c_136,c_146]) ).
tcf(c_238,plain,
multiply(b,iPr_def_12) = additive_identity,
inference(superposition,[status(thm)],[c_137,c_146]) ).
tcf(c_239,plain,
multiply(iPr_def_14,iPr_def_10) = additive_identity,
inference(superposition,[status(thm)],[c_232,c_146]) ).
tcf(c_240,plain,
inverse(multiplicative_identity) = additive_identity,
inference(superposition,[status(thm)],[c_146,c_143]) ).
tcf(c_242,plain,
add(a,iPr_def_11) = multiplicative_identity,
inference(superposition,[status(thm)],[c_136,c_148]) ).
tcf(c_243,plain,
add(b,iPr_def_12) = multiplicative_identity,
inference(superposition,[status(thm)],[c_137,c_148]) ).
tcf(c_245,plain,
inverse(additive_identity) = multiplicative_identity,
inference(superposition,[status(thm)],[c_148,c_141]) ).
tcf(c_264,plain,
! [X0: $i] : multiply(a,add(b,X0)) = add(iPr_def_14,multiply(a,X0)),
inference(superposition,[status(thm)],[c_139,c_149]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : multiply(X0,add(inverse(X0),X1)) = add(additive_identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_146,c_149]) ).
tcf(c_271,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X0)) = multiply(X0,add(X1,X2)),
inference(superposition,[status(thm)],[c_153,c_149]) ).
tcf(c_273,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(superposition,[status(thm)],[c_146,c_149]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
inference(superposition,[status(thm)],[c_143,c_150]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X2,X0),X1),
inference(superposition,[status(thm)],[c_150,c_154]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_148,c_151]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_142,c_151]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(superposition,[status(thm)],[c_148,c_151]) ).
tcf(c_388,plain,
add(iPr_def_12,b) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_243,c_154]) ).
tcf(c_389,plain,
add(iPr_def_11,a) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_242,c_154]) ).
tcf(c_390,plain,
multiply(iPr_def_12,b) = additive_identity,
inference(demodulation,[status(thm)],[c_238,c_153]) ).
tcf(c_391,plain,
multiply(iPr_def_11,a) = additive_identity,
inference(demodulation,[status(thm)],[c_237,c_153]) ).
tcf(c_403,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(demodulation,[status(thm)],[c_328,c_144]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_320,c_143]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_273,c_142]) ).
tcf(c_406,plain,
! [X0: $i,X1: $i] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_267,c_141]) ).
tcf(c_546,plain,
! [X0: $i] : multiply(add(iPr_def_14,X0),iPr_def_10) = add(additive_identity,multiply(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_239,c_150]) ).
tcf(c_556,plain,
! [X0: $i] : multiply(add(iPr_def_12,X0),multiplicative_identity) = add(iPr_def_12,multiply(X0,b)),
inference(superposition,[status(thm)],[c_388,c_151]) ).
tcf(c_559,plain,
! [X0: $i] : multiply(multiplicative_identity,add(iPr_def_11,X0)) = add(iPr_def_11,multiply(a,X0)),
inference(superposition,[status(thm)],[c_389,c_151]) ).
tcf(c_564,plain,
! [X0: $i] : multiply(iPr_def_12,add(X0,b)) = add(multiply(iPr_def_12,X0),additive_identity),
inference(superposition,[status(thm)],[c_390,c_149]) ).
tcf(c_568,plain,
! [X0: $i] : multiply(iPr_def_11,add(X0,a)) = add(multiply(iPr_def_11,X0),additive_identity),
inference(superposition,[status(thm)],[c_391,c_149]) ).
tcf(c_580,plain,
! [X0: $i] : add(multiplicative_identity,multiply(X0,additive_identity)) = add(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_240,c_403]) ).
tcf(c_591,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_146,c_404]) ).
tcf(c_592,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_144,c_404]) ).
tcf(c_608,plain,
! [X0: $i] : multiply(X0,X0) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_148,c_405]) ).
tcf(c_612,plain,
! [X0: $i] : multiply(additive_identity,add(X0,multiplicative_identity)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_245,c_405]) ).
tcf(c_626,plain,
! [X0: $i] : multiply(X0,inverse(inverse(X0))) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_148,c_406]) ).
tcf(c_627,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_142,c_406]) ).
tcf(c_717,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,multiply(X1,X2)),multiply(add(multiplicative_identity,X1),X2)) = add(multiply(X0,X2),multiply(X1,X2)),
inference(superposition,[status(thm)],[c_286,c_152]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(X0,add(multiplicative_identity,X1)),
inference(superposition,[status(thm)],[c_286,c_153]) ).
tcf(c_855,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_154,c_321]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i] : add(X0,add(inverse(X0),multiply(additive_identity,X1))) = add(X0,add(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_321,c_404]) ).
tcf(c_881,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_608,c_144]) ).
tcf(c_883,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_627,c_146]) ).
tcf(c_884,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_592,c_148]) ).
tcf(c_899,plain,
! [X0: $i] : multiply(X0,inverse(inverse(X0))) = X0,
inference(demodulation,[status(thm)],[c_626,c_144]) ).
tcf(c_900,plain,
! [X0: $i] : multiply(additive_identity,X0) = multiply(additive_identity,multiplicative_identity),
inference(demodulation,[status(thm)],[c_612,c_884]) ).
tcf(c_901,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_900,c_144]) ).
tcf(c_902,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = X0,
inference(demodulation,[status(thm)],[c_591,c_142]) ).
tcf(c_903,plain,
! [X0: $i] : add(multiplicative_identity,X0) = add(multiplicative_identity,additive_identity),
inference(demodulation,[status(thm)],[c_580,c_883]) ).
tcf(c_904,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_903,c_142]) ).
tcf(c_917,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_855,c_901]) ).
tcf(c_918,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_917,c_142]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_727,c_904]) ).
tcf(c_930,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_929,c_144]) ).
tcf(c_942,plain,
! [X0: $i] : multiply(iPr_def_11,add(X0,a)) = multiply(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_568,c_142]) ).
tcf(c_946,plain,
! [X0: $i] : multiply(iPr_def_12,add(X0,b)) = multiply(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_564,c_142]) ).
tcf(c_951,plain,
! [X0: $i] : add(iPr_def_11,multiply(a,X0)) = add(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_559,c_143]) ).
tcf(c_954,plain,
! [X0: $i] : add(iPr_def_12,multiply(X0,b)) = add(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_556,c_144]) ).
tcf(c_964,plain,
! [X0: $i] : multiply(iPr_def_10,add(iPr_def_14,X0)) = multiply(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_546,c_153,c_141]) ).
tcf(c_984,plain,
! [X0: $i,X1: $i] : add(X0,add(inverse(X0),X1)) = add(X0,add(inverse(X0),additive_identity)),
inference(demodulation,[status(thm)],[c_880,c_901]) ).
tcf(c_985,plain,
! [X0: $i,X1: $i] : add(X0,add(inverse(X0),X1)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_984,c_148,c_142]) ).
tcf(c_1064,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,multiply(X1,X2)),multiply(multiplicative_identity,X2)) = add(multiply(X0,X2),multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_717,c_904]) ).
tcf(c_1065,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(X1,multiply(X2,X0))) = multiply(add(X2,X1),X0),
inference(demodulation,[status(thm)],[c_1064,c_153,c_143,c_293]) ).
tcf(c_1732,plain,
add(iPr_def_14,multiply(a,a)) = a,
inference(superposition,[status(thm)],[c_918,c_264]) ).
tcf(c_1742,plain,
add(b,iPr_def_14) = b,
inference(superposition,[status(thm)],[c_139,c_930]) ).
tcf(c_1765,plain,
! [X0: $i] : add(inverse(inverse(X0)),X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_899,c_930]) ).
tcf(c_1767,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(X1,multiply(X2,X0))) = add(multiply(X0,X1),multiply(X2,X0)),
inference(superposition,[status(thm)],[c_930,c_152]) ).
tcf(c_1794,plain,
add(iPr_def_14,b) = b,
inference(demodulation,[status(thm)],[c_1742,c_154]) ).
tcf(c_1795,plain,
add(iPr_def_14,a) = a,
inference(demodulation,[status(thm)],[c_1732,c_881]) ).
tcf(c_1797,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_1765,c_154,c_902]) ).
tcf(c_1828,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),X2) = multiply(X2,add(X1,X0)),
inference(demodulation,[status(thm)],[c_1767,c_271,c_1065]) ).
tcf(c_1871,plain,
! [X0: $i] : multiply(add(iPr_def_14,X0),b) = add(iPr_def_14,multiply(X0,b)),
inference(superposition,[status(thm)],[c_1794,c_151]) ).
tcf(c_1888,plain,
inverse(iPr_def_10) = iPr_def_14,
inference(superposition,[status(thm)],[c_232,c_1797]) ).
tcf(c_2321,plain,
! [X0: $i] : multiply(b,add(X0,iPr_def_14)) = add(iPr_def_14,multiply(X0,b)),
inference(demodulation,[status(thm)],[c_1871,c_1828]) ).
tcf(c_2542,plain,
! [X0: $i] : add(iPr_def_10,add(iPr_def_14,X0)) = multiplicative_identity,
inference(superposition,[status(thm)],[c_1888,c_985]) ).
tcf(c_4021,plain,
add(iPr_def_10,b) = multiplicative_identity,
inference(superposition,[status(thm)],[c_1794,c_2542]) ).
tcf(c_4022,plain,
add(iPr_def_10,a) = multiplicative_identity,
inference(superposition,[status(thm)],[c_1795,c_2542]) ).
tcf(c_4851,plain,
multiply(iPr_def_11,multiplicative_identity) = multiply(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_4022,c_942]) ).
tcf(c_5040,plain,
multiply(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_4851,c_144]) ).
tcf(c_5132,plain,
add(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(superposition,[status(thm)],[c_5040,c_930]) ).
tcf(c_5233,plain,
multiply(iPr_def_12,multiplicative_identity) = multiply(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_4021,c_946]) ).
tcf(c_5410,plain,
add(iPr_def_11,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5132,c_154]) ).
tcf(c_5411,plain,
multiply(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(demodulation,[status(thm)],[c_5233,c_144]) ).
tcf(c_5489,plain,
! [X0: $i] : multiply(iPr_def_10,add(X0,iPr_def_10)) = add(multiply(iPr_def_11,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_5410,c_152]) ).
tcf(c_5501,plain,
add(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_5411,c_930]) ).
tcf(c_5618,plain,
add(iPr_def_11,b) = add(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_139,c_951]) ).
tcf(c_5730,plain,
add(iPr_def_12,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5501,c_154]) ).
tcf(c_5745,plain,
! [X0: $i] : add(iPr_def_10,multiply(iPr_def_11,X0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_5489,c_154,c_918]) ).
tcf(c_5858,plain,
multiply(b,add(iPr_def_11,iPr_def_14)) = b,
inference(superposition,[status(thm)],[c_5618,c_918]) ).
tcf(c_6053,plain,
add(iPr_def_14,multiply(iPr_def_11,b)) = b,
inference(demodulation,[status(thm)],[c_5858,c_2321]) ).
tcf(c_6224,plain,
! [X0: $i] : multiply(multiply(iPr_def_11,X0),iPr_def_10) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_5745,c_918]) ).
tcf(c_6422,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,X0)) = multiply(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_6224,c_153]) ).
tcf(c_6667,plain,
multiply(multiply(iPr_def_11,b),iPr_def_10) = multiply(iPr_def_10,b),
inference(superposition,[status(thm)],[c_6053,c_964]) ).
tcf(c_6809,plain,
multiply(iPr_def_10,b) = multiply(iPr_def_11,b),
inference(demodulation,[status(thm)],[c_6667,c_153,c_6422]) ).
tcf(c_8262,plain,
add(iPr_def_12,multiply(iPr_def_11,b)) = add(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_6809,c_954]) ).
tcf(c_8526,plain,
iPr_def_10 = iPr_def_13,
inference(demodulation,[status(thm)],[c_8262,c_154,c_138,c_954,c_5730]) ).
tcf(c_8527,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_8526,c_233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO015-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.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 : Fri Sep 25 06:33:14 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 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
% 0.09/0.44 % Proving...
% 9.34/2.18 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 9.34/2.18 % SZS status Started for theBenchmark.p
% 9.34/2.18 % SZS status Unsatisfiable for theBenchmark.p
% 9.34/2.18
% 9.34/2.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.34/2.18
% 9.34/2.18 % ------ iProver source info
% 9.34/2.18
% 9.34/2.18 % git: date: 2026-07-19 20:42:38 +0200
% 9.34/2.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.34/2.18 % git: non_committed_changes: false
% 9.34/2.18
% 9.34/2.18 % ------ Parsing...% successful
% 9.34/2.18
% 9.34/2.18
% 9.34/2.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.34/2.18
% 9.34/2.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 9.34/2.18
% 9.34/2.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.34/2.18
% 9.34/2.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 9.34/2.18 % ------ Proving...
% 9.34/2.18 % ------ Problem Properties
% 9.34/2.18
% 9.34/2.18 %
% 9.34/2.18 % clauses 22
% 9.34/2.18 % conjectures 1
% 9.34/2.18 % EPR 3
% 9.34/2.18 % Horn 22
% 9.34/2.18 % unary 22
% 9.34/2.18 % binary 0
% 9.34/2.18 % lits 22
% 9.34/2.18 % lits eq 22
% 9.34/2.18 % fd_pure 0
% 9.34/2.18 % fd_pseudo 0
% 9.34/2.18 % fd_cond 0
% 9.34/2.18 % fd_pseudo_cond 0
% 9.34/2.18 % AC symbols 0
% 9.34/2.18
% 9.34/2.18 % ------ Input Options Time Limit: Unbounded
% 9.34/2.18
% 9.34/2.18
% 9.34/2.18 % ------
% 9.34/2.18 % Current options:
% 9.34/2.18 % ------
% 9.34/2.18
% 9.34/2.18
% 9.34/2.18 %
% 9.34/2.18
% 9.34/2.18 % ------ Proving...
% 9.34/2.18 %
% 9.34/2.18
% 9.34/2.18 % SZS status Unsatisfiable for theBenchmark.p
% 9.34/2.18
% 9.34/2.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.34/2.18
% 9.34/2.18
%------------------------------------------------------------------------------