%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 01:00:13 PM UTC 2026
% Result : Unsatisfiable 83.30s 14.39s
% Output : CNFRefutation 83.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 17
% Syntax : Number of formulae : 156 ( 138 unt; 1 def)
% Number of atoms : 533 ( 145 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 113 ( 59 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 237 ( 0 sgn 237 !; 0 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
fof(f4,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
fof(f5,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
fof(f7,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
fof(f8,axiom,
! [X0] : product(X0,multiplicative_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity2) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity6) ).
fof(f16,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',distributivity8) ).
fof(f18,axiom,
! [X0] : sum(X0,inverse(X0),multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',additive_inverse2) ).
fof(f20,axiom,
! [X0] : product(X0,inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
fof(f23,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_is_self_cancelling) ).
fof(f25,axiom,
sum(x,y,x_plus_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_plus_y) ).
fof(f26,axiom,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_inverse_times_y_inverse) ).
fof(f27,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f28,plain,
x_inverse_times_y_inverse != inverse(x_plus_y),
inference(reorient_equations,[],[f27]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_80,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_81,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,plain,
! [X0: $i] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[],[f8]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X2,X6,X5)
| ~ product(X1,X6,X4)
| ~ product(X0,X6,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X0,X5,X6)
| ~ product(X2,X4,X6)
| ~ product(X1,X3,X5)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sum(X5,X1,X6)
| ~ product(X2,X4,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_93,plain,
! [X0: $i] : sum(X0,inverse(X0),multiplicative_identity),
inference(cnf_transformation,[],[f18]) ).
tcf(c_95,plain,
! [X0: $i] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_98,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f23]) ).
tcf(c_100,plain,
sum(x,y,x_plus_y),
inference(cnf_transformation,[],[f25]) ).
tcf(c_101,plain,
product(inverse(x),inverse(y),x_inverse_times_y_inverse),
inference(cnf_transformation,[],[f26]) ).
tcf(c_102,negated_conjecture,
inverse(x_plus_y) != x_inverse_times_y_inverse,
inference(cnf_transformation,[],[f28]) ).
tcf(c_116,plain,
add(x,y) = x_plus_y,
inference(well_definedness,[status(thm)],[c_100]) ).
tcf(c_117,plain,
multiply(inverse(x),inverse(y)) = x_inverse_times_y_inverse,
inference(well_definedness,[status(thm)],[c_101]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_78]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_124,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_125,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_126,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_127,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X6,X2) = X5 )
| ( multiply(X6,X1) != X4 )
| ( multiply(X6,X0) != X3 )
| ( add(X3,X4) != X5 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X2,X6) = X5 )
| ( multiply(X1,X6) != X4 )
| ( multiply(X0,X6) != X3 )
| ( add(X3,X4) != X5 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_87]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( add(X0,X5) = X6 )
| ( multiply(X2,X4) != X6 )
| ( multiply(X1,X3) != X5 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( add(X5,X1) = X6 )
| ( multiply(X2,X4) != X6 )
| ( multiply(X0,X3) != X5 )
| ( add(X3,X1) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_145,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(well_definedness,[status(thm)],[c_93]) ).
tcf(c_147,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_95]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_122]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_120]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X2,X1)) = add(multiply(X0,X2),X1),
inference(unflattening,[status(thm)],[c_142]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_138]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_134]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_130]) ).
tcf(c_381,definition,
iPr_def_10 = inverse(x_plus_y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_382,negated_conjecture,
iPr_def_10 != x_inverse_times_y_inverse,
inference(demodulation,[status(thm)],[c_102,c_381]) ).
tcf(c_54534,plain,
inverse(iPr_def_10) = x_plus_y,
inference(superposition,[status(thm)],[c_381,c_98]) ).
tcf(c_54535,plain,
inverse(x_plus_y) = iPr_def_10,
inference(superposition,[status(thm)],[c_54534,c_98]) ).
tcf(c_54547,plain,
multiply(iPr_def_10,x_plus_y) = additive_identity,
inference(superposition,[status(thm)],[c_54534,c_147]) ).
tcf(c_54574,plain,
! [X0: $i] : add(multiply(x,X0),y) = multiply(x_plus_y,add(X0,y)),
inference(superposition,[status(thm)],[c_116,c_312]) ).
tcf(c_54576,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(multiply(additive_identity,X1),X0),
inference(superposition,[status(thm)],[c_124,c_312]) ).
tcf(c_54578,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),inverse(X0)) = multiply(multiplicative_identity,add(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_145,c_312]) ).
tcf(c_54583,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X1) = add(multiply(X0,additive_identity),X1),
inference(superposition,[status(thm)],[c_124,c_312]) ).
tcf(c_54598,plain,
! [X0: $i] : add(y,multiply(x,X0)) = multiply(x_plus_y,add(X0,y)),
inference(demodulation,[status(thm)],[c_54574,c_303]) ).
tcf(c_54601,plain,
! [X0: $i] : add(y,multiply(x,X0)) = multiply(x_plus_y,add(y,X0)),
inference(superposition,[status(thm)],[c_303,c_54598]) ).
tcf(c_54645,plain,
! [X0: $i] : add(x,multiply(y,X0)) = multiply(x_plus_y,add(x,X0)),
inference(superposition,[status(thm)],[c_116,c_314]) ).
tcf(c_54648,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_125,c_314]) ).
tcf(c_54704,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(multiplicative_identity,X1),X0),
inference(superposition,[status(thm)],[c_126,c_316]) ).
tcf(c_54708,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),inverse(X0)) = add(additive_identity,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_147,c_316]) ).
tcf(c_54779,plain,
! [X0: $i,X1: $i] : add(X0,multiply(multiplicative_identity,X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_126,c_318]) ).
tcf(c_54784,plain,
! [X0: $i] : add(additive_identity,multiply(iPr_def_10,X0)) = multiply(iPr_def_10,add(x_plus_y,X0)),
inference(superposition,[status(thm)],[c_54547,c_318]) ).
tcf(c_55638,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),X1) = add(multiply(additive_identity,X0),X1),
inference(demodulation,[status(thm)],[c_54583,c_301,c_54576]) ).
tcf(c_55759,plain,
! [X0: $i,X1: $i] : add(inverse(X0),multiply(X0,X1)) = add(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c_54578,c_126,c_303,c_54779]) ).
tcf(c_55762,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X1,X0),
inference(superposition,[status(thm)],[c_98,c_55759]) ).
tcf(c_55763,plain,
! [X0: $i] : add(iPr_def_10,multiply(x_plus_y,X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_54535,c_55759]) ).
tcf(c_55857,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = add(X1,X0),
inference(superposition,[status(thm)],[c_301,c_55762]) ).
tcf(c_55858,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(multiplicative_identity,X0),
inference(superposition,[status(thm)],[c_127,c_55762]) ).
tcf(c_55859,plain,
! [X0: $i] : add(inverse(inverse(X0)),X0) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_147,c_55762]) ).
tcf(c_55885,plain,
! [X0: $i] : add(multiplicative_identity,X0) = multiplicative_identity,
inference(light_normalisation,[status(thm)],[c_55858,c_145]) ).
tcf(c_55886,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(light_normalisation,[status(thm)],[c_55859,c_98,c_125]) ).
tcf(c_55968,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(X0,X1)),
inference(superposition,[status(thm)],[c_55886,c_314]) ).
tcf(c_55970,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(add(X0,X1),X0),
inference(superposition,[status(thm)],[c_55886,c_314]) ).
tcf(c_56526,plain,
add(inverse(x),y) = add(y,x_inverse_times_y_inverse),
inference(superposition,[status(thm)],[c_117,c_55857]) ).
tcf(c_56569,plain,
add(y,inverse(x)) = add(y,x_inverse_times_y_inverse),
inference(demodulation,[status(thm)],[c_56526,c_303]) ).
tcf(c_56653,plain,
add(x,multiply(y,additive_identity)) = multiply(x_plus_y,x),
inference(superposition,[status(thm)],[c_125,c_54645]) ).
tcf(c_56729,plain,
add(x,multiply(additive_identity,y)) = multiply(x,x_plus_y),
inference(demodulation,[status(thm)],[c_56653,c_301]) ).
tcf(c_56757,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_303,c_54648]) ).
tcf(c_57485,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_54704,c_126,c_55885]) ).
tcf(c_57506,plain,
add(inverse(y),x_inverse_times_y_inverse) = inverse(y),
inference(superposition,[status(thm)],[c_117,c_57485]) ).
tcf(c_57507,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_301,c_57485]) ).
tcf(c_57523,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,multiply(X1,multiply(X2,X0))) = multiply(add(X0,X1),X0),
inference(superposition,[status(thm)],[c_57485,c_314]) ).
tcf(c_57525,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_57485,c_124]) ).
tcf(c_57540,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,multiply(X1,multiply(X2,X0))) = X0,
inference(light_normalisation,[status(thm)],[c_57523,c_57485,c_55970]) ).
tcf(c_57551,plain,
! [X0: $i,X1: $i] : add(multiply(additive_identity,X0),X1) = add(additive_identity,X1),
inference(demodulation,[status(thm)],[c_55638,c_57525]) ).
tcf(c_57552,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(additive_identity,X0),
inference(demodulation,[status(thm)],[c_54576,c_57551]) ).
tcf(c_57553,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_57552,c_124,c_56757]) ).
tcf(c_57630,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(superposition,[status(thm)],[c_57525,c_301]) ).
tcf(c_57639,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_54648,c_57630]) ).
tcf(c_57641,plain,
add(x,additive_identity) = multiply(x,x_plus_y),
inference(demodulation,[status(thm)],[c_56729,c_57630]) ).
tcf(c_57642,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = X0,
inference(light_normalisation,[status(thm)],[c_57639,c_125,c_55968]) ).
tcf(c_57688,plain,
add(x_inverse_times_y_inverse,inverse(y)) = inverse(y),
inference(demodulation,[status(thm)],[c_57506,c_303]) ).
tcf(c_57854,plain,
multiply(y,x_plus_y) = y,
inference(superposition,[status(thm)],[c_116,c_57553]) ).
tcf(c_58080,plain,
multiply(x,x_plus_y) = x,
inference(demodulation,[status(thm)],[c_57641,c_125]) ).
tcf(c_58086,plain,
add(x_plus_y,x) = x_plus_y,
inference(superposition,[status(thm)],[c_58080,c_57485]) ).
tcf(c_58100,plain,
add(x,x_plus_y) = x_plus_y,
inference(demodulation,[status(thm)],[c_58086,c_303]) ).
tcf(c_58157,plain,
multiply(x_inverse_times_y_inverse,inverse(y)) = x_inverse_times_y_inverse,
inference(superposition,[status(thm)],[c_57688,c_57642]) ).
tcf(c_58167,plain,
! [X0: $i,X1: $i] : add(add(inverse(X0),X1),X0) = add(X0,inverse(X0)),
inference(superposition,[status(thm)],[c_57642,c_55762]) ).
tcf(c_58172,plain,
! [X0: $i,X1: $i] : add(add(inverse(X0),X1),X0) = multiplicative_identity,
inference(light_normalisation,[status(thm)],[c_58167,c_145]) ).
tcf(c_58412,plain,
! [X0: $i,X1: $i] : add(X0,add(inverse(X0),X1)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_58172,c_303]) ).
tcf(c_58426,plain,
! [X0: $i,X1: $i] : add(inverse(X0),add(X0,X1)) = multiplicative_identity,
inference(superposition,[status(thm)],[c_98,c_58412]) ).
tcf(c_58544,plain,
! [X0: $i,X1: $i] : add(inverse(X0),add(X1,X0)) = multiplicative_identity,
inference(superposition,[status(thm)],[c_55762,c_58426]) ).
tcf(c_58557,plain,
add(inverse(x),x_plus_y) = multiplicative_identity,
inference(superposition,[status(thm)],[c_58100,c_58426]) ).
tcf(c_58649,plain,
add(x_plus_y,inverse(x)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_58557,c_303]) ).
tcf(c_58975,plain,
! [X0: $i,X1: $i] : add(inverse(multiply(X0,X1)),X0) = multiplicative_identity,
inference(superposition,[status(thm)],[c_57507,c_58544]) ).
tcf(c_59171,plain,
! [X0: $i,X1: $i] : add(X0,inverse(multiply(X0,X1))) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_58975,c_303]) ).
tcf(c_59174,plain,
add(inverse(x),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(superposition,[status(thm)],[c_117,c_59171]) ).
tcf(c_59175,plain,
! [X0: $i,X1: $i] : add(X0,inverse(multiply(X1,X0))) = multiplicative_identity,
inference(superposition,[status(thm)],[c_301,c_59171]) ).
tcf(c_60445,plain,
add(inverse(y),inverse(x_inverse_times_y_inverse)) = multiplicative_identity,
inference(superposition,[status(thm)],[c_58157,c_59175]) ).
tcf(c_60590,plain,
! [X0: $i] : add(x_plus_y,multiply(X0,y)) = x_plus_y,
inference(superposition,[status(thm)],[c_57854,c_57540]) ).
tcf(c_60737,plain,
! [X0: $i] : add(x_plus_y,multiply(y,X0)) = x_plus_y,
inference(superposition,[status(thm)],[c_301,c_60590]) ).
tcf(c_64695,plain,
! [X0: $i] : multiply(iPr_def_10,add(x_plus_y,X0)) = multiply(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_54784,c_124]) ).
tcf(c_64717,plain,
multiply(iPr_def_10,inverse(x)) = multiply(iPr_def_10,multiplicative_identity),
inference(superposition,[status(thm)],[c_58649,c_64695]) ).
tcf(c_64724,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(y,X0)) = multiply(iPr_def_10,x_plus_y),
inference(superposition,[status(thm)],[c_60737,c_64695]) ).
tcf(c_64757,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(y,X0)) = additive_identity,
inference(light_normalisation,[status(thm)],[c_64724,c_54547]) ).
tcf(c_65022,plain,
multiply(iPr_def_10,y) = additive_identity,
inference(superposition,[status(thm)],[c_57553,c_64757]) ).
tcf(c_65134,plain,
! [X0: $i] : add(additive_identity,multiply(iPr_def_10,X0)) = multiply(iPr_def_10,add(y,X0)),
inference(superposition,[status(thm)],[c_65022,c_318]) ).
tcf(c_65404,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),add(X0,X1)) = multiply(X1,inverse(X0)),
inference(demodulation,[status(thm)],[c_54708,c_124,c_301]) ).
tcf(c_65406,plain,
! [X0: $i,X1: $i] : multiply(X0,add(inverse(X0),X1)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_98,c_65404]) ).
tcf(c_65842,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X1),X0) = multiply(X0,inverse(X0)),
inference(superposition,[status(thm)],[c_57507,c_65406]) ).
tcf(c_65859,plain,
multiply(inverse(x_inverse_times_y_inverse),y) = multiply(y,multiplicative_identity),
inference(superposition,[status(thm)],[c_60445,c_65406]) ).
tcf(c_65860,plain,
multiply(inverse(x_inverse_times_y_inverse),x) = multiply(x,multiplicative_identity),
inference(superposition,[status(thm)],[c_59174,c_65406]) ).
tcf(c_65935,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(X0),X1),X0) = additive_identity,
inference(light_normalisation,[status(thm)],[c_65842,c_147]) ).
tcf(c_66032,plain,
multiply(y,inverse(x_inverse_times_y_inverse)) = y,
inference(demodulation,[status(thm)],[c_65859,c_127,c_301]) ).
tcf(c_66046,plain,
add(inverse(x_inverse_times_y_inverse),y) = inverse(x_inverse_times_y_inverse),
inference(superposition,[status(thm)],[c_66032,c_57485]) ).
tcf(c_66127,plain,
multiply(x,inverse(x_inverse_times_y_inverse)) = x,
inference(demodulation,[status(thm)],[c_65860,c_127,c_301]) ).
tcf(c_66283,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = additive_identity,
inference(demodulation,[status(thm)],[c_65935,c_301]) ).
tcf(c_66301,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(X0))) = additive_identity,
inference(superposition,[status(thm)],[c_65406,c_66283]) ).
tcf(c_66358,plain,
! [X0: $i] : add(multiply(inverse(x_plus_y),X0),iPr_def_10) = add(iPr_def_10,additive_identity),
inference(superposition,[status(thm)],[c_66283,c_55763]) ).
tcf(c_66367,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),iPr_def_10) = add(iPr_def_10,additive_identity),
inference(light_normalisation,[status(thm)],[c_66358,c_54535]) ).
tcf(c_66460,plain,
add(y,inverse(x_inverse_times_y_inverse)) = inverse(x_inverse_times_y_inverse),
inference(demodulation,[status(thm)],[c_66046,c_303]) ).
tcf(c_66473,plain,
add(y,multiply(x,inverse(x_inverse_times_y_inverse))) = multiply(x_plus_y,inverse(x_inverse_times_y_inverse)),
inference(superposition,[status(thm)],[c_66460,c_54601]) ).
tcf(c_66474,plain,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = add(y,x),
inference(light_normalisation,[status(thm)],[c_66473,c_66127]) ).
tcf(c_67117,plain,
multiply(iPr_def_10,inverse(x)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_64717,c_127]) ).
tcf(c_67128,plain,
! [X0: $i] : multiply(iPr_def_10,add(X0,inverse(x))) = add(multiply(iPr_def_10,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_67117,c_318]) ).
tcf(c_67140,plain,
! [X0: $i] : multiply(iPr_def_10,add(X0,inverse(x))) = add(iPr_def_10,additive_identity),
inference(light_normalisation,[status(thm)],[c_67128,c_66367]) ).
tcf(c_67694,plain,
multiply(x_plus_y,inverse(x_inverse_times_y_inverse)) = x_plus_y,
inference(demodulation,[status(thm)],[c_66474,c_116,c_303]) ).
tcf(c_67713,plain,
multiply(x_inverse_times_y_inverse,x_plus_y) = additive_identity,
inference(superposition,[status(thm)],[c_67694,c_66301]) ).
tcf(c_67731,plain,
multiply(x_plus_y,x_inverse_times_y_inverse) = additive_identity,
inference(demodulation,[status(thm)],[c_67713,c_301]) ).
tcf(c_67755,plain,
add(x_inverse_times_y_inverse,iPr_def_10) = add(iPr_def_10,additive_identity),
inference(superposition,[status(thm)],[c_67731,c_55763]) ).
tcf(c_67946,plain,
add(iPr_def_10,x_inverse_times_y_inverse) = iPr_def_10,
inference(demodulation,[status(thm)],[c_67755,c_125,c_303]) ).
tcf(c_67957,plain,
multiply(x_inverse_times_y_inverse,iPr_def_10) = x_inverse_times_y_inverse,
inference(superposition,[status(thm)],[c_67946,c_57553]) ).
tcf(c_68025,plain,
multiply(iPr_def_10,x_inverse_times_y_inverse) = x_inverse_times_y_inverse,
inference(demodulation,[status(thm)],[c_67957,c_301]) ).
tcf(c_105934,plain,
! [X0: $i] : multiply(iPr_def_10,add(X0,inverse(x))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_67140,c_125]) ).
tcf(c_105945,plain,
multiply(iPr_def_10,add(y,x_inverse_times_y_inverse)) = iPr_def_10,
inference(superposition,[status(thm)],[c_56569,c_105934]) ).
tcf(c_106050,plain,
x_inverse_times_y_inverse = iPr_def_10,
inference(demodulation,[status(thm)],[c_105945,c_124,c_65134,c_68025]) ).
tcf(c_106188,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_382,c_106050]) ).
tcf(c_106189,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_106188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO014-3 : TPTP v9.3.1. Bugfixed v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 06:33:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 83.30/14.39 % SZS status Started for theBenchmark.p
% 83.30/14.39 ERROR - "ProverProcess:heur/330959:296.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Failure("Clause.get_demod_eqs: not a demod/lightnorm conclusion ( multiply(multiplicative_identity,X0) != additive_identity | multiply(multiplicative_identity,X1) != additive_identity | X0 = X1 )")
% 83.30/14.39 Fatal error: exception Failure("Clause.get_demod_eqs: not a demod/lightnorm conclusion ( multiply(multiplicative_identity,X0) != additive_identity | multiply(multiplicative_identity,X1) != additive_identity | X0 = X1 )")
% 83.30/14.39 ERROR - cmd was: ulimit -v 4023281; ./res/iproveropt --abstr_ref "[]" --abstr_ref_af_restrict_to_split_sk false --abstr_ref_prep false --abstr_ref_sig_restrict funpre --abstr_ref_under "[]" --abstr_ref_until_sat false --add_important_lit false --bc_imp_inh "[conj_cone]" --brand_transform false --clause_weak_htbl true --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 2 --comb_sup_mult 0 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground true --eq_ax_congr_red true --extra_neg_conj none --gc_record_bc_elim false --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_sos_phase true --inst_sos_sth_lit_sel "[+prop;+non_prol_conj_symb;-eq;+ground;-num_var]" --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --large_theory_mode true --lt_threshold 2000 --min_unsat_core false --non_eq_to_eq false --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sem_filter_out false --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessed_out false --preprocessed_stats false --preprocessing_flag true --prolific_symb_bound 256 --prop_impl_unit "[]" --prop_impl_unit_size 0 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_orphan_elimination true --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300. --res_to_prop_solver active --reset_solvers false --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --soft_assumptions false --soft_lemma_size 3 --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[BwDemod;BwUnitSubsAndRes]" --sup_full_fw "[FwDemodLightNormLoopTriv;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes]" --sup_full_triv "[PropSubs]" --sup_fun_splitting false --sup_immed_bw_immed "[BwUnitSubsAndRes]" --sup_immed_bw_main "[BwUnitSubsAndRes]" --sup_immed_fw_immed "[ACNormalisation;FwDemodLightNormLoopTriv;FwUnitSubsAndRes]" --sup_immed_fw_main "[FwUnitSubsAndRes]" --sup_immed_triv "[]" --sup_indices_passive "[LightNormIndex;UnitSubsumptionIndex]" --sup_input_bw "[BwDemod;BwUnitSubsAndRes;BwSubsumption;BwSubsumptionRes]" --sup_input_fw "[ACNormalisation;FwDemodLightNormLoopTriv;FwUnitSubsAndRes;FwSubsumption;FwSubsumptionRes]" --sup_input_triv "[Unflattening]" --sup_iter_deepening 2 --sup_passive_queue_type priority_queues --sup_passive_queues "[[-conj_dist;-num_symb];[+age;-num_symb];[+score;-num_symb]]" --sup_passive_queues_freq "[8;4;4]" --sup_prop_simpl_given true --sup_prop_simpl_new true --sup_restarts_mult 2 --sup_score sim_d_gen --sup_share_max_num_cl 500 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering invfreq --sup_to_prop_solver passive --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --tptp_safe_out true --out_options none --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 98.67" --time_out_real 296.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_flj16mq3/0oco5jic 2>> /export/starexec/sandbox2/tmp/iprover_out_flj16mq3/0oco5jic_error
% 83.30/14.39 % SZS status Unsatisfiable for theBenchmark.p
% 83.30/14.39
% 83.30/14.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 83.30/14.39
% 83.30/14.39 % ------ iProver source info
% 83.30/14.39
% 83.30/14.39 % git: date: 2026-07-19 20:42:38 +0200
% 83.30/14.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 83.30/14.39 % git: non_committed_changes: false
% 83.30/14.39
% 83.30/14.39 % ------ Parsing...% successful
% 83.30/14.39
% 83.30/14.39
% 83.30/14.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 83.30/14.39
% 83.30/14.39 % ------ Preprocessing... sup_sim: 18 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 83.30/14.39
% 83.30/14.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 83.30/14.39
% 83.30/14.39 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 83.30/14.39 % ------ Proving...
% 83.30/14.39 % ------ Problem Properties
% 83.30/14.39
% 83.30/14.39 %
% 83.30/14.39 % clauses 18
% 83.30/14.39 % conjectures 1
% 83.30/14.39 % EPR 1
% 83.30/14.39 % Horn 18
% 83.30/14.39 % unary 17
% 83.30/14.39 % binary 0
% 83.30/14.39 % lits 22
% 83.30/14.39 % lits eq 22
% 83.30/14.39 % fd_pure 0
% 83.30/14.39 % fd_pseudo 0
% 83.30/14.39 % fd_cond 0
% 83.30/14.39 % fd_pseudo_cond 1
% 83.30/14.39 % AC symbols 0
% 83.30/14.39
% 83.30/14.39 % ------ Schedule dynamic 5 is on
% 83.30/14.39
% 83.30/14.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 83.30/14.39
% 83.30/14.39
% 83.30/14.39 % ------
% 83.30/14.39 % Current options:
% 83.30/14.39 % ------
% 83.30/14.39
% 83.30/14.39
% 83.30/14.39 %
% 83.30/14.39
% 83.30/14.39 % ------ Proving...
% 83.30/14.39 % Proof_search_loop: time out after: 1516 full_loop iterations
% 83.30/14.39
% 83.30/14.39 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 83.30/14.39
% 83.30/14.39
% 83.30/14.39 % ------
% 83.30/14.39 % Current options:
% 83.30/14.39 % ------
% 83.30/14.39
% 83.30/14.39
% 83.30/14.39 %
% 83.30/14.39
% 83.30/14.39 % ------ Proving...
% 83.30/14.39 %
% 83.30/14.39
% 83.30/14.39 % SZS status Unsatisfiable for theBenchmark.p
% 83.30/14.39
% 83.30/14.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 83.30/14.40
%------------------------------------------------------------------------------