%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : BOO007-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 7.23s 1.70s
% Output : CNFRefutation 7.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 150 ( 150 unt; 4 def)
% Number of atoms : 274 ( 149 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 165 ( 0 sgn 165 !; 0 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
fof(f3,axiom,
! [X2,X0,X1] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
fof(f5,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
fof(f6,axiom,
! [X0] : multiply(X0,multiplicative_identity) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
fof(f7,axiom,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
fof(f8,plain,
! [X0] : multiplicative_identity = add(X0,inverse(X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
fof(f10,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[],[f5]) ).
tcf(c_63,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[],[f8]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[],[f10]) ).
tcf(c_66,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_97,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_98,definition,
iPr_def_11 = multiply(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_99,definition,
iPr_def_12 = multiply(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_100,definition,
iPr_def_13 = multiply(a,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_101,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_66,c_99,c_100,c_97,c_98]) ).
tcf(c_102,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = additive_identity,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_103,plain,
! [X0: $i] : add(X0,inverse(X0)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_104,plain,
! [X0: $i] : multiply(X0,multiplicative_identity) = X0,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_105,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(demodulation,[status(thm)],[c_61]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_167,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(superposition,[status(thm)],[c_108,c_104]) ).
tcf(c_169,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(superposition,[status(thm)],[c_105,c_109]) ).
tcf(c_175,plain,
! [X0: $i] : multiply(b,add(c,X0)) = add(iPr_def_12,multiply(b,X0)),
inference(superposition,[status(thm)],[c_99,c_106]) ).
tcf(c_176,plain,
! [X0: $i] : multiply(a,add(b,X0)) = add(iPr_def_10,multiply(a,X0)),
inference(superposition,[status(thm)],[c_97,c_106]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : multiply(X0,add(inverse(X0),X1)) = add(additive_identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_102,c_106]) ).
tcf(c_182,plain,
! [X0: $i] : multiply(a,add(iPr_def_12,X0)) = add(iPr_def_13,multiply(a,X0)),
inference(superposition,[status(thm)],[c_100,c_106]) ).
tcf(c_184,plain,
! [X0: $i] : multiply(a,add(X0,b)) = add(multiply(a,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_97,c_106]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),X0) = multiply(X0,add(X1,multiplicative_identity)),
inference(superposition,[status(thm)],[c_104,c_106]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(superposition,[status(thm)],[c_102,c_106]) ).
tcf(c_189,plain,
! [X0: $i] : multiply(iPr_def_10,add(X0,c)) = add(multiply(iPr_def_10,X0),iPr_def_11),
inference(superposition,[status(thm)],[c_98,c_106]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(additive_identity,X1)),
inference(superposition,[status(thm)],[c_105,c_107]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(superposition,[status(thm)],[c_103,c_107]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,additive_identity)),
inference(superposition,[status(thm)],[c_105,c_107]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = multiply(add(X0,X1),multiplicative_identity),
inference(superposition,[status(thm)],[c_103,c_107]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(add(X0,X1),add(X0,X2)) = add(X0,multiply(X2,X1)),
inference(superposition,[status(thm)],[c_107,c_108]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X0,X1)) = add(X0,multiply(X1,additive_identity)),
inference(demodulation,[status(thm)],[c_235,c_108]) ).
tcf(c_259,plain,
! [X0: $i] : multiply(iPr_def_10,add(X0,c)) = add(iPr_def_11,multiply(iPr_def_10,X0)),
inference(demodulation,[status(thm)],[c_189,c_109]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(X0,add(X1,multiplicative_identity)),
inference(demodulation,[status(thm)],[c_187,c_109]) ).
tcf(c_261,plain,
! [X0: $i] : multiply(a,add(X0,b)) = add(iPr_def_10,multiply(a,X0)),
inference(demodulation,[status(thm)],[c_184,c_109]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,inverse(X0))) = add(X0,X1),
inference(demodulation,[status(thm)],[c_236,c_104]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(demodulation,[status(thm)],[c_231,c_167]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_188,c_105]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_180,c_169]) ).
tcf(c_329,plain,
! [X0: $i] : add(X0,X0) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_102,c_263]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,multiply(X1,multiply(X2,inverse(X0)))) = multiply(add(X0,X1),add(X0,X2)),
inference(superposition,[status(thm)],[c_263,c_107]) ).
tcf(c_338,plain,
! [X0: $i] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_104,c_264]) ).
tcf(c_339,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_102,c_264]) ).
tcf(c_347,plain,
! [X0: $i] : multiply(X0,X0) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_103,c_265]) ).
tcf(c_357,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_105,c_266]) ).
tcf(c_358,plain,
! [X0: $i] : multiply(X0,inverse(inverse(X0))) = multiply(X0,multiplicative_identity),
inference(superposition,[status(thm)],[c_103,c_266]) ).
tcf(c_379,plain,
add(iPr_def_10,multiply(a,inverse(b))) = multiply(a,multiplicative_identity),
inference(superposition,[status(thm)],[c_103,c_176]) ).
tcf(c_458,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,multiply(X1,additive_identity)),
inference(superposition,[status(thm)],[c_109,c_257]) ).
tcf(c_463,plain,
! [X0: $i] : add(additive_identity,multiply(X0,additive_identity)) = multiply(additive_identity,X0),
inference(superposition,[status(thm)],[c_169,c_257]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] : add(X0,add(inverse(X0),multiply(X1,additive_identity))) = add(X0,add(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_257,c_264]) ).
tcf(c_502,plain,
add(iPr_def_10,multiply(additive_identity,c)) = add(iPr_def_11,multiply(iPr_def_10,iPr_def_10)),
inference(superposition,[status(thm)],[c_259,c_230]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(X0,add(X1,multiplicative_identity)),
inference(superposition,[status(thm)],[c_108,c_260]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),add(X1,multiplicative_identity))) = multiply(X0,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_260,c_266]) ).
tcf(c_539,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(add(X1,multiplicative_identity),X0),
inference(superposition,[status(thm)],[c_260,c_108]) ).
tcf(c_604,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_347,c_104]) ).
tcf(c_605,plain,
! [X0: $i] : add(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_329,c_105]) ).
tcf(c_607,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(demodulation,[status(thm)],[c_357,c_102]) ).
tcf(c_612,plain,
! [X0: $i] : add(X0,multiplicative_identity) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_338,c_103]) ).
tcf(c_623,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(demodulation,[status(thm)],[c_463,c_605,c_607]) ).
tcf(c_632,plain,
! [X0: $i] : multiply(X0,inverse(inverse(X0))) = X0,
inference(demodulation,[status(thm)],[c_358,c_104]) ).
tcf(c_633,plain,
! [X0: $i] : add(X0,inverse(inverse(X0))) = X0,
inference(demodulation,[status(thm)],[c_339,c_105]) ).
tcf(c_650,plain,
add(iPr_def_10,multiply(a,inverse(b))) = a,
inference(demodulation,[status(thm)],[c_379,c_104]) ).
tcf(c_659,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = multiply(multiplicative_identity,X0),
inference(demodulation,[status(thm)],[c_539,c_612]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_659,c_167]) ).
tcf(c_664,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = multiply(X0,multiplicative_identity),
inference(demodulation,[status(thm)],[c_505,c_612]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i] : add(X0,multiply(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_664,c_104]) ).
tcf(c_666,plain,
add(iPr_def_10,additive_identity) = add(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_502,c_604,c_623]) ).
tcf(c_667,plain,
add(iPr_def_10,iPr_def_11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_666,c_109,c_105]) ).
tcf(c_679,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = add(X0,additive_identity),
inference(demodulation,[status(thm)],[c_458,c_607]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i] : multiply(X0,add(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_679,c_105]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X0,multiply(inverse(X0),multiplicative_identity)),
inference(demodulation,[status(thm)],[c_534,c_612]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = additive_identity,
inference(demodulation,[status(thm)],[c_713,c_104,c_102]) ).
tcf(c_725,plain,
! [X0: $i,X1: $i] : add(X0,add(inverse(X0),X1)) = add(X0,add(inverse(X0),additive_identity)),
inference(demodulation,[status(thm)],[c_474,c_607]) ).
tcf(c_726,plain,
! [X0: $i,X1: $i] : add(X0,add(inverse(X0),X1)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_725,c_105,c_103]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,multiply(X1,multiply(X2,inverse(X0)))) = add(X0,multiply(X2,X1)),
inference(demodulation,[status(thm)],[c_332,c_238]) ).
tcf(c_1289,plain,
add(b,iPr_def_12) = b,
inference(superposition,[status(thm)],[c_99,c_660]) ).
tcf(c_1335,plain,
add(c,iPr_def_12) = c,
inference(superposition,[status(thm)],[c_99,c_665]) ).
tcf(c_1336,plain,
add(b,iPr_def_10) = b,
inference(superposition,[status(thm)],[c_97,c_665]) ).
tcf(c_1342,plain,
add(c,iPr_def_11) = c,
inference(superposition,[status(thm)],[c_98,c_665]) ).
tcf(c_1343,plain,
add(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_100,c_665]) ).
tcf(c_1451,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),X0) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_633,c_680]) ).
tcf(c_1459,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(add(X1,X0),X2)) = add(X0,multiply(X0,X2)),
inference(superposition,[status(thm)],[c_680,c_106]) ).
tcf(c_1475,plain,
add(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1343,c_109]) ).
tcf(c_1476,plain,
add(iPr_def_11,c) = c,
inference(demodulation,[status(thm)],[c_1342,c_109]) ).
tcf(c_1477,plain,
add(iPr_def_10,b) = b,
inference(demodulation,[status(thm)],[c_1336,c_109]) ).
tcf(c_1478,plain,
add(iPr_def_12,c) = c,
inference(demodulation,[status(thm)],[c_1335,c_109]) ).
tcf(c_1479,plain,
add(iPr_def_12,b) = b,
inference(demodulation,[status(thm)],[c_1289,c_109]) ).
tcf(c_1482,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_1451,c_108,c_632]) ).
tcf(c_1515,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(add(X1,X0),X2)) = X0,
inference(demodulation,[status(thm)],[c_1459,c_660]) ).
tcf(c_1599,plain,
add(iPr_def_10,multiply(a,iPr_def_12)) = multiply(a,b),
inference(superposition,[status(thm)],[c_1479,c_261]) ).
tcf(c_1983,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,add(add(X0,X1),X2)) = X0,
inference(superposition,[status(thm)],[c_109,c_1515]) ).
tcf(c_2006,plain,
! [X0: $i] : multiply(iPr_def_11,add(iPr_def_10,X0)) = iPr_def_11,
inference(superposition,[status(thm)],[c_667,c_1515]) ).
tcf(c_2029,plain,
add(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1599,c_97,c_100]) ).
tcf(c_2491,plain,
! [X0: $i] : multiply(iPr_def_13,add(iPr_def_12,X0)) = iPr_def_13,
inference(superposition,[status(thm)],[c_1475,c_1983]) ).
tcf(c_2515,plain,
multiply(iPr_def_13,iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_2029,c_680]) ).
tcf(c_2537,plain,
multiply(iPr_def_10,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_2515,c_108]) ).
tcf(c_2615,plain,
multiply(iPr_def_11,a) = iPr_def_11,
inference(superposition,[status(thm)],[c_650,c_2006]) ).
tcf(c_2621,plain,
multiply(iPr_def_11,b) = iPr_def_11,
inference(superposition,[status(thm)],[c_1477,c_2006]) ).
tcf(c_3042,plain,
add(b,iPr_def_11) = b,
inference(superposition,[status(thm)],[c_2621,c_665]) ).
tcf(c_3079,plain,
multiply(iPr_def_13,c) = iPr_def_13,
inference(superposition,[status(thm)],[c_1478,c_2491]) ).
tcf(c_3238,plain,
add(iPr_def_11,b) = b,
inference(demodulation,[status(thm)],[c_3042,c_109]) ).
tcf(c_3304,plain,
add(c,iPr_def_13) = c,
inference(superposition,[status(thm)],[c_3079,c_665]) ).
tcf(c_3599,plain,
add(iPr_def_13,c) = c,
inference(demodulation,[status(thm)],[c_3304,c_109]) ).
tcf(c_3773,plain,
add(iPr_def_11,multiply(iPr_def_10,iPr_def_13)) = multiply(iPr_def_10,c),
inference(superposition,[status(thm)],[c_3599,c_259]) ).
tcf(c_3965,plain,
add(iPr_def_13,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3773,c_109,c_98,c_2537]) ).
tcf(c_4083,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = additive_identity,
inference(superposition,[status(thm)],[c_1482,c_714]) ).
tcf(c_4112,plain,
! [X0: $i,X1: $i] : add(inverse(X0),add(X0,X1)) = multiplicative_identity,
inference(superposition,[status(thm)],[c_1482,c_726]) ).
tcf(c_4819,plain,
add(inverse(iPr_def_13),iPr_def_12) = multiplicative_identity,
inference(superposition,[status(thm)],[c_1475,c_4112]) ).
tcf(c_4820,plain,
add(inverse(iPr_def_11),c) = multiplicative_identity,
inference(superposition,[status(thm)],[c_1476,c_4112]) ).
tcf(c_4828,plain,
add(inverse(iPr_def_11),b) = multiplicative_identity,
inference(superposition,[status(thm)],[c_3238,c_4112]) ).
tcf(c_4996,plain,
add(b,inverse(iPr_def_11)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_4828,c_109]) ).
tcf(c_5000,plain,
add(c,inverse(iPr_def_11)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_4820,c_109]) ).
tcf(c_5001,plain,
add(iPr_def_12,inverse(iPr_def_13)) = multiplicative_identity,
inference(demodulation,[status(thm)],[c_4819,c_109]) ).
tcf(c_5773,plain,
! [X0: $i] : add(b,multiply(inverse(iPr_def_11),X0)) = multiply(multiplicative_identity,add(b,X0)),
inference(superposition,[status(thm)],[c_4996,c_107]) ).
tcf(c_5799,plain,
! [X0: $i] : add(b,multiply(inverse(iPr_def_11),X0)) = add(b,X0),
inference(demodulation,[status(thm)],[c_5773,c_167]) ).
tcf(c_6060,plain,
! [X0: $i] : add(c,multiply(inverse(iPr_def_11),X0)) = multiply(multiplicative_identity,add(c,X0)),
inference(superposition,[status(thm)],[c_5000,c_107]) ).
tcf(c_6086,plain,
! [X0: $i] : add(iPr_def_12,multiply(X0,inverse(iPr_def_13))) = multiply(add(iPr_def_12,X0),multiplicative_identity),
inference(superposition,[status(thm)],[c_5001,c_107]) ).
tcf(c_6124,plain,
! [X0: $i] : add(iPr_def_12,multiply(X0,inverse(iPr_def_13))) = add(iPr_def_12,X0),
inference(demodulation,[status(thm)],[c_6086,c_104]) ).
tcf(c_6127,plain,
! [X0: $i] : add(c,multiply(inverse(iPr_def_11),X0)) = add(c,X0),
inference(demodulation,[status(thm)],[c_6060,c_167]) ).
tcf(c_12071,plain,
! [X0: $i] : add(b,multiply(iPr_def_11,X0)) = add(b,additive_identity),
inference(superposition,[status(thm)],[c_4083,c_5799]) ).
tcf(c_12469,plain,
! [X0: $i] : add(b,multiply(iPr_def_11,X0)) = b,
inference(demodulation,[status(thm)],[c_12071,c_105]) ).
tcf(c_13066,plain,
! [X0: $i] : multiply(multiply(iPr_def_11,X0),b) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_12469,c_680]) ).
tcf(c_13293,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,X0)) = multiply(iPr_def_11,X0),
inference(demodulation,[status(thm)],[c_13066,c_108]) ).
tcf(c_15359,plain,
! [X0: $i] : add(iPr_def_13,multiply(a,multiply(X0,inverse(iPr_def_13)))) = multiply(a,add(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_6124,c_182]) ).
tcf(c_15382,plain,
! [X0: $i] : add(iPr_def_13,multiply(X0,a)) = add(iPr_def_13,multiply(a,X0)),
inference(demodulation,[status(thm)],[c_15359,c_182,c_743]) ).
tcf(c_16250,plain,
! [X0: $i] : add(c,multiply(iPr_def_11,X0)) = add(c,additive_identity),
inference(superposition,[status(thm)],[c_4083,c_6127]) ).
tcf(c_16476,plain,
! [X0: $i] : add(c,multiply(iPr_def_11,X0)) = c,
inference(demodulation,[status(thm)],[c_16250,c_105]) ).
tcf(c_16855,plain,
! [X0: $i] : add(iPr_def_12,multiply(b,multiply(iPr_def_11,X0))) = multiply(b,c),
inference(superposition,[status(thm)],[c_16476,c_175]) ).
tcf(c_16946,plain,
! [X0: $i] : add(iPr_def_12,multiply(iPr_def_11,X0)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_16855,c_99,c_13293]) ).
tcf(c_17369,plain,
add(iPr_def_12,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_16946,c_6124]) ).
tcf(c_17912,plain,
add(iPr_def_13,multiply(a,iPr_def_11)) = multiply(a,iPr_def_12),
inference(superposition,[status(thm)],[c_17369,c_182]) ).
tcf(c_18168,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_17912,c_100,c_2615,c_3965,c_15382]) ).
tcf(c_18169,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_18168,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO007-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 25 06:29:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running UEQ theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 7.23/1.70 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 7.23/1.70 % SZS status Started for theBenchmark.p
% 7.23/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 7.23/1.70
% 7.23/1.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.23/1.70
% 7.23/1.70 % ------ iProver source info
% 7.23/1.70
% 7.23/1.70 % git: date: 2026-07-19 20:42:38 +0200
% 7.23/1.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.23/1.70 % git: non_committed_changes: false
% 7.23/1.70
% 7.23/1.70 % ------ Parsing...% successful
% 7.23/1.70
% 7.23/1.70
% 7.23/1.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.23/1.70
% 7.23/1.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.23/1.70
% 7.23/1.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.23/1.70
% 7.23/1.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.23/1.70 % ------ Proving...
% 7.23/1.70 % ------ Problem Properties
% 7.23/1.70
% 7.23/1.70 %
% 7.23/1.70 % clauses 13
% 7.23/1.70 % conjectures 1
% 7.23/1.70 % EPR 1
% 7.23/1.70 % Horn 13
% 7.23/1.70 % unary 13
% 7.23/1.70 % binary 0
% 7.23/1.70 % lits 13
% 7.23/1.70 % lits eq 13
% 7.23/1.70 % fd_pure 0
% 7.23/1.70 % fd_pseudo 0
% 7.23/1.70 % fd_cond 0
% 7.23/1.70 % fd_pseudo_cond 0
% 7.23/1.70 % AC symbols 0
% 7.23/1.70
% 7.23/1.70 % ------ Input Options Time Limit: Unbounded
% 7.23/1.70
% 7.23/1.70
% 7.23/1.70 % ------
% 7.23/1.70 % Current options:
% 7.23/1.70 % ------
% 7.23/1.70
% 7.23/1.70
% 7.23/1.70 %
% 7.23/1.70
% 7.23/1.70 % ------ Proving...
% 7.23/1.70 %
% 7.23/1.70
% 7.23/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 7.23/1.70
% 7.23/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.23/1.70
% 7.23/1.70
%------------------------------------------------------------------------------