%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% 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 01:34:45 PM UTC 2026
% Result : Unsatisfiable 3.66s 1.37s
% Output : CNFRefutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 136 ( 136 unt; 0 def)
% Number of atoms : 348 ( 135 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 287 ( 0 sgn 287 !; 0 ?; 279 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f6,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f7,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),
inference(definition_unfolding,[],[f5,f2,f2,f2,f2]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),double_divide(identity,identity)) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i] : double_divide(X0,double_divide(X0,identity)) = identity,
inference(cnf_transformation,[],[f6]) ).
tcf(c_56,negated_conjecture,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(cnf_transformation,[],[f7]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(X0,X1),double_divide(double_divide(X2,double_divide(double_divide(X1,double_divide(X3,X2)),double_divide(X3,identity))),identity))),double_divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))) = double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_67,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,identity))),double_divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_90,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(X0,identity),X0),
inference(superposition,[status(thm)],[c_67,c_65]) ).
tcf(c_92,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(double_divide(X1,identity),double_divide(X0,identity))) = double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(X0,double_divide(double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity))),double_divide(X4,X0)),double_divide(X4,identity))) = double_divide(double_divide(identity,X2),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_54,c_65]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(X0,double_divide(X1,double_divide(double_divide(X2,double_divide(X3,X1)),double_divide(X3,identity)))),double_divide(double_divide(identity,double_divide(X2,double_divide(identity,identity))),identity))) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_65,c_65]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))) = double_divide(X3,double_divide(double_divide(X1,double_divide(X4,X3)),double_divide(X4,identity))),
inference(superposition,[status(thm)],[c_65,c_65]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X1,X0)),double_divide(X1,identity))) = identity,
inference(superposition,[status(thm)],[c_65,c_67]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(double_divide(identity,identity),double_divide(X2,X1)),double_divide(X2,identity))),identity))),double_divide(identity,identity)) = double_divide(X3,double_divide(double_divide(X0,double_divide(X4,X3)),double_divide(X4,identity))),
inference(superposition,[status(thm)],[c_54,c_63]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(double_divide(identity,identity),double_divide(X2,X1)),double_divide(X2,identity))),identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(X0,identity),double_divide(double_divide(double_divide(identity,identity),double_divide(X1,double_divide(double_divide(identity,double_divide(X2,X1)),double_divide(X2,identity)))),identity))),double_divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_65,c_63]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(X0,X1),double_divide(double_divide(X2,double_divide(double_divide(X1,double_divide(X3,X2)),double_divide(X3,identity))),identity))) = double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_63,c_54]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(X0,double_divide(double_divide(identity,identity),double_divide(double_divide(X1,X2),double_divide(double_divide(X3,double_divide(double_divide(X2,double_divide(X4,X3)),double_divide(X4,identity))),identity)))),double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),identity))),double_divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_63,c_63]) ).
tcf(c_152,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),X0) = identity,
inference(demodulation,[status(thm)],[c_90,c_67]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_119]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(double_divide(X1,identity),double_divide(X0,identity))) = double_divide(identity,double_divide(identity,double_divide(X1,identity))),
inference(demodulation,[status(thm)],[c_95,c_92]) ).
tcf(c_163,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_102,c_156]) ).
tcf(c_165,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(double_divide(identity,double_divide(X0,identity)))) = X0,
inference(demodulation,[status(thm)],[c_129,c_120,c_152,c_158,c_163]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(X0,X1),double_divide(iPr_def_10(X1),identity))) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(demodulation,[status(thm)],[c_147,c_92,c_156]) ).
tcf(c_168,plain,
! [X0: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(X0,double_divide(iPr_def_10(double_divide(identity,identity)),identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(demodulation,[status(thm)],[c_127,c_156]) ).
tcf(c_172,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_122,c_156,c_168]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(X0,iPr_def_10(X1)),double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),identity))) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_112,c_92,c_156,c_172]) ).
tcf(c_177,plain,
! [X0: $i] : double_divide(iPr_def_10(X0),double_divide(identity,identity)) = X0,
inference(demodulation,[status(thm)],[c_151,c_156,c_166,c_172,c_175]) ).
tcf(c_318,plain,
! [X0: $i] : iPr_def_10(double_divide(identity,double_divide(X0,identity))) = double_divide(X0,double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_165,c_177]) ).
tcf(c_319,plain,
double_divide(identity,identity) = iPr_def_10(identity),
inference(superposition,[status(thm)],[c_55,c_172]) ).
tcf(c_323,plain,
! [X0: $i] : iPr_def_10(double_divide(X0,double_divide(identity,identity))) = X0,
inference(demodulation,[status(thm)],[c_165,c_318]) ).
tcf(c_325,plain,
! [X0: $i] : double_divide(iPr_def_10(X0),iPr_def_10(identity)) = X0,
inference(demodulation,[status(thm)],[c_177,c_319]) ).
tcf(c_342,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(iPr_def_10(X0))) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_163,c_323]) ).
tcf(c_363,plain,
double_divide(identity,identity) = identity,
inference(superposition,[status(thm)],[c_55,c_120]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X0,identity)),double_divide(double_divide(identity,identity),double_divide(X1,identity))) = identity,
inference(superposition,[status(thm)],[c_120,c_120]) ).
tcf(c_389,plain,
iPr_def_10(identity) = identity,
inference(demodulation,[status(thm)],[c_120,c_156]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X0,identity)),double_divide(iPr_def_10(identity),double_divide(X1,identity))) = identity,
inference(light_normalisation,[status(thm)],[c_377,c_319]) ).
tcf(c_439,plain,
! [X0: $i] : double_divide(iPr_def_10(X0),identity) = X0,
inference(demodulation,[status(thm)],[c_325,c_389]) ).
tcf(c_446,plain,
! [X0: $i] : iPr_def_10(double_divide(X0,identity)) = X0,
inference(demodulation,[status(thm)],[c_323,c_363]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,double_divide(X1,identity))) = iPr_def_10(double_divide(double_divide(X1,X0),identity)),
inference(superposition,[status(thm)],[c_152,c_156]) ).
tcf(c_478,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,identity)),double_divide(double_divide(X1,iPr_def_10(X0)),double_divide(identity,identity))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_172,c_156]) ).
tcf(c_479,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(X1,identity),double_divide(double_divide(X0,identity),identity))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_152,c_156]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,identity),double_divide(iPr_def_10(X1),double_divide(double_divide(X1,double_divide(X0,X2)),identity))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_156,c_156]) ).
tcf(c_484,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(X1,identity)))) = double_divide(iPr_def_10(X0),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_156,c_163]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,double_divide(X1,identity))) = double_divide(X1,X0),
inference(demodulation,[status(thm)],[c_474,c_446]) ).
tcf(c_729,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,identity)),double_divide(double_divide(X1,iPr_def_10(X0)),identity)) = iPr_def_10(X1),
inference(light_normalisation,[status(thm)],[c_478,c_363]) ).
tcf(c_730,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(X1,identity)))) = X0,
inference(light_normalisation,[status(thm)],[c_484,c_363,c_439]) ).
tcf(c_733,plain,
! [X0: $i] : double_divide(X0,identity) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_172,c_728]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),iPr_def_10(X2))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_156,c_733]) ).
tcf(c_738,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,iPr_def_10(double_divide(b3,a3))),identity),
inference(demodulation,[status(thm)],[c_56,c_733]) ).
tcf(c_739,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_439,c_733]) ).
tcf(c_740,plain,
iPr_def_10(double_divide(iPr_def_10(double_divide(c3,b3)),a3)) != iPr_def_10(double_divide(c3,iPr_def_10(double_divide(b3,a3)))),
inference(demodulation,[status(thm)],[c_738,c_733]) ).
tcf(c_777,plain,
! [X0: $i] : double_divide(identity,X0) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_342,c_739]) ).
tcf(c_837,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,iPr_def_10(X1))) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_733,c_728]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,X1)) = double_divide(iPr_def_10(X1),X0),
inference(superposition,[status(thm)],[c_439,c_728]) ).
tcf(c_872,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(double_divide(double_divide(X0,X1),X1))) = X0,
inference(superposition,[status(thm)],[c_439,c_730]) ).
tcf(c_890,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,X1),iPr_def_10(iPr_def_10(X1)))) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_439,c_734]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,double_divide(X0,identity)),double_divide(double_divide(X1,double_divide(X0,X2)),iPr_def_10(X2))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_728,c_734]) ).
tcf(c_898,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(iPr_def_10(X2),X0)),X2)) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_739,c_734]) ).
tcf(c_925,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,double_divide(double_divide(X0,identity),identity))) = iPr_def_10(iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_439,c_479]) ).
tcf(c_961,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(X1,iPr_def_10(iPr_def_10(X0))),identity)) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_439,c_729]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(X1,X2)),identity),double_divide(iPr_def_10(X2),iPr_def_10(iPr_def_10(X0)))) = iPr_def_10(double_divide(X1,identity)),
inference(superposition,[status(thm)],[c_483,c_734]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,iPr_def_10(X0)),double_divide(X1,identity)),double_divide(iPr_def_10(identity),double_divide(double_divide(double_divide(X0,identity),double_divide(double_divide(X1,identity),identity)),identity))) = identity,
inference(superposition,[status(thm)],[c_479,c_435]) ).
tcf(c_1066,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(X0,X1),double_divide(iPr_def_10(double_divide(identity,double_divide(X0,identity))),identity))) = double_divide(identity,double_divide(identity,double_divide(X1,identity))),
inference(superposition,[status(thm)],[c_728,c_166]) ).
tcf(c_1089,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_872,c_739]) ).
tcf(c_1101,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),X1) = double_divide(X1,iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_839,c_777]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(demodulation,[status(thm)],[c_837,c_739,c_777]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(iPr_def_10(iPr_def_10(X0)),double_divide(X1,X0))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_890,c_1102]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(X0,double_divide(X1,X0))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_1153,c_739,c_777]) ).
tcf(c_1180,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = iPr_def_10(iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_925,c_1089]) ).
tcf(c_1181,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_1180,c_739]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,double_divide(X2,double_divide(iPr_def_10(X1),X0)))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_898,c_1102]) ).
tcf(c_1214,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X1,iPr_def_10(iPr_def_10(X0))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_961,c_1102]) ).
tcf(c_1215,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),iPr_def_10(double_divide(X1,X0))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_1214,c_739,c_777]) ).
tcf(c_1360,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(iPr_def_10(X1),double_divide(X2,double_divide(X0,X1)))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_893,c_1102,c_1181]) ).
tcf(c_1416,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),iPr_def_10(iPr_def_10(X1))),double_divide(identity,double_divide(X1,double_divide(X2,X0)))) = iPr_def_10(double_divide(X2,identity)),
inference(demodulation,[status(thm)],[c_1012,c_1102]) ).
tcf(c_1417,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),X1),iPr_def_10(double_divide(X1,double_divide(X2,X0)))) = X2,
inference(demodulation,[status(thm)],[c_1416,c_733,c_739,c_777]) ).
tcf(c_1499,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(X0,X1),double_divide(identity,iPr_def_10(X0)))) = double_divide(identity,X1),
inference(demodulation,[status(thm)],[c_1066,c_1101,c_1154,c_1181]) ).
tcf(c_1500,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(identity),double_divide(double_divide(X0,X1),X0)) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_1499,c_739,c_777]) ).
tcf(c_1501,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,X1),X0)) = iPr_def_10(X1),
inference(light_normalisation,[status(thm)],[c_1500,c_389]) ).
tcf(c_1502,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(double_divide(X0,X1),X0)) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_1501,c_777]) ).
tcf(c_1534,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,iPr_def_10(X0)),double_divide(X1,identity)),double_divide(iPr_def_10(identity),double_divide(identity,double_divide(double_divide(X0,identity),X1)))) = identity,
inference(demodulation,[status(thm)],[c_1032,c_1089,c_1102]) ).
tcf(c_1535,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),double_divide(iPr_def_10(identity),iPr_def_10(double_divide(iPr_def_10(X0),X1)))) = identity,
inference(demodulation,[status(thm)],[c_1534,c_733,c_739,c_777]) ).
tcf(c_1536,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),double_divide(identity,iPr_def_10(double_divide(iPr_def_10(X0),X1)))) = identity,
inference(light_normalisation,[status(thm)],[c_1535,c_389]) ).
tcf(c_1537,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),double_divide(iPr_def_10(X0),X1)) = identity,
inference(demodulation,[status(thm)],[c_1536,c_739,c_777]) ).
tcf(c_1623,plain,
iPr_def_10(double_divide(a3,iPr_def_10(double_divide(c3,b3)))) != iPr_def_10(double_divide(c3,iPr_def_10(double_divide(b3,a3)))),
inference(demodulation,[status(thm)],[c_740,c_1101]) ).
tcf(c_1624,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(iPr_def_10(X1),double_divide(X2,double_divide(X1,X0)))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_734,c_1101]) ).
tcf(c_1625,plain,
iPr_def_10(double_divide(a3,iPr_def_10(double_divide(b3,c3)))) != iPr_def_10(double_divide(c3,iPr_def_10(double_divide(a3,b3)))),
inference(demodulation,[status(thm)],[c_1623,c_1102]) ).
tcf(c_1719,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_1181,c_1181]) ).
tcf(c_1780,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),iPr_def_10(X1)) = iPr_def_10(double_divide(X0,X1)),
inference(superposition,[status(thm)],[c_1502,c_1215]) ).
tcf(c_1969,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,identity)) = iPr_def_10(double_divide(X1,iPr_def_10(X0))),
inference(superposition,[status(thm)],[c_1537,c_1184]) ).
tcf(c_1977,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),double_divide(X1,double_divide(X2,X0))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_1181,c_1184]) ).
tcf(c_1999,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(iPr_def_10(iPr_def_10(X1)),X2)),double_divide(X1,iPr_def_10(X0))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_1184,c_1184]) ).
tcf(c_2002,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1719,c_1102]) ).
tcf(c_2046,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(X0,iPr_def_10(X1))) = double_divide(X1,iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_1969,c_733]) ).
tcf(c_2174,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),double_divide(X1,double_divide(X0,X2))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_1999,c_739,c_1102]) ).
tcf(c_2244,plain,
iPr_def_10(double_divide(c3,iPr_def_10(double_divide(a3,b3)))) != double_divide(double_divide(b3,c3),iPr_def_10(a3)),
inference(demodulation,[status(thm)],[c_1625,c_2046]) ).
tcf(c_2245,plain,
double_divide(double_divide(a3,b3),iPr_def_10(c3)) != double_divide(double_divide(b3,c3),iPr_def_10(a3)),
inference(demodulation,[status(thm)],[c_2244,c_2046]) ).
tcf(c_2246,plain,
double_divide(iPr_def_10(a3),double_divide(b3,c3)) != double_divide(iPr_def_10(c3),double_divide(a3,b3)),
inference(demodulation,[status(thm)],[c_2245,c_1102]) ).
tcf(c_3132,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,double_divide(iPr_def_10(X0),X2))) = double_divide(X2,iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_1184,c_2002]) ).
tcf(c_3167,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(X0,iPr_def_10(X1))) = double_divide(iPr_def_10(X0),X1),
inference(superposition,[status(thm)],[c_739,c_1780]) ).
tcf(c_3236,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(iPr_def_10(X1),double_divide(double_divide(X0,X1),X2))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_1102,c_1360]) ).
tcf(c_3254,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(iPr_def_10(double_divide(X1,X0)),double_divide(X2,X1))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_1181,c_1360]) ).
tcf(c_3259,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(iPr_def_10(double_divide(X0,X1)),double_divide(X2,X1))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_2002,c_1360]) ).
tcf(c_3315,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(double_divide(X0,double_divide(X1,X2))),X1) = double_divide(iPr_def_10(X2),X0),
inference(superposition,[status(thm)],[c_1417,c_1181]) ).
tcf(c_3365,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(X1,double_divide(X0,X2))) = double_divide(X2,iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_1624,c_2002]) ).
tcf(c_3462,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,iPr_def_10(double_divide(X1,double_divide(X0,X2)))) = double_divide(iPr_def_10(X2),X1),
inference(demodulation,[status(thm)],[c_3315,c_1102]) ).
tcf(c_3652,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X1),X2)) = iPr_def_10(double_divide(X0,double_divide(X1,iPr_def_10(X2)))),
inference(superposition,[status(thm)],[c_3167,c_1780]) ).
tcf(c_3698,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(X1,X2)),iPr_def_10(X1)) = double_divide(X2,iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_1977,c_1181]) ).
tcf(c_3760,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),iPr_def_10(X2)) = double_divide(X1,double_divide(X2,X0)),
inference(superposition,[status(thm)],[c_1181,c_3132]) ).
tcf(c_3798,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(iPr_def_10(X1),X2)) = iPr_def_10(double_divide(X2,double_divide(X0,X1))),
inference(superposition,[status(thm)],[c_1181,c_3236]) ).
tcf(c_3827,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),iPr_def_10(X1)),iPr_def_10(X2)) = iPr_def_10(double_divide(double_divide(X1,X0),X2)),
inference(superposition,[status(thm)],[c_3236,c_2174]) ).
tcf(c_3896,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),iPr_def_10(X2)) = double_divide(double_divide(X1,X2),iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_3254,c_3132]) ).
tcf(c_3942,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(iPr_def_10(double_divide(X0,double_divide(iPr_def_10(X1),X2))),identity)) = iPr_def_10(double_divide(X1,iPr_def_10(X2))),
inference(superposition,[status(thm)],[c_1537,c_3259]) ).
tcf(c_4012,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),iPr_def_10(double_divide(X0,X2))) = double_divide(X2,iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_3698,c_3896]) ).
tcf(c_4040,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,iPr_def_10(X2))) = iPr_def_10(double_divide(double_divide(X0,X2),X1)),
inference(demodulation,[status(thm)],[c_3827,c_3760]) ).
tcf(c_4064,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(double_divide(double_divide(X0,X1),X2))) = iPr_def_10(iPr_def_10(double_divide(X2,double_divide(X1,X0)))),
inference(demodulation,[status(thm)],[c_3652,c_3798,c_4040]) ).
tcf(c_4065,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),X2) = double_divide(X2,double_divide(X1,X0)),
inference(demodulation,[status(thm)],[c_4064,c_739]) ).
tcf(c_4089,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(double_divide(X0,double_divide(identity,double_divide(double_divide(X0,X1),X2))))) = iPr_def_10(double_divide(X1,iPr_def_10(X2))),
inference(demodulation,[status(thm)],[c_3942,c_3798,c_4040,c_4065]) ).
tcf(c_4090,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,iPr_def_10(double_divide(double_divide(X0,X1),X2))) = double_divide(iPr_def_10(X1),X2),
inference(demodulation,[status(thm)],[c_4089,c_739,c_777,c_3167]) ).
tcf(c_4402,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),iPr_def_10(X2)) = double_divide(iPr_def_10(X1),double_divide(X2,X0)),
inference(superposition,[status(thm)],[c_1181,c_3365]) ).
tcf(c_4485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,iPr_def_10(double_divide(double_divide(X0,X1),double_divide(X2,X3)))) = double_divide(iPr_def_10(X1),double_divide(X3,X2)),
inference(superposition,[status(thm)],[c_4065,c_3462]) ).
tcf(c_4620,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(X1,X2)) = double_divide(iPr_def_10(X0),double_divide(X2,X1)),
inference(demodulation,[status(thm)],[c_4485,c_4090]) ).
tcf(c_4978,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,iPr_def_10(double_divide(X1,X2))) = double_divide(X2,iPr_def_10(double_divide(X1,X0))),
inference(superposition,[status(thm)],[c_2002,c_4012]) ).
tcf(c_4999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,X1),iPr_def_10(double_divide(double_divide(X2,X3),X0))) = double_divide(double_divide(X3,X2),iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_4065,c_4012]) ).
tcf(c_5118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,iPr_def_10(double_divide(double_divide(X1,X2),double_divide(X0,X3)))) = double_divide(double_divide(X2,X1),iPr_def_10(X3)),
inference(demodulation,[status(thm)],[c_4999,c_4978]) ).
tcf(c_5119,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(X1,X2)) = double_divide(iPr_def_10(X1),double_divide(X0,X2)),
inference(demodulation,[status(thm)],[c_5118,c_3462,c_4402]) ).
tcf(c_5303,plain,
double_divide(iPr_def_10(a3),double_divide(b3,c3)) != double_divide(iPr_def_10(a3),double_divide(c3,b3)),
inference(demodulation,[status(thm)],[c_2246,c_5119]) ).
tcf(c_5304,plain,
$false,
inference(ground_joinability,[status(thm)],[c_5303,c_4620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP575-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Wed Sep 23 15:09:54 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.45 Running UEQ theorem proving
% 0.11/0.45 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
% 0.11/0.48
% 0.11/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.48
% 0.11/0.48 % Detected problem language: tptp
% 0.20/0.49 % Proving...
% 3.66/1.37 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.66/1.37 % SZS status Started for theBenchmark.p
% 3.66/1.37 % SZS status Unsatisfiable for theBenchmark.p
% 3.66/1.37
% 3.66/1.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.66/1.37
% 3.66/1.37 % ------ iProver source info
% 3.66/1.37
% 3.66/1.37 % git: date: 2026-07-19 20:42:38 +0200
% 3.66/1.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.66/1.37 % git: non_committed_changes: false
% 3.66/1.37
% 3.66/1.37 % ------ Parsing...% successful
% 3.66/1.37
% 3.66/1.37
% 3.66/1.37 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.66/1.37 % ------ Proving...
% 3.66/1.37 % ------ Problem Properties
% 3.66/1.37
% 3.66/1.37 %
% 3.66/1.37 % clauses 3
% 3.66/1.37 % conjectures 1
% 3.66/1.37 % EPR 0
% 3.66/1.37 % Horn 3
% 3.66/1.37 % unary 3
% 3.66/1.37 % binary 0
% 3.66/1.37 % lits 3
% 3.66/1.37 % lits eq 3
% 3.66/1.37 % fd_pure 0
% 3.66/1.37 % fd_pseudo 0
% 3.66/1.37 % fd_cond 0
% 3.66/1.37 % fd_pseudo_cond 0
% 3.66/1.37 % AC symbols 0
% 3.66/1.37
% 3.66/1.37 % ------ Input Options Time Limit: Unbounded
% 3.66/1.37
% 3.66/1.37
% 3.66/1.37 % ------
% 3.66/1.37 % Current options:
% 3.66/1.37 % ------
% 3.66/1.37
% 3.66/1.37
% 3.66/1.37 %
% 3.66/1.37
% 3.66/1.37 % ------ Proving...
% 3.66/1.37 %
% 3.66/1.37
% 3.66/1.37 % SZS status Unsatisfiable for theBenchmark.p
% 3.66/1.37
% 3.66/1.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.66/1.37
% 3.66/1.37
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