%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP567-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 01:34:44 PM UTC 2026
% Result : Unsatisfiable 3.22s 6.41s
% Output : CNFRefutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 99 ( 99 unt; 0 def)
% Number of atoms : 245 ( 98 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 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 : 200 ( 0 sgn 200 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(identity,identity)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,axiom,
! [X0] : inverse(X0) = double_divide(X0,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f4,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/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(X0,X2)),double_divide(identity,X2))),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(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),double_divide(identity,double_divide(identity,identity)))),double_divide(identity,identity)) = X3,
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(X0,X2)),double_divide(identity,X2))) = 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(X0,double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,double_divide(identity,identity))),identity)),double_divide(identity,identity)) = X1,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_69,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),double_divide(identity,identity)) = X0,
inference(demodulation,[status(thm)],[c_67,c_55]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),identity)),double_divide(identity,identity)) = X3,
inference(demodulation,[status(thm)],[c_63,c_55]) ).
tcf(c_77,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(X0,identity),
inference(superposition,[status(thm)],[c_69,c_54]) ).
tcf(c_93,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),double_divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_55,c_68]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(X1,double_divide(X0,double_divide(identity,identity))),X1),
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,double_divide(identity,identity))),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_115,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(X1,X3)),double_divide(identity,X3))),double_divide(X0,X4)),double_divide(identity,X4))) = double_divide(double_divide(identity,X2),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_54,c_65]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(identity,X1))) = double_divide(double_divide(identity,identity),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_55,c_65]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(double_divide(X1,identity),double_divide(X0,X2)),double_divide(identity,X2))) = double_divide(double_divide(identity,X1),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_69,c_65]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(double_divide(identity,identity),double_divide(X0,X1)),double_divide(identity,X1))),double_divide(X2,identity)),double_divide(identity,identity)) = double_divide(X3,double_divide(double_divide(X2,double_divide(X3,X4)),double_divide(identity,X4))),
inference(superposition,[status(thm)],[c_54,c_70]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(double_divide(identity,identity),double_divide(X0,X1)),double_divide(identity,X1))),double_divide(X2,identity)),double_divide(identity,identity)) = double_divide(X3,double_divide(double_divide(X2,double_divide(X3,double_divide(identity,identity))),identity)),
inference(superposition,[status(thm)],[c_68,c_70]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : double_divide(double_divide(double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),identity)),double_divide(double_divide(X4,X3),double_divide(identity,double_divide(identity,identity)))),double_divide(double_divide(X5,X4),identity)),double_divide(identity,identity)) = X5,
inference(superposition,[status(thm)],[c_70,c_70]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),identity)),double_divide(double_divide(X4,X3),double_divide(identity,double_divide(identity,identity)))) = double_divide(double_divide(identity,double_divide(X4,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_70,c_65]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(double_divide(X3,X1),identity)) = double_divide(double_divide(identity,double_divide(X3,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_70,c_54]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(identity,double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(X3,X1),X3),
inference(superposition,[status(thm)],[c_70,c_65]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))) = double_divide(double_divide(double_divide(X3,X1),X3),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_70,c_54]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : double_divide(X0,double_divide(double_divide(double_divide(double_divide(X1,double_divide(double_divide(X2,double_divide(X1,X3)),double_divide(identity,X3))),double_divide(double_divide(X4,X2),identity)),double_divide(X0,X5)),double_divide(identity,X5))) = double_divide(double_divide(identity,X4),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_70,c_65]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(identity,X1))) = identity,
inference(demodulation,[status(thm)],[c_116,c_69]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(identity,X2))) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_172]) ).
tcf(c_183,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = iPr_def_10(double_divide(X0,identity)),
inference(demodulation,[status(thm)],[c_120,c_182]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(X1,double_divide(identity,identity))),X0) = double_divide(X1,identity),
inference(demodulation,[status(thm)],[c_101,c_77]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,double_divide(identity,identity))),identity)) = double_divide(X1,identity),
inference(demodulation,[status(thm)],[c_112,c_77]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = double_divide(iPr_def_10(X1),identity),
inference(demodulation,[status(thm)],[c_171,c_77,c_182]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),double_divide(double_divide(X1,X0),identity)) = double_divide(X1,identity),
inference(demodulation,[status(thm)],[c_169,c_77,c_182]) ).
tcf(c_205,plain,
! [X0: $i] : iPr_def_10(double_divide(X0,identity)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_115,c_182,c_183]) ).
tcf(c_208,plain,
! [X0: $i] : double_divide(double_divide(iPr_def_10(iPr_def_10(identity)),double_divide(X0,identity)),double_divide(identity,identity)) = double_divide(X0,identity),
inference(demodulation,[status(thm)],[c_162,c_182,c_186,c_205]) ).
tcf(c_209,plain,
! [X0: $i] : double_divide(X0,identity) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_158,c_182,c_205,c_208]) ).
tcf(c_215,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(iPr_def_10(X0),iPr_def_10(double_divide(X1,X0)))) = iPr_def_10(iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_173,c_182,c_183,c_205,c_209]) ).
tcf(c_221,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),iPr_def_10(double_divide(X1,X0))),double_divide(double_divide(X2,X1),double_divide(identity,iPr_def_10(identity)))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_166,c_77,c_182,c_209]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(X0),iPr_def_10(double_divide(X1,X0))),iPr_def_10(identity)) = X1,
inference(demodulation,[status(thm)],[c_165,c_182,c_209,c_221]) ).
tcf(c_232,plain,
! [X0: $i] : double_divide(iPr_def_10(X0),double_divide(identity,identity)) = X0,
inference(demodulation,[status(thm)],[c_54,c_182]) ).
tcf(c_233,plain,
! [X0: $i] : double_divide(iPr_def_10(X0),iPr_def_10(identity)) = X0,
inference(demodulation,[status(thm)],[c_232,c_209]) ).
tcf(c_237,plain,
! [X0: $i] : double_divide(X0,iPr_def_10(X0)) = identity,
inference(demodulation,[status(thm)],[c_55,c_209]) ).
tcf(c_238,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_209]) ).
tcf(c_239,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_238,c_209]) ).
tcf(c_447,plain,
! [X0: $i] : double_divide(iPr_def_10(X0),identity) = iPr_def_10(double_divide(identity,X0)),
inference(superposition,[status(thm)],[c_193,c_209]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),iPr_def_10(double_divide(X1,X0))) = double_divide(X1,identity),
inference(superposition,[status(thm)],[c_209,c_201]) ).
tcf(c_458,plain,
! [X0: $i] : double_divide(iPr_def_10(iPr_def_10(identity)),double_divide(X0,identity)) = double_divide(iPr_def_10(X0),identity),
inference(superposition,[status(thm)],[c_233,c_201]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(double_divide(double_divide(X0,X1),identity)),identity) = double_divide(double_divide(X0,identity),iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_201,c_193]) ).
tcf(c_478,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(iPr_def_10(X0)),double_divide(double_divide(X1,double_divide(iPr_def_10(X2),iPr_def_10(double_divide(X0,X2)))),identity)) = double_divide(X1,identity),
inference(superposition,[status(thm)],[c_215,c_201]) ).
tcf(c_487,plain,
! [X0: $i] : double_divide(double_divide(iPr_def_10(double_divide(identity,identity)),iPr_def_10(iPr_def_10(double_divide(X0,identity)))),iPr_def_10(identity)) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_183,c_222]) ).
tcf(c_502,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(double_divide(iPr_def_10(X0),identity),identity)),double_divide(identity,identity)) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_193,c_93]) ).
tcf(c_529,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(identity,X1))),iPr_def_10(identity)),iPr_def_10(identity)) = X0,
inference(superposition,[status(thm)],[c_178,c_222]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(identity,X1))),identity) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_178,c_193]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(X1,double_divide(identity,identity))),identity) = double_divide(iPr_def_10(X0),double_divide(double_divide(X1,identity),identity)),
inference(superposition,[status(thm)],[c_184,c_201]) ).
tcf(c_589,plain,
! [X0: $i] : iPr_def_10(double_divide(identity,X0)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_447,c_209]) ).
tcf(c_604,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_452,c_209]) ).
tcf(c_629,plain,
! [X0: $i] : double_divide(iPr_def_10(iPr_def_10(identity)),iPr_def_10(X0)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_458,c_209]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(iPr_def_10(double_divide(X0,X1)))) = double_divide(iPr_def_10(X0),iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_461,c_209]) ).
tcf(c_663,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(identity,X1)))) = double_divide(identity,X0),
inference(demodulation,[status(thm)],[c_533,c_209]) ).
tcf(c_667,plain,
! [X0: $i] : double_divide(identity,X0) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_502,c_93]) ).
tcf(c_670,plain,
! [X0: $i] : double_divide(double_divide(iPr_def_10(X0),iPr_def_10(identity)),iPr_def_10(identity)) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_487,c_589,c_629,c_653,c_667]) ).
tcf(c_671,plain,
! [X0: $i] : double_divide(X0,iPr_def_10(identity)) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_670,c_233]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),double_divide(double_divide(X1,identity),identity)) = double_divide(double_divide(X0,iPr_def_10(X1)),identity),
inference(demodulation,[status(thm)],[c_551,c_667,c_671]) ).
tcf(c_693,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),iPr_def_10(iPr_def_10(X1))) = iPr_def_10(double_divide(X0,iPr_def_10(X1))),
inference(demodulation,[status(thm)],[c_692,c_209]) ).
tcf(c_702,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_529,c_663,c_667,c_671]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(X1,iPr_def_10(X0)),identity)) = double_divide(X1,identity),
inference(demodulation,[status(thm)],[c_478,c_604,c_702]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i] : double_divide(X0,iPr_def_10(double_divide(X1,iPr_def_10(X0)))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_744,c_209]) ).
tcf(c_813,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(iPr_def_10(double_divide(X0,X1)),identity)) = iPr_def_10(double_divide(identity,X1)),
inference(superposition,[status(thm)],[c_193,c_182]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(iPr_def_10(X1),identity),double_divide(identity,X2))) = iPr_def_10(double_divide(double_divide(X0,X2),X1)),
inference(superposition,[status(thm)],[c_193,c_182]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(X1,identity),double_divide(identity,iPr_def_10(X0)))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_237,c_182]) ).
tcf(c_1786,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(iPr_def_10(X1),X0)) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_823,c_209,c_667,c_702]) ).
tcf(c_1787,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_813,c_209,c_589,c_702]) ).
tcf(c_1790,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_816,c_209,c_667,c_702]) ).
tcf(c_1811,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,iPr_def_10(X1)),iPr_def_10(X1))) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_667,c_182]) ).
tcf(c_1821,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(double_divide(X0,iPr_def_10(X1)),iPr_def_10(X1))) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_1811,c_667]) ).
tcf(c_1850,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(identity,X2)) = double_divide(X1,iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_182,c_1787]) ).
tcf(c_1863,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(double_divide(X0,X1)),identity) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_1787,c_193]) ).
tcf(c_1883,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),X1) = double_divide(X1,iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_1786,c_1787]) ).
tcf(c_1992,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(X0,iPr_def_10(X1))) = double_divide(X1,iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_1821,c_745]) ).
tcf(c_2028,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_702,c_693]) ).
tcf(c_2032,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_702,c_693]) ).
tcf(c_2124,plain,
! [X0: $i,X1: $i] : double_divide(identity,iPr_def_10(double_divide(X0,X1))) = double_divide(X1,X0),
inference(demodulation,[status(thm)],[c_1863,c_1883]) ).
tcf(c_2125,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(demodulation,[status(thm)],[c_2124,c_667,c_702]) ).
tcf(c_2251,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X2,X0))) = double_divide(X2,iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_1850,c_2125]) ).
tcf(c_2252,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(X1,double_divide(X2,X0))) = double_divide(X2,iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_2251,c_667]) ).
tcf(c_2353,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_239,c_1883]) ).
tcf(c_2355,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_2353,c_1992,c_2125]) ).
tcf(c_2448,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(iPr_def_10(X0),X1)) = double_divide(iPr_def_10(X1),X0),
inference(superposition,[status(thm)],[c_2125,c_2028]) ).
tcf(c_2623,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(X1,iPr_def_10(X2))) = double_divide(X2,double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_2252,c_1787]) ).
tcf(c_2729,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(double_divide(iPr_def_10(X0),X1),X2)) = double_divide(X1,double_divide(X2,X0)),
inference(demodulation,[status(thm)],[c_2623,c_1790]) ).
tcf(c_3708,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(iPr_def_10(double_divide(X0,X1)),X2)) = double_divide(iPr_def_10(X1),double_divide(X2,X0)),
inference(superposition,[status(thm)],[c_2032,c_2729]) ).
tcf(c_3782,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(X2,X0)),
inference(demodulation,[status(thm)],[c_3708,c_2448]) ).
tcf(c_3989,plain,
double_divide(iPr_def_10(a3),double_divide(b3,c3)) != double_divide(iPr_def_10(a3),double_divide(b3,c3)),
inference(demodulation,[status(thm)],[c_2355,c_3782]) ).
tcf(c_3991,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_3989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP567-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.59 % Computer : n017.cluster.edu
% 0.10/5.59 % Model : x86_64 x86_64
% 0.10/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.59 % Memory : 8046.5625MB
% 0.10/5.59 % OS : Linux 6.8.0-71-generic
% 0.10/5.59 % CPULimit : 300
% 0.10/5.59 % WCLimit : 300
% 0.10/5.59 % DateTime : Wed Sep 23 15:01:40 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.63 Running UEQ theorem proving
% 0.14/5.63 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.64
% 0.14/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.64
% 0.14/5.64 % Detected problem language: tptp
% 0.14/5.65 % Proving...
% 3.22/6.41 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 3.22/6.41 % SZS status Started for theBenchmark.p
% 3.22/6.41 % SZS status Unsatisfiable for theBenchmark.p
% 3.22/6.41
% 3.22/6.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.22/6.41
% 3.22/6.41 % ------ iProver source info
% 3.22/6.41
% 3.22/6.41 % git: date: 2026-07-19 20:42:38 +0200
% 3.22/6.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.22/6.41 % git: non_committed_changes: false
% 3.22/6.41
% 3.22/6.41 % ------ Parsing...% successful
% 3.22/6.41
% 3.22/6.41
% 3.22/6.41 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.22/6.41 % ------ Proving...
% 3.22/6.41 % ------ Problem Properties
% 3.22/6.41
% 3.22/6.41 %
% 3.22/6.41 % clauses 3
% 3.22/6.41 % conjectures 1
% 3.22/6.41 % EPR 0
% 3.22/6.41 % Horn 3
% 3.22/6.41 % unary 3
% 3.22/6.41 % binary 0
% 3.22/6.41 % lits 3
% 3.22/6.41 % lits eq 3
% 3.22/6.41 % fd_pure 0
% 3.22/6.41 % fd_pseudo 0
% 3.22/6.41 % fd_cond 0
% 3.22/6.41 % fd_pseudo_cond 0
% 3.22/6.41 % AC symbols 0
% 3.22/6.41
% 3.22/6.41 % ------ Input Options Time Limit: Unbounded
% 3.22/6.41
% 3.22/6.41
% 3.22/6.41 % ------
% 3.22/6.41 % Current options:
% 3.22/6.41 % ------
% 3.22/6.41
% 3.22/6.41
% 3.22/6.41 %
% 3.22/6.41
% 3.22/6.41 % ------ Proving...
% 3.22/6.41 %
% 3.22/6.41
% 3.22/6.41 % SZS status Unsatisfiable for theBenchmark.p
% 3.22/6.41
% 3.22/6.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.22/6.41
% 3.22/6.41
%------------------------------------------------------------------------------