%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP102-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n016.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 01:30:44 PM UTC 2026
% Result : Unsatisfiable 4.43s 1.11s
% Output : CNFRefutation 4.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 126 ( 118 unt; 0 def)
% Number of atoms : 148 ( 147 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 30 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 274 ( 0 sgn 274 !; 0 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),double_divide(X1,identity))),double_divide(identity,identity)) = X2,
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(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f6,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(identity,a2)
| identity != multiply(inverse(a1),a1) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f4,f3]) ).
fof(f8,plain,
( double_divide(double_divide(b4,a4),identity) != double_divide(double_divide(a4,b4),identity)
| 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)
| a2 != double_divide(double_divide(a2,identity),identity)
| identity != double_divide(double_divide(a1,double_divide(a1,identity)),identity) ),
inference(definition_unfolding,[],[f6,f2,f3,f2,f2,f2,f2,f2,f2,f2]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),X2),double_divide(X1,identity))),double_divide(identity,identity)) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i] : double_divide(X0,double_divide(X0,identity)) = identity,
inference(cnf_transformation,[],[f7]) ).
tcf(c_56,negated_conjecture,
( ( double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity) )
| ( double_divide(double_divide(a2,identity),identity) != a2 )
| ( double_divide(double_divide(a1,double_divide(a1,identity)),identity) != identity )
| ( 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,[],[f8]) ).
tcf(c_68,plain,
( ( double_divide(identity,identity) != identity )
| ( double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity) )
| ( double_divide(double_divide(a2,identity),identity) != a2 )
| ( 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(demodulation,[status(thm)],[c_56,c_55]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)) = double_divide(double_divide(X1,X0),identity),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,identity),double_divide(double_divide(identity,X1),double_divide(X0,identity))),double_divide(identity,identity)) = X1,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(double_divide(double_divide(X0,X1),X2),double_divide(X0,identity)),double_divide(X2,double_divide(X1,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(identity,X1)),X2),double_divide(X0,identity)) = double_divide(double_divide(X1,X2),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,identity),X1),double_divide(X0,identity)) = double_divide(double_divide(double_divide(identity,identity),X1),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_54,c_73]) ).
tcf(c_92,plain,
! [X0: $i] : double_divide(double_divide(double_divide(double_divide(identity,X0),identity),identity),double_divide(identity,identity)) = X0,
inference(superposition,[status(thm)],[c_55,c_73]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(double_divide(identity,X0),double_divide(X1,identity)),double_divide(X0,double_divide(double_divide(X1,identity),identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(superposition,[status(thm)],[c_73,c_54]) ).
tcf(c_104,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,X0),identity),
inference(superposition,[status(thm)],[c_55,c_71]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,identity),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X1,identity)),
inference(superposition,[status(thm)],[c_71,c_76]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(double_divide(X0,X1),identity),X2),double_divide(double_divide(X1,double_divide(identity,double_divide(X0,identity))),identity)) = double_divide(double_divide(identity,X2),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_71,c_76]) ).
tcf(c_130,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(X1,X0),double_divide(identity,identity)),double_divide(double_divide(X2,double_divide(identity,X1)),identity))),double_divide(identity,identity)) = double_divide(X2,identity),
inference(superposition,[status(thm)],[c_76,c_54]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,X0),double_divide(double_divide(X0,X1),double_divide(identity,identity))),double_divide(identity,identity)) = X1,
inference(superposition,[status(thm)],[c_76,c_54]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(identity,X1)),double_divide(identity,identity)),double_divide(double_divide(X2,double_divide(identity,X0)),identity)) = double_divide(double_divide(X1,double_divide(X2,identity)),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_76,c_76]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)) = double_divide(double_divide(X1,double_divide(identity,double_divide(identity,X0))),identity),
inference(superposition,[status(thm)],[c_76,c_71]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(identity,double_divide(identity,X1))),identity) = double_divide(double_divide(X0,X1),identity),
inference(demodulation,[status(thm)],[c_135,c_71]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X1,identity)) = double_divide(double_divide(identity,double_divide(identity,X0)),identity),
inference(demodulation,[status(thm)],[c_123,c_104]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(double_divide(double_divide(X0,X1),X1),double_divide(X0,identity)),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(superposition,[status(thm)],[c_55,c_75]) ).
tcf(c_196,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(double_divide(double_divide(X0,X1),X1),double_divide(X0,identity))),identity) = double_divide(identity,identity),
inference(demodulation,[status(thm)],[c_183,c_104]) ).
tcf(c_244,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),identity) = X0,
inference(demodulation,[status(thm)],[c_92,c_136,c_138]) ).
tcf(c_246,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),double_divide(identity,identity)) = X0,
inference(demodulation,[status(thm)],[c_104,c_244]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,X1),identity),double_divide(X1,identity)) = double_divide(identity,X0),
inference(demodulation,[status(thm)],[c_138,c_244]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,X1),X1),double_divide(X0,identity)) = double_divide(identity,identity),
inference(demodulation,[status(thm)],[c_196,c_244]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(identity,X1)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,X1),X0),identity),
inference(superposition,[status(thm)],[c_244,c_71]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(double_divide(double_divide(double_divide(identity,X1),X0),X2),X1)),double_divide(identity,identity)) = X2,
inference(superposition,[status(thm)],[c_244,c_54]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(double_divide(identity,X0),double_divide(identity,X1)),X2),X0) = double_divide(double_divide(X1,X2),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_244,c_76]) ).
tcf(c_267,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),double_divide(identity,identity)) = double_divide(double_divide(identity,X0),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_244,c_76]) ).
tcf(c_269,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(identity,identity)) = X0,
inference(demodulation,[status(thm)],[c_267,c_246]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,identity),X0),double_divide(identity,identity)) = double_divide(double_divide(X1,X0),X1),
inference(superposition,[status(thm)],[c_244,c_91]) ).
tcf(c_291,plain,
! [X0: $i] : double_divide(double_divide(double_divide(X0,identity),identity),double_divide(X0,identity)) = double_divide(identity,double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_244,c_91]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(double_divide(identity,identity),double_divide(identity,X0)),double_divide(identity,identity)),double_divide(double_divide(X1,identity),identity)) = double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_91,c_76]) ).
tcf(c_300,plain,
! [X0: $i] : double_divide(double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)),double_divide(double_divide(X0,identity),identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(X0,identity)),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_91,c_91]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(double_divide(X0,identity),double_divide(identity,X1)),double_divide(X0,identity)),double_divide(double_divide(identity,identity),identity)) = double_divide(double_divide(X1,double_divide(identity,identity)),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_91,c_76]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X1,identity))),double_divide(X0,identity)) = double_divide(double_divide(X1,double_divide(identity,identity)),identity),
inference(superposition,[status(thm)],[c_91,c_71]) ).
tcf(c_315,plain,
double_divide(identity,identity) = identity,
inference(demodulation,[status(thm)],[c_291,c_55,c_250]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = double_divide(double_divide(identity,X1),identity),
inference(demodulation,[status(thm)],[c_284,c_315]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = X1,
inference(demodulation,[status(thm)],[c_316,c_244]) ).
tcf(c_318,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),identity) = double_divide(identity,double_divide(X0,identity)),
inference(demodulation,[status(thm)],[c_311,c_315,c_317]) ).
tcf(c_326,plain,
! [X0: $i] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(demodulation,[status(thm)],[c_307,c_315,c_317,c_318]) ).
tcf(c_327,plain,
! [X0: $i] : double_divide(X0,identity) = double_divide(identity,X0),
inference(demodulation,[status(thm)],[c_300,c_317,c_318,c_326]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(X1,identity))) = double_divide(double_divide(identity,X0),X1),
inference(demodulation,[status(thm)],[c_296,c_315,c_317,c_318,c_326,c_327]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(double_divide(identity,X0),double_divide(X1,identity)),double_divide(X0,X1))) = identity,
inference(demodulation,[status(thm)],[c_95,c_315,c_318,c_326,c_327]) ).
tcf(c_436,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(identity,double_divide(identity,X1)))) = double_divide(identity,double_divide(X0,X1)),
inference(demodulation,[status(thm)],[c_136,c_327]) ).
tcf(c_444,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,X1)),identity) = double_divide(X0,double_divide(identity,double_divide(identity,X1))),
inference(superposition,[status(thm)],[c_436,c_244]) ).
tcf(c_449,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,double_divide(identity,X1))) = double_divide(X0,X1),
inference(demodulation,[status(thm)],[c_444,c_244]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,X1)))) = X1,
inference(demodulation,[status(thm)],[c_131,c_315,c_327]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,X0),double_divide(X1,identity))),identity)) = double_divide(X0,X1),
inference(superposition,[status(thm)],[c_366,c_457]) ).
tcf(c_485,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,X1))) = double_divide(X1,identity),
inference(superposition,[status(thm)],[c_457,c_244]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,X2))))) = double_divide(identity,double_divide(X0,double_divide(identity,X2))),
inference(superposition,[status(thm)],[c_457,c_436]) ).
tcf(c_490,plain,
! [X0: $i] : double_divide(identity,double_divide(double_divide(identity,identity),X0)) = X0,
inference(superposition,[status(thm)],[c_457,c_436]) ).
tcf(c_491,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,X0)) = X0,
inference(demodulation,[status(thm)],[c_490,c_315]) ).
tcf(c_496,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(identity,X0)),X1) = double_divide(X0,X1),
inference(demodulation,[status(thm)],[c_464,c_326,c_328]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(X1,identity))) = double_divide(identity,double_divide(X0,double_divide(identity,X1))),
inference(demodulation,[status(thm)],[c_486,c_485]) ).
tcf(c_503,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(identity,X1))) = double_divide(double_divide(identity,X0),X1),
inference(demodulation,[status(thm)],[c_502,c_328]) ).
tcf(c_542,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(double_divide(identity,double_divide(X1,X0)),double_divide(double_divide(identity,X2),X1)))) = double_divide(X2,identity),
inference(demodulation,[status(thm)],[c_130,c_315,c_327,c_503]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),double_divide(double_divide(identity,identity),double_divide(double_divide(identity,X1),X0)))) = double_divide(X1,identity),
inference(superposition,[status(thm)],[c_55,c_542]) ).
tcf(c_579,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X1,X0)),double_divide(double_divide(identity,X2),X1))) = double_divide(double_divide(X2,identity),identity),
inference(superposition,[status(thm)],[c_542,c_244]) ).
tcf(c_580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(identity,double_divide(X0,double_divide(X1,double_divide(double_divide(identity,double_divide(X2,X1)),double_divide(double_divide(identity,X3),X2))))) = double_divide(identity,double_divide(X0,double_divide(identity,double_divide(X3,identity)))),
inference(superposition,[status(thm)],[c_542,c_436]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X1,X0)),double_divide(double_divide(identity,X2),X1))) = X2,
inference(demodulation,[status(thm)],[c_579,c_318,c_326]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(identity,X1),X0)) = double_divide(X1,identity),
inference(demodulation,[status(thm)],[c_551,c_315,c_326,c_503]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(identity,double_divide(X1,identity)))) = double_divide(identity,double_divide(X0,X1)),
inference(demodulation,[status(thm)],[c_580,c_593]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(X1,identity)) = double_divide(identity,double_divide(X0,X1)),
inference(demodulation,[status(thm)],[c_612,c_503]) ).
tcf(c_665,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,double_divide(X0,X1)),X2),double_divide(identity,double_divide(X1,X0))) = X2,
inference(demodulation,[status(thm)],[c_126,c_269,c_327,c_503,c_613]) ).
tcf(c_667,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,X1)),identity) = double_divide(identity,double_divide(identity,double_divide(X1,X0))),
inference(superposition,[status(thm)],[c_55,c_665]) ).
tcf(c_713,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(X0,X1)),X2)),double_divide(identity,X2))) = double_divide(identity,double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_665,c_457]) ).
tcf(c_717,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(identity,double_divide(X1,X2))),double_divide(identity,identity)) = double_divide(double_divide(identity,X0),double_divide(double_divide(identity,double_divide(X2,X1)),identity)),
inference(superposition,[status(thm)],[c_665,c_76]) ).
tcf(c_722,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(demodulation,[status(thm)],[c_667,c_244,c_491]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(double_divide(identity,X0),double_divide(identity,double_divide(double_divide(identity,double_divide(X1,X2)),X0)))) = double_divide(identity,double_divide(X2,X1)),
inference(demodulation,[status(thm)],[c_713,c_722]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,X1)) = double_divide(identity,double_divide(X1,X0)),
inference(demodulation,[status(thm)],[c_731,c_327,c_496,c_503,c_597]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(identity,double_divide(X1,X2)))) = double_divide(double_divide(identity,identity),double_divide(X0,double_divide(identity,double_divide(X2,X1)))),
inference(demodulation,[status(thm)],[c_717,c_722]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(X1,X2)) = double_divide(double_divide(identity,X0),double_divide(X2,X1)),
inference(demodulation,[status(thm)],[c_741,c_315,c_449,c_503]) ).
tcf(c_847,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),X1)),double_divide(double_divide(identity,X2),X1)) = double_divide(double_divide(identity,X0),X2),
inference(demodulation,[status(thm)],[c_134,c_260,c_315,c_327,c_328,c_503,c_722]) ).
tcf(c_853,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,identity),double_divide(double_divide(identity,X0),double_divide(double_divide(identity,X1),identity))) = double_divide(double_divide(identity,X1),X0),
inference(superposition,[status(thm)],[c_55,c_847]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,X0),X1)) = double_divide(double_divide(identity,X1),X0),
inference(demodulation,[status(thm)],[c_853,c_315,c_503,c_613]) ).
tcf(c_1295,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X1,X0))) = double_divide(identity,X1),
inference(demodulation,[status(thm)],[c_248,c_327,c_722]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,identity),identity),double_divide(identity,double_divide(double_divide(double_divide(identity,identity),X1),double_divide(identity,identity)))) = double_divide(identity,double_divide(double_divide(X0,identity),X1)),
inference(superposition,[status(thm)],[c_91,c_1295]) ).
tcf(c_1317,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,double_divide(X0,X1)),identity),double_divide(identity,X2)) = double_divide(identity,double_divide(double_divide(identity,double_divide(X1,X0)),X2)),
inference(superposition,[status(thm)],[c_665,c_1295]) ).
tcf(c_1332,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,X0),X1),double_divide(double_divide(X2,identity),identity)) = double_divide(double_divide(double_divide(X0,X2),X1),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_1295,c_76]) ).
tcf(c_1349,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,X0),X1),X2) = double_divide(identity,double_divide(double_divide(X0,X2),X1)),
inference(demodulation,[status(thm)],[c_1332,c_315,c_318,c_326,c_722]) ).
tcf(c_1354,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(double_divide(double_divide(X0,X1),double_divide(identity,X2)),identity)) = double_divide(identity,double_divide(double_divide(identity,double_divide(X1,X0)),X2)),
inference(demodulation,[status(thm)],[c_1317,c_1349]) ).
tcf(c_1355,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),double_divide(identity,X2)) = double_divide(double_divide(identity,X2),double_divide(X1,X0)),
inference(demodulation,[status(thm)],[c_1354,c_326,c_893]) ).
tcf(c_1371,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,identity),identity),double_divide(identity,double_divide(identity,double_divide(double_divide(identity,double_divide(identity,identity)),X1)))) = double_divide(identity,double_divide(double_divide(X0,identity),X1)),
inference(demodulation,[status(thm)],[c_1310,c_1349]) ).
tcf(c_1372,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),X1)) = double_divide(X0,double_divide(identity,X1)),
inference(demodulation,[status(thm)],[c_1371,c_318,c_326,c_449,c_496]) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(X1,double_divide(identity,double_divide(double_divide(X1,X2),X0))))) = X2,
inference(demodulation,[status(thm)],[c_261,c_315,c_722,c_742,c_1349,c_1355]) ).
tcf(c_1502,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(X1,double_divide(identity,double_divide(double_divide(X1,X2),identity))))) = double_divide(identity,double_divide(X0,X2)),
inference(superposition,[status(thm)],[c_1437,c_436]) ).
tcf(c_1506,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(identity,double_divide(double_divide(X0,X1),X2))) = double_divide(identity,double_divide(double_divide(identity,X2),X1)),
inference(superposition,[status(thm)],[c_1437,c_457]) ).
tcf(c_1519,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(identity,double_divide(double_divide(X0,X1),X2))) = double_divide(double_divide(identity,X1),X2),
inference(demodulation,[status(thm)],[c_1506,c_893]) ).
tcf(c_1524,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),identity))) = double_divide(identity,double_divide(X0,X1)),
inference(demodulation,[status(thm)],[c_1502,c_1519]) ).
tcf(c_1525,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,X1)) = double_divide(identity,double_divide(X0,X1)),
inference(demodulation,[status(thm)],[c_1524,c_328]) ).
tcf(c_1625,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),X2)) = double_divide(identity,double_divide(X2,X1)),
inference(demodulation,[status(thm)],[c_264,c_315,c_327,c_503,c_722,c_1349]) ).
tcf(c_1640,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(identity,double_divide(X1,X2)))) = double_divide(double_divide(identity,X1),double_divide(X2,X0)),
inference(superposition,[status(thm)],[c_457,c_1625]) ).
tcf(c_1643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(identity,double_divide(X0,double_divide(X1,double_divide(identity,double_divide(double_divide(X1,X2),X3))))) = double_divide(X3,double_divide(X2,X0)),
inference(superposition,[status(thm)],[c_1437,c_1625]) ).
tcf(c_1659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(identity,double_divide(double_divide(identity,X0),X1)),double_divide(double_divide(identity,double_divide(double_divide(identity,X0),X2)),X3)) = double_divide(identity,double_divide(X3,double_divide(double_divide(identity,X2),X1))),
inference(superposition,[status(thm)],[c_847,c_1625]) ).
tcf(c_1668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,double_divide(double_divide(identity,double_divide(X1,X2)),double_divide(X3,identity))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(X3,X0),X2)),X1),
inference(superposition,[status(thm)],[c_1625,c_54]) ).
tcf(c_1679,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(double_divide(identity,double_divide(identity,X1)),X2))) = double_divide(identity,double_divide(X0,double_divide(identity,double_divide(identity,double_divide(X2,X1))))),
inference(superposition,[status(thm)],[c_1625,c_436]) ).
tcf(c_1696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(identity,double_divide(identity,double_divide(X0,X1))),double_divide(double_divide(identity,X2),double_divide(double_divide(identity,double_divide(double_divide(identity,X3),X1)),X0))) = double_divide(double_divide(identity,X3),X2),
inference(superposition,[status(thm)],[c_1625,c_847]) ).
tcf(c_1711,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,double_divide(X0,X1)),X2),identity) = double_divide(identity,double_divide(X1,double_divide(identity,double_divide(X0,X2)))),
inference(superposition,[status(thm)],[c_1625,c_542]) ).
tcf(c_1714,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(double_divide(identity,X2),X0)) = double_divide(double_divide(identity,double_divide(identity,X1)),X2),
inference(superposition,[status(thm)],[c_1625,c_847]) ).
tcf(c_1728,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(X1,X2)) = double_divide(double_divide(identity,X1),double_divide(X2,X0)),
inference(demodulation,[status(thm)],[c_1640,c_503]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(X0,X1),double_divide(identity,X2))) = double_divide(double_divide(identity,double_divide(identity,X1)),X2),
inference(demodulation,[status(thm)],[c_1714,c_1728]) ).
tcf(c_1731,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(X0,X1),double_divide(identity,X2))) = double_divide(X1,X2),
inference(demodulation,[status(thm)],[c_1730,c_496]) ).
tcf(c_1732,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),double_divide(identity,X2)) = double_divide(double_divide(identity,X1),double_divide(X0,X2)),
inference(demodulation,[status(thm)],[c_1711,c_503,c_1349,c_1372]) ).
tcf(c_1738,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(double_divide(identity,X1),X2))) = double_divide(X2,double_divide(X1,X0)),
inference(demodulation,[status(thm)],[c_1643,c_1519]) ).
tcf(c_1763,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(X0,double_divide(identity,double_divide(identity,double_divide(X1,X2))))) = double_divide(X1,double_divide(double_divide(identity,X2),X0)),
inference(demodulation,[status(thm)],[c_1679,c_1738]) ).
tcf(c_1764,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(identity,X1),X2)) = double_divide(identity,double_divide(X2,double_divide(X0,X1))),
inference(demodulation,[status(thm)],[c_1763,c_503,c_1525]) ).
tcf(c_1786,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,double_divide(double_divide(identity,identity),double_divide(double_divide(X1,X2),X3))),double_divide(identity,identity)) = double_divide(double_divide(identity,double_divide(double_divide(X3,X0),X2)),X1),
inference(demodulation,[status(thm)],[c_1668,c_1728]) ).
tcf(c_1787,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(identity,double_divide(double_divide(X0,X1),X2)),X3) = double_divide(double_divide(identity,X1),double_divide(double_divide(X3,X2),X0)),
inference(demodulation,[status(thm)],[c_1786,c_315,c_893,c_1349,c_1355]) ).
tcf(c_1794,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,double_divide(double_divide(identity,X2),X1))) = double_divide(double_divide(identity,X2),X0),
inference(demodulation,[status(thm)],[c_1696,c_1728,c_1731,c_1738,c_1764]) ).
tcf(c_1795,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),X1) = double_divide(X1,double_divide(X0,identity)),
inference(demodulation,[status(thm)],[c_1794,c_597]) ).
tcf(c_1809,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(double_divide(identity,X0),double_divide(double_divide(X1,X2),identity)),X3),identity)) = double_divide(X3,double_divide(X2,X1)),
inference(demodulation,[status(thm)],[c_1659,c_1738,c_1787]) ).
tcf(c_1810,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_1809,c_328,c_491,c_613,c_1349,c_1625]) ).
tcf(c_2180,plain,
( ( identity != identity )
| ( double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity) )
| ( double_divide(double_divide(a2,identity),identity) != a2 )
| ( 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(demodulation,[status(thm)],[c_68,c_315]) ).
tcf(c_2185,plain,
( ( double_divide(double_divide(a4,b4),identity) != double_divide(double_divide(b4,a4),identity) )
| ( double_divide(double_divide(a2,identity),identity) != a2 )
| ( 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(equality_resolution_simp,[status(thm)],[c_2180]) ).
tcf(c_2186,plain,
( ( a2 != a2 )
| ( double_divide(identity,double_divide(b4,a4)) != double_divide(identity,double_divide(b4,a4)) )
| ( double_divide(double_divide(a3,identity),double_divide(b3,c3)) != double_divide(double_divide(a3,identity),double_divide(b3,c3)) ) ),
inference(demodulation,[status(thm)],[c_2185,c_318,c_326,c_328,c_732,c_742,c_1372,c_1732,c_1795,c_1810]) ).
tcf(c_2187,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP102-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:36:40 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 4.43/1.11 % SZS status Started for theBenchmark.p
% 4.43/1.11 % SZS status Unsatisfiable for theBenchmark.p
% 4.43/1.11
% 4.43/1.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.43/1.11
% 4.43/1.11 % ------ iProver source info
% 4.43/1.11
% 4.43/1.11 % git: date: 2026-07-19 20:42:38 +0200
% 4.43/1.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.43/1.11 % git: non_committed_changes: false
% 4.43/1.11
% 4.43/1.11 % ------ Parsing...% successful
% 4.43/1.11
% 4.43/1.11
% 4.43/1.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.43/1.11
% 4.43/1.11 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 4.43/1.11
% 4.43/1.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 0 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 4.43/1.11
% 4.43/1.11 % ------ Preprocessing...
% 4.43/1.11 % ------ Proving...
% 4.43/1.11 % ------ Problem Properties
% 4.43/1.11
% 4.43/1.11 %
% 4.43/1.11 % clauses 3
% 4.43/1.11 % conjectures 1
% 4.43/1.11 % EPR 0
% 4.43/1.11 % Horn 3
% 4.43/1.11 % unary 2
% 4.43/1.11 % binary 0
% 4.43/1.11 % lits 6
% 4.43/1.11 % lits eq 6
% 4.43/1.11 % fd_pure 0
% 4.43/1.11 % fd_pseudo 0
% 4.43/1.11 % fd_cond 0
% 4.43/1.11 % fd_pseudo_cond 0
% 4.43/1.11 % AC symbols 0
% 4.43/1.11
% 4.43/1.11 % ------ Input Options Time Limit: Unbounded
% 4.43/1.11
% 4.43/1.11
% 4.43/1.11 % ------
% 4.43/1.11 % Current options:
% 4.43/1.11 % ------
% 4.43/1.11
% 4.43/1.11
% 4.43/1.11 %
% 4.43/1.11
% 4.43/1.11 % ------ Proving...
% 4.43/1.11 %
% 4.43/1.11
% 4.43/1.11 % SZS status Unsatisfiable for theBenchmark.p
% 4.43/1.11
% 4.43/1.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.43/1.11
% 4.43/1.11
%------------------------------------------------------------------------------