%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP100-1 : 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 : n008.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 0.88s 1.66s
% Output : CNFRefutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 116 ( 108 unt; 0 def)
% Number of atoms : 407 ( 137 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 55 ( 33 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 261 ( 0 sgn 261 !; 0 ?; 253 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),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(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(X1,double_divide(X0,X2)),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,[],[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_106,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(X2,identity))),double_divide(double_divide(X3,X1),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = X3,
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(double_divide(X1,identity),double_divide(double_divide(X0,identity),identity))),double_divide(identity,identity)) = X1,
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_112,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_114,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),double_divide(identity,identity)) = X0,
inference(demodulation,[status(thm)],[c_112,c_55]) ).
tcf(c_118,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_123,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(X1,identity),double_divide(double_divide(X0,identity),identity))),double_divide(double_divide(X2,X1),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = X2,
inference(superposition,[status(thm)],[c_55,c_106]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X1,identity))),identity),double_divide(identity,identity)) = identity,
inference(superposition,[status(thm)],[c_55,c_106]) ).
tcf(c_126,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(X1,identity))),double_divide(X2,double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = double_divide(X3,double_divide(double_divide(X2,double_divide(X3,X4)),double_divide(X4,identity))),
inference(superposition,[status(thm)],[c_54,c_106]) ).
tcf(c_132,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(X2,identity))),double_divide(double_divide(X3,X1),double_divide(double_divide(identity,identity),identity))) = double_divide(double_divide(identity,double_divide(X3,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_106,c_54]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(double_divide(identity,identity),double_divide(X0,X1)),double_divide(X1,identity))),double_divide(X2,double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = double_divide(double_divide(X3,double_divide(double_divide(X4,double_divide(X3,X5)),double_divide(X5,identity))),double_divide(double_divide(X2,X4),double_divide(double_divide(identity,identity),identity))),
inference(superposition,[status(thm)],[c_106,c_106]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X1,identity))) = identity,
inference(demodulation,[status(thm)],[c_125,c_114]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_126]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(double_divide(identity,identity),double_divide(X0,X1)),double_divide(X1,identity))),double_divide(X2,double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = iPr_def_10(X2),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_126]) ).
tcf(c_149,plain,
! [X0: $i] : double_divide(double_divide(iPr_def_10(double_divide(identity,identity)),double_divide(X0,double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_146,c_145]) ).
tcf(c_153,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(X0,double_divide(identity,identity))),double_divide(identity,identity)) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_133,c_132,c_145,c_149]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(X1,identity),double_divide(double_divide(X0,identity),identity))) = double_divide(double_divide(identity,double_divide(X1,double_divide(identity,identity))),double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_111,c_54]) ).
tcf(c_220,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(demodulation,[status(thm)],[c_217,c_153]) ).
tcf(c_231,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_114,c_54]) ).
tcf(c_234,plain,
! [X0: $i] : double_divide(X0,identity) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_231,c_153]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(double_divide(X1,X0),iPr_def_10(iPr_def_10(identity)))),iPr_def_10(identity)) = X1,
inference(demodulation,[status(thm)],[c_123,c_220,c_234]) ).
tcf(c_333,plain,
iPr_def_10(identity) = identity,
inference(demodulation,[status(thm)],[c_135,c_145]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(double_divide(X1,X0),identity)),identity) = X1,
inference(superposition,[status(thm)],[c_333,c_294]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(iPr_def_10(X0),iPr_def_10(double_divide(X1,X0)))) = X1,
inference(demodulation,[status(thm)],[c_334,c_234]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),iPr_def_10(X2))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_145,c_234]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(double_divide(X3,X1),double_divide(double_divide(identity,identity),identity)))) = double_divide(identity,double_divide(X3,iPr_def_10(identity))),
inference(superposition,[status(thm)],[c_106,c_340]) ).
tcf(c_346,plain,
! [X0: $i] : double_divide(identity,double_divide(X0,iPr_def_10(identity))) = iPr_def_10(double_divide(X0,identity)),
inference(superposition,[status(thm)],[c_114,c_340]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(double_divide(X1,X0),iPr_def_10(double_divide(identity,identity)))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_114,c_340]) ).
tcf(c_353,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(double_divide(X1,X0),iPr_def_10(iPr_def_10(identity)))),double_divide(double_divide(X2,X1),iPr_def_10(iPr_def_10(identity)))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_294,c_340]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(X1,double_divide(X0,identity)),identity)) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_333,c_340]) ).
tcf(c_356,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,double_divide(double_divide(X1,iPr_def_10(X2)),iPr_def_10(double_divide(double_divide(X2,double_divide(X0,X3)),iPr_def_10(X3))))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_340,c_340]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(iPr_def_10(X0),iPr_def_10(iPr_def_10(X2)))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_340,c_340]) ).
tcf(c_367,plain,
! [X0: $i] : double_divide(identity,double_divide(X0,identity)) = iPr_def_10(double_divide(X0,identity)),
inference(light_normalisation,[status(thm)],[c_346,c_333]) ).
tcf(c_368,plain,
! [X0: $i] : double_divide(identity,iPr_def_10(X0)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_367,c_234]) ).
tcf(c_370,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_355,c_234]) ).
tcf(c_375,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_352,c_234,c_333]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(double_divide(X1,X0),identity)),double_divide(double_divide(X2,X1),identity)) = iPr_def_10(X2),
inference(light_normalisation,[status(thm)],[c_353,c_333]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),iPr_def_10(double_divide(X1,X0))),iPr_def_10(double_divide(X2,X1))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_389,c_234]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X0,X2)),double_divide(X2,identity))),double_divide(double_divide(X3,X1),double_divide(double_divide(identity,identity),identity)))) = double_divide(identity,double_divide(X3,identity)),
inference(light_normalisation,[status(thm)],[c_344,c_333]) ).
tcf(c_401,plain,
! [X0: $i] : double_divide(identity,iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_400,c_234,c_333,c_339,c_340]) ).
tcf(c_447,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(iPr_def_10(X0))) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_149,c_234,c_333,c_368]) ).
tcf(c_450,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(double_divide(X1,iPr_def_10(iPr_def_10(X0))),iPr_def_10(iPr_def_10(identity)))),iPr_def_10(identity)) = X1,
inference(superposition,[status(thm)],[c_447,c_294]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(double_divide(X1,iPr_def_10(iPr_def_10(X0))),identity)),identity) = X1,
inference(light_normalisation,[status(thm)],[c_450,c_333]) ).
tcf(c_454,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_453,c_234,c_370]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(iPr_def_10(X1),X0)) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_220,c_234,c_454]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(iPr_def_10(X1),X2)),iPr_def_10(X2)),iPr_def_10(X0)) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_340,c_461]) ).
tcf(c_471,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X0),double_divide(X1,identity))),double_divide(double_divide(X2,X1),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = X2,
inference(superposition,[status(thm)],[c_461,c_106]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X0),double_divide(X1,identity))),double_divide(identity,identity)) = X1,
inference(superposition,[status(thm)],[c_461,c_54]) ).
tcf(c_480,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X0),iPr_def_10(X1)))) = X1,
inference(demodulation,[status(thm)],[c_472,c_234,c_333]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X0),iPr_def_10(X1))),iPr_def_10(double_divide(X2,X1)))) = X2,
inference(demodulation,[status(thm)],[c_471,c_234,c_333]) ).
tcf(c_543,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(c3,double_divide(double_divide(b3,a3),identity)),identity) != iPr_def_10(double_divide(double_divide(double_divide(c3,b3),identity),a3)) ) ),
inference(superposition,[status(thm)],[c_234,c_118]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X1,identity))),double_divide(iPr_def_10(X2),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = X2,
inference(superposition,[status(thm)],[c_234,c_106]) ).
tcf(c_586,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),iPr_def_10(X1))),double_divide(iPr_def_10(X2),iPr_def_10(iPr_def_10(identity)))),iPr_def_10(identity)) = X2,
inference(demodulation,[status(thm)],[c_544,c_234]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(X0,double_divide(double_divide(identity,double_divide(X0,X1)),iPr_def_10(X1))),double_divide(iPr_def_10(X2),identity)),identity) = X2,
inference(light_normalisation,[status(thm)],[c_586,c_333]) ).
tcf(c_588,plain,
! [X0: $i] : iPr_def_10(double_divide(identity,X0)) = X0,
inference(demodulation,[status(thm)],[c_587,c_234,c_333,c_340,c_454]) ).
tcf(c_595,plain,
( ( iPr_def_10(identity) != identity )
| ( iPr_def_10(iPr_def_10(a2)) != a2 )
| ( iPr_def_10(double_divide(a4,b4)) != iPr_def_10(double_divide(b4,a4)) )
| ( 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_543,c_234]) ).
tcf(c_600,plain,
( ( iPr_def_10(double_divide(a4,b4)) != iPr_def_10(double_divide(b4,a4)) )
| ( 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(ground_joinability,[status(thm)],[c_595,c_333,c_454]) ).
tcf(c_637,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,identity),double_divide(double_divide(X1,iPr_def_10(X2)),iPr_def_10(double_divide(double_divide(X2,X0),iPr_def_10(double_divide(identity,identity)))))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_114,c_356]) ).
tcf(c_675,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(double_divide(X1,iPr_def_10(X2)),iPr_def_10(double_divide(double_divide(X2,X0),iPr_def_10(double_divide(identity,identity)))))) = iPr_def_10(X1),
inference(light_normalisation,[status(thm)],[c_637,c_234]) ).
tcf(c_676,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(double_divide(X1,iPr_def_10(X2)),double_divide(X2,X0))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_675,c_234,c_454,c_588]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(X1,X2)),double_divide(iPr_def_10(X0),X2)) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_359,c_454]) ).
tcf(c_815,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,double_divide(X1,double_divide(double_divide(X2,double_divide(iPr_def_10(X0),X3)),iPr_def_10(X3)))),iPr_def_10(X2)) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_340,c_791]) ).
tcf(c_822,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X1),iPr_def_10(X2))) = iPr_def_10(double_divide(X0,double_divide(X1,X2))),
inference(superposition,[status(thm)],[c_791,c_340]) ).
tcf(c_824,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X1),double_divide(X2,identity))),double_divide(identity,identity)) = double_divide(X0,double_divide(X1,X2)),
inference(superposition,[status(thm)],[c_791,c_54]) ).
tcf(c_825,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(double_divide(iPr_def_10(X0),X1)),double_divide(iPr_def_10(X2),iPr_def_10(iPr_def_10(identity)))),iPr_def_10(identity)) = double_divide(X0,double_divide(X2,X1)),
inference(superposition,[status(thm)],[c_791,c_294]) ).
tcf(c_853,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X1),iPr_def_10(X2)))) = double_divide(X0,double_divide(X1,X2)),
inference(demodulation,[status(thm)],[c_824,c_234,c_333]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(double_divide(double_divide(iPr_def_10(X0),X1),double_divide(X2,iPr_def_10(identity)))),iPr_def_10(identity)) = double_divide(X0,double_divide(X2,X1)),
inference(demodulation,[status(thm)],[c_825,c_822]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(double_divide(double_divide(iPr_def_10(X0),X1),double_divide(X2,identity))),identity) = double_divide(X0,double_divide(X2,X1)),
inference(light_normalisation,[status(thm)],[c_861,c_333]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(iPr_def_10(X0),X1),iPr_def_10(X2)) = double_divide(X0,double_divide(X2,X1)),
inference(demodulation,[status(thm)],[c_862,c_234,c_454]) ).
tcf(c_1074,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(double_divide(iPr_def_10(X0),X1)),iPr_def_10(iPr_def_10(X2))) = iPr_def_10(double_divide(X0,double_divide(X2,X1))),
inference(superposition,[status(thm)],[c_791,c_375]) ).
tcf(c_1101,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(double_divide(iPr_def_10(X0),X1)),X2) = iPr_def_10(double_divide(X0,double_divide(X2,X1))),
inference(demodulation,[status(thm)],[c_1074,c_454]) ).
tcf(c_1134,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(X1,X2),iPr_def_10(double_divide(X2,X0)))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_390,c_863]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,iPr_def_10(double_divide(double_divide(identity,identity),X0)))) = iPr_def_10(double_divide(X1,identity)),
inference(superposition,[status(thm)],[c_114,c_1134]) ).
tcf(c_1176,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X1),iPr_def_10(double_divide(X2,X1)))) = iPr_def_10(double_divide(X0,X2)),
inference(superposition,[status(thm)],[c_1134,c_791]) ).
tcf(c_1188,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(X0,double_divide(X1,double_divide(X2,X1)))) = iPr_def_10(double_divide(X0,X2)),
inference(demodulation,[status(thm)],[c_1176,c_822]) ).
tcf(c_1196,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_1141,c_234,c_333,c_454,c_588]) ).
tcf(c_1686,plain,
! [X0: $i] : double_divide(identity,X0) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_454,c_401]) ).
tcf(c_1727,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(iPr_def_10(iPr_def_10(X0)),iPr_def_10(X1)),iPr_def_10(identity)) = double_divide(iPr_def_10(identity),double_divide(iPr_def_10(X1),X0)),
inference(superposition,[status(thm)],[c_464,c_294]) ).
tcf(c_1751,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),identity) = double_divide(identity,double_divide(iPr_def_10(X1),X0)),
inference(light_normalisation,[status(thm)],[c_1727,c_333,c_454]) ).
tcf(c_1752,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(iPr_def_10(X0),X1)) = iPr_def_10(double_divide(X1,iPr_def_10(X0))),
inference(demodulation,[status(thm)],[c_1751,c_234,c_1686]) ).
tcf(c_1862,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_480,c_853]) ).
tcf(c_1871,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),iPr_def_10(X1)) = iPr_def_10(double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_375,c_1862]) ).
tcf(c_1875,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_370,c_1862]) ).
tcf(c_2099,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_489,c_853,c_1862,c_1875]) ).
tcf(c_2115,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X1),X2)) = double_divide(X1,double_divide(X0,X2)),
inference(superposition,[status(thm)],[c_791,c_2099]) ).
tcf(c_2121,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,iPr_def_10(X2))) = iPr_def_10(double_divide(X1,double_divide(X0,X2))),
inference(superposition,[status(thm)],[c_2099,c_340]) ).
tcf(c_2123,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(X1,double_divide(X2,identity))),double_divide(identity,identity)) = double_divide(X1,double_divide(X0,X2)),
inference(superposition,[status(thm)],[c_2099,c_54]) ).
tcf(c_2182,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(X0,double_divide(X1,iPr_def_10(X2)))) = double_divide(X1,double_divide(X0,X2)),
inference(demodulation,[status(thm)],[c_2123,c_234,c_333,c_1686]) ).
tcf(c_2393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,iPr_def_10(double_divide(double_divide(X1,double_divide(iPr_def_10(X0),X2)),double_divide(X3,X2)))),iPr_def_10(X1)) = iPr_def_10(X3),
inference(demodulation,[status(thm)],[c_815,c_2121]) ).
tcf(c_2398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(double_divide(X0,double_divide(double_divide(X1,double_divide(iPr_def_10(X2),iPr_def_10(X3))),X3))) = double_divide(double_divide(X2,iPr_def_10(iPr_def_10(X0))),iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_340,c_2393]) ).
tcf(c_2401,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,iPr_def_10(X1)),iPr_def_10(X2)) = iPr_def_10(double_divide(X2,double_divide(iPr_def_10(X0),X1))),
inference(superposition,[status(thm)],[c_1862,c_2393]) ).
tcf(c_2443,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,iPr_def_10(double_divide(double_divide(X1,double_divide(iPr_def_10(X0),X2)),double_divide(X3,X2)))) = double_divide(double_divide(iPr_def_10(iPr_def_10(X1)),double_divide(iPr_def_10(X3),iPr_def_10(iPr_def_10(identity)))),iPr_def_10(identity)),
inference(superposition,[status(thm)],[c_2393,c_294]) ).
tcf(c_2444,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,iPr_def_10(double_divide(double_divide(X1,double_divide(iPr_def_10(X0),X2)),double_divide(X3,X2)))) = double_divide(iPr_def_10(X3),iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_2393,c_2099]) ).
tcf(c_2453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : iPr_def_10(double_divide(X0,iPr_def_10(double_divide(double_divide(X1,double_divide(iPr_def_10(X0),X2)),double_divide(X3,X2))))) = double_divide(iPr_def_10(X4),double_divide(iPr_def_10(X3),double_divide(X1,X4))),
inference(superposition,[status(thm)],[c_2393,c_676]) ).
tcf(c_2490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,iPr_def_10(double_divide(double_divide(X1,double_divide(iPr_def_10(X0),X2)),double_divide(X3,X2)))) = iPr_def_10(double_divide(X1,X3)),
inference(demodulation,[status(thm)],[c_2444,c_1871]) ).
tcf(c_2518,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(double_divide(X0,double_divide(double_divide(X1,double_divide(iPr_def_10(X2),iPr_def_10(X3))),X3))) = iPr_def_10(double_divide(X1,double_divide(iPr_def_10(X2),iPr_def_10(X0)))),
inference(demodulation,[status(thm)],[c_2398,c_2401]) ).
tcf(c_2519,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),iPr_def_10(X2)) = double_divide(iPr_def_10(X0),double_divide(X1,X2)),
inference(demodulation,[status(thm)],[c_2518,c_1101,c_1188,c_1875,c_2121,c_2182]) ).
tcf(c_2531,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0),double_divide(iPr_def_10(X1),double_divide(X2,X0))) = iPr_def_10(iPr_def_10(double_divide(X2,X1))),
inference(demodulation,[status(thm)],[c_2453,c_2490]) ).
tcf(c_2532,plain,
! [X0: $i,X1: $i] : double_divide(X0,X1) = double_divide(X1,X0),
inference(demodulation,[status(thm)],[c_2531,c_454,c_1196,c_2115]) ).
tcf(c_2562,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(iPr_def_10(iPr_def_10(X0))),double_divide(identity,double_divide(iPr_def_10(X1),iPr_def_10(iPr_def_10(identity))))) = iPr_def_10(double_divide(X0,X1)),
inference(demodulation,[status(thm)],[c_2443,c_2490,c_2519,c_2532]) ).
tcf(c_2563,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0),double_divide(identity,double_divide(iPr_def_10(X1),identity))) = iPr_def_10(double_divide(X0,X1)),
inference(light_normalisation,[status(thm)],[c_2562,c_333,c_454]) ).
tcf(c_2564,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(X0,X1)) = iPr_def_10(double_divide(X1,X0)),
inference(demodulation,[status(thm)],[c_2563,c_234,c_333,c_1686,c_1752,c_1871,c_1875]) ).
tcf(c_2596,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(backward_subsumption_resolution,[status(thm)],[c_600,c_2564]) ).
tcf(c_2597,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(a3,b3)))),
inference(demodulation,[status(thm)],[c_2596,c_2564]) ).
tcf(c_2598,plain,
double_divide(double_divide(a3,b3),iPr_def_10(c3)) != double_divide(double_divide(c3,b3),iPr_def_10(a3)),
inference(demodulation,[status(thm)],[c_2597,c_1875]) ).
tcf(c_2599,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2598,c_2519,c_2532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP100-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 13:31:54 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 0.88/1.66 % SZS status Started for theBenchmark.p
% 0.88/1.66 % SZS status Unsatisfiable for theBenchmark.p
% 0.88/1.66
% 0.88/1.66 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.88/1.66
% 0.88/1.66 % ------ iProver source info
% 0.88/1.66
% 0.88/1.66 % git: date: 2026-07-19 20:42:38 +0200
% 0.88/1.66 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.88/1.66 % git: non_committed_changes: false
% 0.88/1.66
% 0.88/1.66 % ------ Parsing...% successful
% 0.88/1.66
% 0.88/1.66
% 0.88/1.66 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.88/1.66
% 0.88/1.66 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.88/1.66
% 0.88/1.66 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.88/1.66
% 0.88/1.66 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.88/1.66 % ------ Proving...
% 0.88/1.66 % ------ Problem Properties
% 0.88/1.66
% 0.88/1.66 %
% 0.88/1.66 % clauses 3
% 0.88/1.66 % conjectures 1
% 0.88/1.66 % EPR 0
% 0.88/1.66 % Horn 3
% 0.88/1.66 % unary 2
% 0.88/1.66 % binary 0
% 0.88/1.66 % lits 6
% 0.88/1.66 % lits eq 6
% 0.88/1.66 % fd_pure 0
% 0.88/1.66 % fd_pseudo 0
% 0.88/1.66 % fd_cond 0
% 0.88/1.66 % fd_pseudo_cond 0
% 0.88/1.66 % AC symbols 0
% 0.88/1.66
% 0.88/1.66 % ------ Input Options Time Limit: Unbounded
% 0.88/1.66
% 0.88/1.66
% 0.88/1.66 % ------
% 0.88/1.66 % Current options:
% 0.88/1.66 % ------
% 0.88/1.66
% 0.88/1.66
% 0.88/1.66 %
% 0.88/1.66
% 0.88/1.66 % ------ Proving...
% 0.88/1.66 %
% 0.88/1.66
% 0.88/1.66 % SZS status Unsatisfiable for theBenchmark.p
% 0.88/1.66
% 0.88/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.88/1.66
% 0.88/1.66
%------------------------------------------------------------------------------