%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP077-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 01:30:40 PM UTC 2026
% Result : Unsatisfiable 6.28s 6.97s
% Output : CNFRefutation 6.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 5
% Syntax : Number of formulae : 114 ( 105 unt; 0 def)
% Number of atoms : 128 ( 127 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 29 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 14 ( 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 204 ( 0 sgn 204 !; 0 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))),X1),identity)) = X2,
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,plain,
! [X0] : double_divide(X0,identity) = inverse(X0),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0] : identity = double_divide(X0,inverse(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f6,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f7,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(identity,a2)
| identity != multiply(inverse(a1),a1) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,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)
| a2 != double_divide(double_divide(a2,identity),identity)
| identity != double_divide(double_divide(a1,double_divide(a1,identity)),identity) ),
inference(definition_unfolding,[],[f7,f2,f4,f2,f2,f2,f2,f2]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,double_divide(X0,identity)),
inference(definition_unfolding,[],[f5,f4]) ).
tcf(c_54,negated_conjecture,
( ( 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_55,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))),X1),identity)) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i] : double_divide(X0,double_divide(X0,identity)) = identity,
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
( ( double_divide(identity,identity) != 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_54,c_56]) ).
tcf(c_109,plain,
! [X0: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,identity),double_divide(X0,identity)),identity)) = identity,
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),X1),identity)) = double_divide(X1,identity),
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))),X1),identity) = double_divide(X3,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X3,identity),X2)),X0),identity)),
inference(superposition,[status(thm)],[c_55,c_55]) ).
tcf(c_119,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(superposition,[status(thm)],[c_56,c_109]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),X1),identity)) = double_divide(double_divide(double_divide(identity,identity),double_divide(X1,identity)),identity),
inference(superposition,[status(thm)],[c_109,c_55]) ).
tcf(c_124,plain,
! [X0: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(X0,identity)),identity) = double_divide(X0,identity),
inference(light_normalisation,[status(thm)],[c_121,c_111]) ).
tcf(c_144,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(superposition,[status(thm)],[c_56,c_124]) ).
tcf(c_146,plain,
! [X0: $i] : double_divide(double_divide(double_divide(identity,identity),double_divide(X0,identity)),double_divide(X0,identity)) = identity,
inference(superposition,[status(thm)],[c_124,c_56]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),identity),double_divide(X1,X2))),X1),identity),identity) = double_divide(X0,double_divide(X2,identity)),
inference(superposition,[status(thm)],[c_55,c_111]) ).
tcf(c_169,plain,
! [X0: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),identity),identity) = double_divide(X0,double_divide(identity,identity)),
inference(superposition,[status(thm)],[c_56,c_111]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,identity))),X2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(X2,identity),identity)),X1),identity),
inference(superposition,[status(thm)],[c_111,c_55]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,identity),identity),double_divide(X1,X0))),X1),identity)) = identity,
inference(superposition,[status(thm)],[c_55,c_146]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(X1,X0))),X1),identity)) = identity,
inference(light_normalisation,[status(thm)],[c_229,c_144]) ).
tcf(c_310,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(double_divide(identity,identity),identity),
inference(superposition,[status(thm)],[c_239,c_169]) ).
tcf(c_317,plain,
double_divide(identity,identity) = identity,
inference(light_normalisation,[status(thm)],[c_310,c_119,c_144]) ).
tcf(c_324,plain,
( ( 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(backward_subsumption_resolution,[status(thm)],[c_69,c_317]) ).
tcf(c_326,plain,
! [X0: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),identity),identity) = double_divide(X0,identity),
inference(demodulation,[status(thm)],[c_169,c_317]) ).
tcf(c_329,plain,
! [X0: $i] : double_divide(double_divide(identity,double_divide(X0,identity)),identity) = double_divide(X0,identity),
inference(demodulation,[status(thm)],[c_124,c_317]) ).
tcf(c_374,plain,
! [X0: $i] : double_divide(identity,double_divide(double_divide(identity,X0),identity)) = double_divide(X0,identity),
inference(superposition,[status(thm)],[c_317,c_111]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(X0,X1))),X0),identity)) = X1,
inference(superposition,[status(thm)],[c_317,c_55]) ).
tcf(c_413,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),double_divide(X0,X1))),X0),identity) = double_divide(X1,identity),
inference(superposition,[status(thm)],[c_55,c_329]) ).
tcf(c_414,plain,
! [X0: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,identity),identity)),X0),identity) = double_divide(double_divide(X0,identity),identity),
inference(superposition,[status(thm)],[c_111,c_329]) ).
tcf(c_422,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),identity) = double_divide(double_divide(identity,X0),identity),
inference(light_normalisation,[status(thm)],[c_414,c_317]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,double_divide(identity,double_divide(X0,X1))),X0),identity) = double_divide(X1,identity),
inference(light_normalisation,[status(thm)],[c_413,c_317]) ).
tcf(c_424,plain,
( ( double_divide(double_divide(identity,a2),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_324,c_422]) ).
tcf(c_439,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),identity) = double_divide(identity,double_divide(X0,identity)),
inference(superposition,[status(thm)],[c_329,c_374]) ).
tcf(c_479,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),identity) = double_divide(identity,double_divide(X0,identity)),
inference(light_normalisation,[status(thm)],[c_422,c_439]) ).
tcf(c_481,plain,
! [X0: $i] : double_divide(identity,double_divide(double_divide(X0,identity),identity)) = double_divide(X0,identity),
inference(demodulation,[status(thm)],[c_329,c_479]) ).
tcf(c_482,plain,
( ( double_divide(identity,double_divide(a2,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_424,c_479]) ).
tcf(c_483,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,double_divide(X0,identity))) = double_divide(X0,identity),
inference(light_normalisation,[status(thm)],[c_481,c_439]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(X0,identity)),double_divide(X1,X2))),X1),identity)) = X2,
inference(superposition,[status(thm)],[c_479,c_55]) ).
tcf(c_490,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X0,identity))) = identity,
inference(superposition,[status(thm)],[c_479,c_56]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),X1),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),identity)),identity),identity),
inference(superposition,[status(thm)],[c_317,c_112]) ).
tcf(c_574,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),X1)),identity),double_divide(X2,X3))),X2),identity),identity),double_divide(X4,X1))),X4),identity) = double_divide(X0,double_divide(X3,identity)),
inference(superposition,[status(thm)],[c_55,c_112]) ).
tcf(c_596,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),X2)),X0),identity))) = X2,
inference(superposition,[status(thm)],[c_112,c_55]) ).
tcf(c_602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(double_divide(double_divide(identity,double_divide(double_divide(X1,identity),double_divide(X2,X3))),X2),identity))),X4),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(X4,identity),X3)),X1),identity),
inference(superposition,[status(thm)],[c_112,c_55]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),identity),identity) = double_divide(X1,double_divide(double_divide(double_divide(X1,identity),X0),identity)),
inference(light_normalisation,[status(thm)],[c_565,c_439,c_483]) ).
tcf(c_611,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(double_divide(double_divide(X0,identity),X1),identity)) = double_divide(X1,identity),
inference(light_normalisation,[status(thm)],[c_610,c_326]) ).
tcf(c_848,plain,
! [X0: $i] : double_divide(identity,double_divide(X0,identity)) = X0,
inference(light_normalisation,[status(thm)],[c_375,c_423]) ).
tcf(c_849,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),X0) = identity,
inference(demodulation,[status(thm)],[c_490,c_848]) ).
tcf(c_850,plain,
! [X0: $i] : double_divide(double_divide(X0,identity),identity) = X0,
inference(demodulation,[status(thm)],[c_439,c_848]) ).
tcf(c_851,plain,
! [X0: $i] : double_divide(double_divide(identity,X0),identity) = X0,
inference(demodulation,[status(thm)],[c_479,c_848]) ).
tcf(c_853,plain,
( ( a2 != 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_482,c_848]) ).
tcf(c_854,plain,
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_853]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,identity))),X2),identity)) = double_divide(double_divide(double_divide(identity,double_divide(double_divide(X2,identity),X1)),identity),identity),
inference(superposition,[status(thm)],[c_848,c_112]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))),X1),identity) = double_divide(double_divide(identity,identity),double_divide(double_divide(double_divide(identity,double_divide(identity,X2)),X0),identity)),
inference(superposition,[status(thm)],[c_849,c_112]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,X2))),X1),identity) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,X2)),X0),identity)),
inference(light_normalisation,[status(thm)],[c_897,c_317]) ).
tcf(c_905,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),X1)),X2),identity)) = double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(identity,X1)),X2),identity)),
inference(demodulation,[status(thm)],[c_112,c_902]) ).
tcf(c_912,plain,
! [X0: $i] : double_divide(X0,identity) = double_divide(identity,X0),
inference(superposition,[status(thm)],[c_850,c_848]) ).
tcf(c_915,plain,
! [X0: $i] : double_divide(identity,double_divide(identity,X0)) = X0,
inference(demodulation,[status(thm)],[c_851,c_912]) ).
tcf(c_944,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(demodulation,[status(thm)],[c_854,c_912]) ).
tcf(c_1090,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_596,c_848,c_905,c_915]) ).
tcf(c_1099,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_1090,c_1090]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,double_divide(double_divide(X0,identity),X1))) = double_divide(X1,identity),
inference(demodulation,[status(thm)],[c_611,c_912]) ).
tcf(c_1139,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(X1,identity)),identity) = double_divide(X1,double_divide(identity,X0)),
inference(superposition,[status(thm)],[c_1090,c_1132]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(identity,double_divide(double_divide(identity,X0),X1))) = double_divide(X1,identity),
inference(superposition,[status(thm)],[c_912,c_1132]) ).
tcf(c_1146,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),X1)) = double_divide(double_divide(X1,identity),X0),
inference(superposition,[status(thm)],[c_1132,c_1099]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(X1,identity))) = double_divide(X1,double_divide(identity,X0)),
inference(demodulation,[status(thm)],[c_1139,c_912]) ).
tcf(c_1174,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(X0,double_divide(identity,X1))) = double_divide(X1,double_divide(identity,X0)),
inference(superposition,[status(thm)],[c_912,c_1167]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,X1)) = double_divide(identity,double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_1099,c_1167]) ).
tcf(c_1179,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,double_divide(identity,X1)),identity) = double_divide(X1,double_divide(X0,identity)),
inference(superposition,[status(thm)],[c_1167,c_1099]) ).
tcf(c_1187,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demodulation,[status(thm)],[c_944,c_1174]) ).
tcf(c_1237,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,X0),X1)) = double_divide(double_divide(X1,identity),X0),
inference(superposition,[status(thm)],[c_1141,c_1099]) ).
tcf(c_1243,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(identity,X0)),X1)),identity) = double_divide(X0,double_divide(identity,double_divide(X1,identity))),
inference(superposition,[status(thm)],[c_1141,c_1141]) ).
tcf(c_1248,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,double_divide(X0,X1)),identity) = double_divide(X0,double_divide(identity,double_divide(X1,identity))),
inference(light_normalisation,[status(thm)],[c_1243,c_915]) ).
tcf(c_1251,plain,
double_divide(double_divide(a3,identity),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demodulation,[status(thm)],[c_1187,c_1237]) ).
tcf(c_1257,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demodulation,[status(thm)],[c_1251,c_912]) ).
tcf(c_1268,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(identity,X1)) = double_divide(identity,double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_1099,c_1146]) ).
tcf(c_1352,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(X1,identity)) = double_divide(identity,double_divide(X1,X0)),
inference(superposition,[status(thm)],[c_912,c_1177]) ).
tcf(c_1353,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(identity,X0),X1)) = double_divide(double_divide(identity,X1),X0),
inference(superposition,[status(thm)],[c_915,c_1177]) ).
tcf(c_1356,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),X1)) = double_divide(double_divide(identity,X1),X0),
inference(superposition,[status(thm)],[c_1090,c_1177]) ).
tcf(c_1359,plain,
! [X0: $i] : double_divide(double_divide(double_divide(identity,X0),identity),identity) = double_divide(identity,double_divide(identity,double_divide(X0,identity))),
inference(superposition,[status(thm)],[c_1177,c_1146]) ).
tcf(c_1513,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,identity)) = double_divide(X0,double_divide(identity,X1)),
inference(demodulation,[status(thm)],[c_1179,c_912,c_1174]) ).
tcf(c_1526,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),double_divide(X1,double_divide(identity,X0))) = X1,
inference(superposition,[status(thm)],[c_1513,c_1090]) ).
tcf(c_1544,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(identity,X0),double_divide(identity,double_divide(X1,identity))) = double_divide(identity,double_divide(double_divide(identity,X1),X0)),
inference(superposition,[status(thm)],[c_1513,c_1177]) ).
tcf(c_1546,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,identity))) = double_divide(double_divide(double_divide(identity,X1),identity),X0),
inference(superposition,[status(thm)],[c_1513,c_1146]) ).
tcf(c_1676,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,identity),X1) = double_divide(double_divide(identity,X0),X1),
inference(superposition,[status(thm)],[c_1099,c_1526]) ).
tcf(c_1956,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,identity))) = double_divide(X1,double_divide(identity,double_divide(identity,X0))),
inference(superposition,[status(thm)],[c_1676,c_1167]) ).
tcf(c_1972,plain,
! [X0: $i,X1: $i] : double_divide(identity,double_divide(double_divide(X0,identity),double_divide(X1,identity))) = double_divide(X1,X0),
inference(light_normalisation,[status(thm)],[c_1956,c_915,c_1546]) ).
tcf(c_2135,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(X0,double_divide(X1,X2))),X1),X0)) = X2,
inference(demodulation,[status(thm)],[c_489,c_1352,c_1353]) ).
tcf(c_2194,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(double_divide(double_divide(identity,double_divide(X0,X1)),double_divide(X2,identity)),X0)) = double_divide(X1,double_divide(identity,X2)),
inference(superposition,[status(thm)],[c_1526,c_2135]) ).
tcf(c_2684,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(double_divide(X1,identity),X2)) = double_divide(identity,double_divide(double_divide(double_divide(identity,X2),X1),X0)),
inference(superposition,[status(thm)],[c_1237,c_1177]) ).
tcf(c_2807,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,identity),double_divide(double_divide(X1,identity),X2)) = double_divide(identity,double_divide(double_divide(double_divide(identity,X2),X1),X0)),
inference(superposition,[status(thm)],[c_1237,c_1268]) ).
tcf(c_3311,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(double_divide(identity,X0),X1),identity) = double_divide(double_divide(X1,identity),X0),
inference(superposition,[status(thm)],[c_1356,c_1099]) ).
tcf(c_3351,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,double_divide(X0,double_divide(X1,X2))),X1) = double_divide(X0,double_divide(X2,identity)),
inference(demodulation,[status(thm)],[c_168,c_1248,c_1352,c_1353,c_1356,c_1544,c_1676]) ).
tcf(c_3422,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,identity),double_divide(identity,double_divide(X1,double_divide(identity,X2)))) = double_divide(identity,double_divide(double_divide(X1,double_divide(X2,identity)),X0)),
inference(superposition,[status(thm)],[c_3351,c_1146]) ).
tcf(c_3668,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(X0,identity),identity)),X1),identity) = double_divide(X2,double_divide(double_divide(double_divide(X1,X2),X0),identity)),
inference(light_normalisation,[status(thm)],[c_176,c_858,c_1972]) ).
tcf(c_3669,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(identity,double_divide(double_divide(X1,X0),X2))) = double_divide(double_divide(identity,X1),X2),
inference(demodulation,[status(thm)],[c_3668,c_317,c_1353,c_1513,c_2807,c_3311]) ).
tcf(c_3694,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,X0),double_divide(X1,double_divide(X0,X2))) = double_divide(X2,double_divide(identity,X1)),
inference(superposition,[status(thm)],[c_1090,c_3669]) ).
tcf(c_3717,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(identity,double_divide(X0,X1)),X2) = double_divide(X0,double_divide(identity,double_divide(X1,X2))),
inference(superposition,[status(thm)],[c_1099,c_3669]) ).
tcf(c_3729,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(superposition,[status(thm)],[c_3669,c_1099]) ).
tcf(c_4174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(identity,X0),X1),identity),double_divide(X2,X3))),X2),identity),identity),double_divide(X4,X0))),X4),identity) = double_divide(X1,double_divide(X3,identity)),
inference(light_normalisation,[status(thm)],[c_574,c_1356]) ).
tcf(c_4175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(double_divide(double_divide(identity,double_divide(double_divide(double_divide(X0,identity),X1),double_divide(X2,X3))),X2),identity),identity),double_divide(X4,X1))),X4),identity) = double_divide(X0,double_divide(X3,identity)),
inference(light_normalisation,[status(thm)],[c_4174,c_3311]) ).
tcf(c_4176,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,double_divide(double_divide(identity,X0),X2))) = double_divide(X2,double_divide(X1,identity)),
inference(demodulation,[status(thm)],[c_4175,c_902,c_1353,c_1356,c_2194,c_3694]) ).
tcf(c_4244,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,double_divide(X1,identity)),X2) = double_divide(X1,double_divide(double_divide(identity,X2),X0)),
inference(superposition,[status(thm)],[c_4176,c_1099]) ).
tcf(c_5830,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(identity,double_divide(double_divide(X0,X1),double_divide(double_divide(identity,X2),double_divide(X0,X3)))) = double_divide(double_divide(X3,X2),X1),
inference(demodulation,[status(thm)],[c_602,c_858,c_912,c_915,c_1356,c_1359,c_2684,c_3422,c_3717,c_3729,c_4244]) ).
tcf(c_5842,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(identity,double_divide(identity,double_divide(double_divide(identity,X0),double_divide(X1,X2)))) = double_divide(double_divide(X2,X0),double_divide(X1,identity)),
inference(superposition,[status(thm)],[c_56,c_5830]) ).
tcf(c_6278,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,X1),double_divide(X2,identity)) = double_divide(double_divide(identity,X1),double_divide(X2,X0)),
inference(demodulation,[status(thm)],[c_5842,c_915]) ).
tcf(c_6354,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(X2,X0)),
inference(superposition,[status(thm)],[c_6278,c_1513]) ).
tcf(c_6428,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(identity,a3),double_divide(c3,b3)),
inference(demodulation,[status(thm)],[c_1257,c_6354]) ).
tcf(c_6429,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_6428]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP077-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.58 % Computer : n006.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Wed Sep 23 13:28:13 UTC 2026
% 0.10/5.59 % CPUTime :
% 0.10/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.63 Running first-order theorem proving
% 0.13/5.63 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.64
% 0.13/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.64
% 0.13/5.64 % Detected problem language: tptp
% 0.13/5.65 % Proving...
% 6.28/6.97 % SZS status Started for theBenchmark.p
% 6.28/6.97 % SZS status Unsatisfiable for theBenchmark.p
% 6.28/6.97
% 6.28/6.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.28/6.97
% 6.28/6.97 % ------ iProver source info
% 6.28/6.97
% 6.28/6.97 % git: date: 2026-07-19 20:42:38 +0200
% 6.28/6.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.28/6.97 % git: non_committed_changes: false
% 6.28/6.97
% 6.28/6.97 % ------ Parsing...% successful
% 6.28/6.97
% 6.28/6.97
% 6.28/6.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.28/6.97
% 6.28/6.97 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.28/6.97
% 6.28/6.97 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.28/6.97
% 6.28/6.97 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.28/6.97 % ------ Proving...
% 6.28/6.97 % ------ Problem Properties
% 6.28/6.97
% 6.28/6.97 %
% 6.28/6.97 % clauses 3
% 6.28/6.97 % conjectures 0
% 6.28/6.97 % EPR 0
% 6.28/6.97 % Horn 3
% 6.28/6.97 % unary 2
% 6.28/6.97 % binary 0
% 6.28/6.97 % lits 5
% 6.28/6.97 % lits eq 5
% 6.28/6.97 % fd_pure 0
% 6.28/6.97 % fd_pseudo 0
% 6.28/6.97 % fd_cond 0
% 6.28/6.97 % fd_pseudo_cond 0
% 6.28/6.97 % AC symbols 0
% 6.28/6.97
% 6.28/6.97 % ------ Schedule dynamic 5 is on
% 6.28/6.97
% 6.28/6.97 % ------ no conjectures: strip conj schedule
% 6.28/6.97
% 6.28/6.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 6.28/6.97
% 6.28/6.97
% 6.28/6.97 % ------
% 6.28/6.97 % Current options:
% 6.28/6.97 % ------
% 6.28/6.97
% 6.28/6.97
% 6.28/6.97 %
% 6.28/6.97
% 6.28/6.97 % ------ Proving...
% 6.28/6.97 %
% 6.28/6.97
% 6.28/6.97 % SZS status Unsatisfiable for theBenchmark.p
% 6.28/6.97
% 6.28/6.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.28/6.98
% 6.28/6.98
%------------------------------------------------------------------------------