%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP504-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:34:26 PM UTC 2026
% Result : Unsatisfiable 8.52s 11.80s
% Output : CNFRefutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 111 ( 111 unt; 0 def)
% Number of atoms : 409 ( 110 equ)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 304 ( 0 sgn 304 !; 0 ?; 298 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : double_divide(double_divide(X0,inverse(double_divide(X1,X2))),double_divide(inverse(X1),inverse(double_divide(X3,double_divide(X0,X3))))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,axiom,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
fof(f4,plain,
inverse(double_divide(c3,inverse(double_divide(b3,a3)))) != inverse(double_divide(inverse(double_divide(c3,b3)),a3)),
inference(definition_unfolding,[],[f3,f2,f2,f2,f2]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,inverse(double_divide(X1,X2))),double_divide(inverse(X1),inverse(double_divide(X3,double_divide(X0,X3))))) = X2,
inference(cnf_transformation,[],[f1]) ).
tcf(c_53,negated_conjecture,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,inverse(double_divide(b3,a3)))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : double_divide(double_divide(X0,inverse(X1)),double_divide(inverse(double_divide(X2,inverse(double_divide(X3,X1)))),inverse(double_divide(X4,double_divide(X0,X4))))) = double_divide(inverse(X3),inverse(double_divide(X5,double_divide(X2,X5)))),
inference(superposition,[status(thm)],[c_52,c_52]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : double_divide(double_divide(double_divide(X0,inverse(double_divide(X1,X2))),inverse(double_divide(X3,X4))),double_divide(inverse(X3),inverse(double_divide(double_divide(inverse(X1),inverse(double_divide(X5,double_divide(X0,X5)))),X2)))) = X4,
inference(superposition,[status(thm)],[c_52,c_52]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(inverse(X0),inverse(double_divide(X1,double_divide(X2,X1)))) = iPr_def_10(X0,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_61]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(X0,inverse(X1)),double_divide(inverse(double_divide(X2,inverse(double_divide(X3,X1)))),inverse(double_divide(X4,double_divide(X0,X4))))) = iPr_def_10(X3,X2),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_61]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,inverse(X1)),iPr_def_10(double_divide(X2,inverse(double_divide(X3,X1))),X0)) = iPr_def_10(X3,X2),
inference(demodulation,[status(thm)],[c_64,c_63]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,inverse(double_divide(X1,X2))),iPr_def_10(X1,X0)) = X2,
inference(demodulation,[status(thm)],[c_52,c_63]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(inverse(X0),inverse(double_divide(iPr_def_10(X1,X2),X3))) = iPr_def_10(X0,double_divide(X2,inverse(double_divide(X1,X3)))),
inference(superposition,[status(thm)],[c_66,c_63]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,inverse(iPr_def_10(X1,X2))),iPr_def_10(inverse(X1),X0)) = inverse(double_divide(X3,double_divide(X2,X3))),
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0,X1),iPr_def_10(X2,inverse(X0))) = double_divide(X1,X2),
inference(superposition,[status(thm)],[c_63,c_66]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(iPr_def_10(X0,X1),iPr_def_10(double_divide(X2,inverse(double_divide(X3,double_divide(X4,double_divide(X1,X4))))),inverse(X0))) = iPr_def_10(X3,X2),
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,inverse(double_divide(X1,X2))),iPr_def_10(iPr_def_10(X3,X1),X0)) = iPr_def_10(X2,inverse(X3)),
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(X0,inverse(iPr_def_10(X1,X2))),iPr_def_10(double_divide(X3,inverse(X4)),X0)) = iPr_def_10(double_divide(X2,inverse(double_divide(X1,X4))),X3),
inference(superposition,[status(thm)],[c_66,c_65]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(double_divide(X0,inverse(double_divide(X1,iPr_def_10(X2,inverse(X1))))),inverse(double_divide(X3,X4))),double_divide(inverse(X3),inverse(double_divide(X0,X2)))) = X4,
inference(superposition,[status(thm)],[c_66,c_62]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] : inverse(double_divide(X0,double_divide(X1,X0))) = iPr_def_11(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_84]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,inverse(iPr_def_10(X1,X2))),iPr_def_10(inverse(X1),X0)) = iPr_def_11(X2),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_84]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,double_divide(X1,inverse(double_divide(X2,double_divide(X3,double_divide(X0,X3)))))) = iPr_def_10(X2,X1),
inference(demodulation,[status(thm)],[c_87,c_85]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] : double_divide(inverse(X0),iPr_def_11(X1)) = iPr_def_10(X0,X1),
inference(demodulation,[status(thm)],[c_63,c_118]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(double_divide(X0,inverse(double_divide(X1,X2)))) = inverse(double_divide(iPr_def_10(X1,X0),X2)),
inference(superposition,[status(thm)],[c_66,c_118]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(double_divide(X0,iPr_def_11(X1)),iPr_def_10(X2,X0)) = double_divide(X1,X2),
inference(superposition,[status(thm)],[c_118,c_66]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(X0,iPr_def_11(X1)),iPr_def_10(double_divide(X2,inverse(double_divide(X3,double_divide(X4,double_divide(X1,X4))))),X0)) = iPr_def_10(X3,X2),
inference(superposition,[status(thm)],[c_118,c_65]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(X0,double_divide(X1,X0)),X2) = double_divide(iPr_def_11(X1),iPr_def_11(X2)),
inference(superposition,[status(thm)],[c_118,c_144]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : inverse(double_divide(iPr_def_11(X0),iPr_def_10(X1,X0))) = iPr_def_11(inverse(X1)),
inference(superposition,[status(thm)],[c_144,c_118]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,double_divide(X1,iPr_def_11(X2))) = iPr_def_10(double_divide(X0,X2),X1),
inference(superposition,[status(thm)],[c_118,c_121]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(double_divide(X0,inverse(iPr_def_10(X1,X2))),iPr_def_10(X3,X0)) = double_divide(X2,inverse(double_divide(X1,double_divide(X4,double_divide(X3,X4))))),
inference(superposition,[status(thm)],[c_121,c_66]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,iPr_def_11(X1)),iPr_def_10(iPr_def_10(X2,X3),X0)) = iPr_def_10(double_divide(X1,X3),inverse(X2)),
inference(superposition,[status(thm)],[c_118,c_88]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(X0,double_divide(X1,inverse(double_divide(X2,double_divide(X3,iPr_def_10(X2,X1)))))) = double_divide(inverse(X0),iPr_def_11(X3)),
inference(superposition,[status(thm)],[c_118,c_83]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : double_divide(double_divide(X0,inverse(iPr_def_10(X1,X2))),iPr_def_10(double_divide(X3,iPr_def_11(X4)),X0)) = iPr_def_10(double_divide(X2,inverse(double_divide(X1,double_divide(X5,double_divide(X4,X5))))),X3),
inference(superposition,[status(thm)],[c_118,c_91]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(double_divide(X0,inverse(double_divide(X1,double_divide(X2,iPr_def_10(X1,X0))))),X3) = iPr_def_10(X2,X3),
inference(superposition,[status(thm)],[c_91,c_65]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(X0,X1),inverse(X2)) = double_divide(X0,iPr_def_10(X2,X1)),
inference(demodulation,[status(thm)],[c_269,c_165]) ).
tcf(c_420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(X0,double_divide(X1,inverse(double_divide(X2,double_divide(X3,iPr_def_10(X2,X1)))))) = iPr_def_10(X0,X3),
inference(demodulation,[status(thm)],[c_284,c_144]) ).
tcf(c_425,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,inverse(iPr_def_10(X1,X2))),iPr_def_10(X3,X0)) = iPr_def_12(X1,X2,X3),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_264]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(X2,double_divide(X3,X2))))) = iPr_def_12(X1,X0,X3),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_264]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,iPr_def_12(X1,X2,X0)) = iPr_def_10(X1,X2),
inference(demodulation,[status(thm)],[c_166,c_165,c_426]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_12(X0,X1,double_divide(X2,iPr_def_11(X3))) = iPr_def_10(iPr_def_12(X0,X1,X3),X2),
inference(demodulation,[status(thm)],[c_305,c_425,c_426]) ).
tcf(c_543,plain,
! [X0: $i,X1: $i] : iPr_def_12(X0,X1,inverse(X0)) = iPr_def_11(X1),
inference(demodulation,[status(thm)],[c_119,c_425]) ).
tcf(c_678,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(double_divide(X0,double_divide(X1,X0)),X2,iPr_def_11(X1)) = iPr_def_11(X2),
inference(superposition,[status(thm)],[c_118,c_543]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(double_divide(iPr_def_11(X0),iPr_def_10(X1,X0)),X2,iPr_def_11(inverse(X1))) = iPr_def_11(X2),
inference(superposition,[status(thm)],[c_239,c_543]) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i] : inverse(iPr_def_10(double_divide(iPr_def_11(X0),X0),X1)) = iPr_def_11(X1),
inference(superposition,[status(thm)],[c_256,c_118]) ).
tcf(c_1053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(double_divide(iPr_def_12(X0,X1,X2),iPr_def_10(X0,X1)),X3) = double_divide(iPr_def_11(X2),iPr_def_11(X3)),
inference(superposition,[status(thm)],[c_427,c_237]) ).
tcf(c_1063,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,iPr_def_10(X1,double_divide(X2,X0))) = double_divide(iPr_def_11(X2),iPr_def_11(inverse(X1))),
inference(superposition,[status(thm)],[c_237,c_419]) ).
tcf(c_1143,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(double_divide(X0,X1),X2,X0) = double_divide(X2,iPr_def_11(X1)),
inference(superposition,[status(thm)],[c_118,c_426]) ).
tcf(c_1158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(iPr_def_12(X2,X3,X4),iPr_def_10(X2,X3))))) = iPr_def_12(X1,X0,X4),
inference(superposition,[status(thm)],[c_427,c_426]) ).
tcf(c_1164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(iPr_def_12(X0,X1,X2),iPr_def_10(X0,X1)) = double_divide(X3,double_divide(X2,X3)),
inference(superposition,[status(thm)],[c_426,c_66]) ).
tcf(c_1252,plain,
! [X0: $i,X1: $i] : double_divide(X0,double_divide(X1,X0)) = iPr_def_13(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_1164]) ).
tcf(c_1253,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_12(X0,X1,X2),iPr_def_10(X0,X1)) = iPr_def_13(X2),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1164]) ).
tcf(c_1256,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_11(X0),iPr_def_11(X1)) = iPr_def_10(iPr_def_13(X0),X1),
inference(demodulation,[status(thm)],[c_1053,c_1253]) ).
tcf(c_1269,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(X1,iPr_def_13(X2)))) = iPr_def_12(X1,X0,X2),
inference(demodulation,[status(thm)],[c_1158,c_1253]) ).
tcf(c_1386,plain,
! [X0: $i] : inverse(iPr_def_13(X0)) = iPr_def_11(X0),
inference(demodulation,[status(thm)],[c_118,c_1252]) ).
tcf(c_2557,plain,
! [X0: $i,X1: $i] : double_divide(double_divide(X0,X1),iPr_def_13(X0)) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_1252,c_1252]) ).
tcf(c_2562,plain,
! [X0: $i,X1: $i] : iPr_def_10(double_divide(iPr_def_11(X0),X0),X1) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_1252,c_256]) ).
tcf(c_2576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,iPr_def_11(X1)),iPr_def_10(X2,X0)) = iPr_def_12(double_divide(iPr_def_11(X3),X3),X1,X2),
inference(superposition,[status(thm)],[c_1019,c_425]) ).
tcf(c_2597,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,iPr_def_11(double_divide(X1,X2))) = iPr_def_12(iPr_def_13(X1),X0,X2),
inference(superposition,[status(thm)],[c_1252,c_1143]) ).
tcf(c_2600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_12(double_divide(X0,X1),X2,double_divide(X3,iPr_def_11(X0))) = double_divide(X2,iPr_def_11(iPr_def_10(X1,X3))),
inference(superposition,[status(thm)],[c_165,c_1143]) ).
tcf(c_2609,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_11(X0),iPr_def_10(X1,X0)) = iPr_def_13(inverse(X1)),
inference(superposition,[status(thm)],[c_543,c_1253]) ).
tcf(c_2625,plain,
! [X0: $i,X1: $i] : iPr_def_12(iPr_def_13(X0),X1,iPr_def_11(X0)) = iPr_def_11(X1),
inference(superposition,[status(thm)],[c_1252,c_678]) ).
tcf(c_2724,plain,
! [X0: $i,X1: $i] : double_divide(X0,iPr_def_11(iPr_def_10(X1,inverse(X1)))) = iPr_def_11(X0),
inference(superposition,[status(thm)],[c_999,c_1143]) ).
tcf(c_2776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(double_divide(X0,inverse(double_divide(iPr_def_11(X1),iPr_def_11(inverse(X2))))),iPr_def_10(X3,X0)) = iPr_def_10(X2,double_divide(X1,X3)),
inference(superposition,[status(thm)],[c_1063,c_66]) ).
tcf(c_2810,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,iPr_def_11(iPr_def_10(X1,X2))) = iPr_def_10(double_divide(X0,iPr_def_11(X1)),X2),
inference(demodulation,[status(thm)],[c_2600,c_438,c_1143]) ).
tcf(c_2813,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(double_divide(iPr_def_11(X0),X0),X1,X2) = double_divide(X1,X2),
inference(demodulation,[status(thm)],[c_2576,c_165]) ).
tcf(c_2836,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(iPr_def_13(X0),inverse(X1),X2) = iPr_def_10(X1,double_divide(X0,X2)),
inference(demodulation,[status(thm)],[c_2776,c_425,c_1256]) ).
tcf(c_3038,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(iPr_def_13(iPr_def_11(X0)),X0),X1) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_1256,c_2562]) ).
tcf(c_3083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,iPr_def_11(iPr_def_10(X1,inverse(double_divide(X2,inverse(double_divide(X3,double_divide(X1,iPr_def_10(X3,X2))))))))) = iPr_def_11(X0),
inference(superposition,[status(thm)],[c_311,c_2724]) ).
tcf(c_3092,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_11(iPr_def_10(X0,inverse(X0))),iPr_def_11(X1)) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_2724,c_1252]) ).
tcf(c_3099,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,iPr_def_10(X1,inverse(X1))) = iPr_def_11(inverse(X0)),
inference(superposition,[status(thm)],[c_2724,c_144]) ).
tcf(c_3100,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_10(X0,inverse(X0)),X1) = double_divide(iPr_def_11(X2),iPr_def_10(X1,X2)),
inference(superposition,[status(thm)],[c_2724,c_165]) ).
tcf(c_3131,plain,
! [X0: $i,X1: $i] : double_divide(X0,inverse(double_divide(iPr_def_11(X1),X1))) = iPr_def_11(X0),
inference(superposition,[status(thm)],[c_2813,c_543]) ).
tcf(c_3163,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_12(iPr_def_13(X0),X1,X2),iPr_def_13(X1)) = iPr_def_13(iPr_def_11(double_divide(X0,X2))),
inference(superposition,[status(thm)],[c_2597,c_2557]) ).
tcf(c_3204,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,double_divide(X1,iPr_def_11(X1))) = iPr_def_11(inverse(X0)),
inference(superposition,[status(thm)],[c_2836,c_2625]) ).
tcf(c_3282,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_13(iPr_def_10(X0,inverse(X0))),X1) = iPr_def_13(X1),
inference(demodulation,[status(thm)],[c_3092,c_1256]) ).
tcf(c_3289,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_10(X0,inverse(X0)),X1) = iPr_def_13(inverse(X1)),
inference(demodulation,[status(thm)],[c_3100,c_2609]) ).
tcf(c_3338,plain,
! [X0: $i,X1: $i] : double_divide(X0,iPr_def_10(X1,iPr_def_11(X1))) = iPr_def_11(X0),
inference(demodulation,[status(thm)],[c_3083,c_311,c_419,c_2810]) ).
tcf(c_5536,plain,
! [X0: $i,X1: $i] : iPr_def_11(double_divide(iPr_def_11(X0),iPr_def_11(X1))) = double_divide(X1,X0),
inference(superposition,[status(thm)],[c_3338,c_165]) ).
tcf(c_5537,plain,
! [X0: $i] : iPr_def_11(iPr_def_11(iPr_def_11(X0))) = iPr_def_13(inverse(X0)),
inference(superposition,[status(thm)],[c_3338,c_2609]) ).
tcf(c_5543,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_12(X0,iPr_def_11(X0),X1)) = iPr_def_13(X1),
inference(superposition,[status(thm)],[c_3338,c_1253]) ).
tcf(c_5582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_13(double_divide(X0,inverse(double_divide(X1,double_divide(X2,iPr_def_10(X1,X0)))))) = iPr_def_10(iPr_def_10(iPr_def_13(iPr_def_11(X3)),X3),X2),
inference(superposition,[status(thm)],[c_3038,c_420]) ).
tcf(c_5632,plain,
! [X0: $i,X1: $i] : double_divide(iPr_def_11(X0),iPr_def_10(iPr_def_11(X1),X0)) = X1,
inference(superposition,[status(thm)],[c_3131,c_66]) ).
tcf(c_5645,plain,
! [X0: $i,X1: $i] : iPr_def_12(iPr_def_11(iPr_def_13(X0)),X1,X0) = iPr_def_11(X1),
inference(superposition,[status(thm)],[c_3131,c_1269]) ).
tcf(c_5670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_11(inverse(double_divide(X0,inverse(double_divide(X1,double_divide(X2,iPr_def_10(X1,X0))))))) = iPr_def_10(X2,double_divide(X3,iPr_def_11(X3))),
inference(superposition,[status(thm)],[c_3204,c_311]) ).
tcf(c_5690,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(iPr_def_12(iPr_def_13(iPr_def_10(X0,inverse(X0))),X1,X2),iPr_def_13(X1)) = iPr_def_13(X2),
inference(superposition,[status(thm)],[c_3282,c_1253]) ).
tcf(c_5752,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(X0,X1),iPr_def_10(X2,inverse(X2))) = double_divide(X0,iPr_def_13(inverse(iPr_def_11(X1)))),
inference(superposition,[status(thm)],[c_3289,c_256]) ).
tcf(c_5772,plain,
! [X0: $i] : iPr_def_13(inverse(iPr_def_11(X0))) = X0,
inference(demodulation,[status(thm)],[c_5632,c_2609]) ).
tcf(c_5773,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_10(iPr_def_13(X0),X1)) = double_divide(X1,X0),
inference(demodulation,[status(thm)],[c_5536,c_1256]) ).
tcf(c_5798,plain,
! [X0: $i] : iPr_def_13(iPr_def_11(iPr_def_13(inverse(X0)))) = iPr_def_13(X0),
inference(demodulation,[status(thm)],[c_5690,c_3163,c_3289]) ).
tcf(c_5809,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(double_divide(X0,X1),iPr_def_10(X2,inverse(X2))) = double_divide(X0,X1),
inference(demodulation,[status(thm)],[c_5752,c_5772]) ).
tcf(c_5810,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(double_divide(X0,X1))) = double_divide(X0,X1),
inference(demodulation,[status(thm)],[c_5809,c_3099]) ).
tcf(c_5884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(X2,iPr_def_10(X1,X0))))) = iPr_def_10(X2,double_divide(X3,iPr_def_11(X3))),
inference(demodulation,[status(thm)],[c_5670,c_5810]) ).
tcf(c_5885,plain,
! [X0: $i,X1: $i,X2: $i] : double_divide(X0,inverse(double_divide(X1,double_divide(X2,iPr_def_10(X1,X0))))) = iPr_def_11(inverse(X2)),
inference(demodulation,[status(thm)],[c_5884,c_3204]) ).
tcf(c_5898,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(iPr_def_13(iPr_def_11(X0)),X0),X1) = iPr_def_13(iPr_def_11(inverse(X1))),
inference(demodulation,[status(thm)],[c_5582,c_5885]) ).
tcf(c_5899,plain,
! [X0: $i] : iPr_def_13(iPr_def_11(inverse(X0))) = iPr_def_13(X0),
inference(demodulation,[status(thm)],[c_5898,c_3038]) ).
tcf(c_6126,plain,
! [X0: $i] : iPr_def_11(inverse(iPr_def_11(X0))) = inverse(X0),
inference(superposition,[status(thm)],[c_5772,c_1386]) ).
tcf(c_6182,plain,
! [X0: $i] : iPr_def_11(iPr_def_11(inverse(X0))) = inverse(iPr_def_13(X0)),
inference(superposition,[status(thm)],[c_5899,c_1386]) ).
tcf(c_6185,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_11(inverse(double_divide(iPr_def_10(X0,X1),X2)))) = iPr_def_13(inverse(double_divide(X1,inverse(double_divide(X0,X2))))),
inference(superposition,[status(thm)],[c_164,c_5537]) ).
tcf(c_6207,plain,
! [X0: $i] : iPr_def_13(iPr_def_11(iPr_def_13(iPr_def_11(X0)))) = iPr_def_13(iPr_def_13(X0)),
inference(superposition,[status(thm)],[c_1386,c_5798]) ).
tcf(c_6256,plain,
! [X0: $i] : iPr_def_11(iPr_def_11(iPr_def_11(iPr_def_11(iPr_def_13(X0))))) = iPr_def_13(X0),
inference(superposition,[status(thm)],[c_5645,c_5543]) ).
tcf(c_6276,plain,
! [X0: $i,X1: $i] : iPr_def_13(inverse(double_divide(X0,X1))) = iPr_def_10(iPr_def_13(X1),X0),
inference(superposition,[status(thm)],[c_5773,c_5772]) ).
tcf(c_6331,plain,
! [X0: $i] : iPr_def_11(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_106,c_5810]) ).
tcf(c_6375,plain,
! [X0: $i] : inverse(X0) = iPr_def_11(X0),
inference(demodulation,[status(thm)],[c_6126,c_6331]) ).
tcf(c_6377,plain,
! [X0: $i] : iPr_def_11(iPr_def_13(X0)) = iPr_def_11(X0),
inference(demodulation,[status(thm)],[c_6182,c_6331,c_6375]) ).
tcf(c_6380,plain,
! [X0: $i] : iPr_def_11(iPr_def_11(iPr_def_11(iPr_def_11(X0)))) = iPr_def_13(X0),
inference(demodulation,[status(thm)],[c_6256,c_6377]) ).
tcf(c_6381,plain,
! [X0: $i] : iPr_def_13(X0) = X0,
inference(demodulation,[status(thm)],[c_6380,c_5537,c_5772]) ).
tcf(c_6383,plain,
! [X0: $i] : iPr_def_11(iPr_def_11(X0)) = X0,
inference(demodulation,[status(thm)],[c_6207,c_6377,c_6381]) ).
tcf(c_6391,plain,
! [X0: $i,X1: $i] : iPr_def_11(double_divide(X0,X1)) = iPr_def_10(X1,X0),
inference(demodulation,[status(thm)],[c_6276,c_6375,c_6381]) ).
tcf(c_6462,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(X0,X1),X2) = iPr_def_10(X0,iPr_def_10(X1,X2)),
inference(demodulation,[status(thm)],[c_6185,c_6375,c_6381,c_6383,c_6391]) ).
tcf(c_6501,plain,
inverse(double_divide(inverse(double_divide(c3,b3)),a3)) != inverse(double_divide(c3,iPr_def_11(double_divide(b3,a3)))),
inference(demodulation,[status(thm)],[c_53,c_6375]) ).
tcf(c_6506,plain,
$false,
inference(ground_joinability,[status(thm)],[c_6501,c_6375,c_6391,c_6462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP504-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/10.39 % Computer : n004.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Wed Sep 23 14:56:18 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.43 Running UEQ theorem proving
% 0.14/10.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.44
% 0.14/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.44
% 0.14/10.44 % Detected problem language: tptp
% 0.14/10.45 % Proving...
% 8.52/11.80 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.52/11.80 % SZS status Started for theBenchmark.p
% 8.52/11.80 % SZS status Unsatisfiable for theBenchmark.p
% 8.52/11.80
% 8.52/11.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.52/11.80
% 8.52/11.80 % ------ iProver source info
% 8.52/11.80
% 8.52/11.80 % git: date: 2026-07-19 20:42:38 +0200
% 8.52/11.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.52/11.80 % git: non_committed_changes: false
% 8.52/11.80
% 8.52/11.80 % ------ Parsing...% successful
% 8.52/11.80
% 8.52/11.80
% 8.52/11.80 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 8.52/11.80 % ------ Proving...
% 8.52/11.80 % ------ Problem Properties
% 8.52/11.80
% 8.52/11.80 %
% 8.52/11.80 % clauses 2
% 8.52/11.80 % conjectures 1
% 8.52/11.80 % EPR 0
% 8.52/11.80 % Horn 2
% 8.52/11.80 % unary 2
% 8.52/11.80 % binary 0
% 8.52/11.80 % lits 2
% 8.52/11.80 % lits eq 2
% 8.52/11.80 % fd_pure 0
% 8.52/11.80 % fd_pseudo 0
% 8.52/11.80 % fd_cond 0
% 8.52/11.80 % fd_pseudo_cond 0
% 8.52/11.80 % AC symbols 0
% 8.52/11.80
% 8.52/11.80 % ------ Input Options Time Limit: Unbounded
% 8.52/11.80
% 8.52/11.80
% 8.52/11.80 % ------
% 8.52/11.80 % Current options:
% 8.52/11.80 % ------
% 8.52/11.80
% 8.52/11.80
% 8.52/11.80 %
% 8.52/11.80
% 8.52/11.80 % ------ Proving...
% 8.52/11.80 %
% 8.52/11.80
% 8.52/11.80 % SZS status Unsatisfiable for theBenchmark.p
% 8.52/11.80
% 8.52/11.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.52/11.81
% 8.52/11.81
%------------------------------------------------------------------------------