%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP615-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Sep 24 12:34:48 PM UTC 2026
% Result : Unsatisfiable 7.98s 1.43s
% Output : CNFRefutation 7.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 86 ( 86 unt; 4 def)
% Number of atoms : 86 ( 85 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 152 ( 152 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(inverse(double_divide(inverse(double_divide(X0,inverse(X1))),X2)),double_divide(X0,X2)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f8,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f9,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f10,definition,
sF2_fnc = multiply(a3,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f11,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f6,f10,f9,f8,f7]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(multiply(X0,inverse(double_divide(X1,inverse(X2)))),double_divide(X1,X0)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(multiply(X0,multiply(inverse(X1),X2)),double_divide(X2,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : double_divide(multiply(X0,multiply(multiply(X1,X2),X3)),double_divide(X3,X0)) = double_divide(X2,X1),
inference(paramodulation,[status(thm)],[f5,f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : double_divide(multiply(double_divide(X0,X1),multiply(inverse(X2),multiply(X1,multiply(inverse(X3),X0)))),X3) = X2,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(double_divide(X0,X1),multiply(X1,multiply(inverse(X2),X0))) = inverse(X2),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(X1,X2),multiply(inverse(X3),multiply(X2,multiply(inverse(X0),X1))))) = inverse(X3),
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f20,plain,
! [X0,X1,X2] : double_divide(inverse(X0),double_divide(multiply(inverse(X0),X1),double_divide(X1,inverse(X2)))) = X2,
inference(paramodulation,[status(thm)],[f16,f13]) ).
fof(f24,plain,
! [X0,X1] : double_divide(multiply(X0,multiply(sF3_fnc,X1)),double_divide(X1,X0)) = double_divide(c3,b3),
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f25,plain,
! [X0,X1] : double_divide(multiply(X0,multiply(sF0_fnc,X1)),double_divide(X1,X0)) = double_divide(c3,sF1_fnc),
inference(paramodulation,[status(thm)],[f8,f14]) ).
fof(f27,plain,
! [X0,X1] : double_divide(multiply(X0,multiply(sF1_fnc,X1)),double_divide(X1,X0)) = double_divide(b3,a3),
inference(paramodulation,[status(thm)],[f7,f14]) ).
fof(f42,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF3_fnc,X0))) = inverse(double_divide(c3,b3)),
inference(paramodulation,[status(thm)],[f24,f5]) ).
fof(f43,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF3_fnc,X0))) = multiply(b3,c3),
inference(forward_demodulation,[status(thm)],[f5,f42]) ).
fof(f44,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF3_fnc,X0))) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f9,f43]) ).
fof(f48,plain,
! [X0] : multiply(double_divide(multiply(sF3_fnc,X0),double_divide(X0,sF3_fnc)),sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f44,f44]) ).
fof(f77,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF0_fnc,X0))) = inverse(double_divide(c3,sF1_fnc)),
inference(paramodulation,[status(thm)],[f25,f5]) ).
fof(f78,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF0_fnc,X0))) = multiply(sF1_fnc,c3),
inference(forward_demodulation,[status(thm)],[f5,f77]) ).
fof(f79,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF0_fnc,X0))) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f8,f78]) ).
fof(f85,plain,
! [X0] : multiply(double_divide(multiply(sF0_fnc,X0),double_divide(X0,sF0_fnc)),sF0_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f79,f79]) ).
fof(f151,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF1_fnc,X0))) = inverse(double_divide(b3,a3)),
inference(paramodulation,[status(thm)],[f27,f5]) ).
fof(f152,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF1_fnc,X0))) = multiply(a3,b3),
inference(forward_demodulation,[status(thm)],[f5,f151]) ).
fof(f153,plain,
! [X0,X1] : multiply(double_divide(X0,X1),multiply(X1,multiply(sF1_fnc,X0))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f7,f152]) ).
fof(f185,plain,
! [X0] : multiply(double_divide(multiply(sF1_fnc,X0),double_divide(X0,sF1_fnc)),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f153,f153]) ).
fof(f348,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(double_divide(multiply(X1,multiply(inverse(inverse(X2)),X3)),double_divide(X3,X1)),inverse(X0))) = inverse(X2),
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f369,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(X0),double_divide(multiply(double_divide(X1,X2),multiply(inverse(X0),multiply(X2,multiply(inverse(sF0_fnc),X1)))),sF0_fnc)),sF0_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f17,f85]) ).
fof(f375,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(X0),double_divide(multiply(double_divide(X1,X2),multiply(inverse(X0),multiply(X2,multiply(inverse(sF3_fnc),X1)))),sF3_fnc)),sF3_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f17,f48]) ).
fof(f379,plain,
! [X0,X1,X2,X3] : double_divide(multiply(double_divide(multiply(X0,multiply(inverse(inverse(X1)),X2)),double_divide(X2,X0)),inverse(X3)),X3) = X1,
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f383,plain,
! [X0,X1,X2] : multiply(double_divide(inverse(X0),double_divide(multiply(double_divide(X1,X2),multiply(inverse(X0),multiply(X2,multiply(inverse(sF1_fnc),X1)))),sF1_fnc)),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f17,f185]) ).
fof(f387,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),inverse(X0))) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f13,f348]) ).
fof(f390,plain,
! [X0] : multiply(double_divide(inverse(X0),X0),sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f15,f369]) ).
fof(f391,plain,
! [X0] : multiply(double_divide(inverse(X0),X0),sF3_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f15,f375]) ).
fof(f392,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X1) = X0,
inference(forward_demodulation,[status(thm)],[f13,f379]) ).
fof(f393,plain,
! [X0] : multiply(double_divide(inverse(X0),X0),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f15,f383]) ).
fof(f411,plain,
! [X0,X1,X2] : double_divide(multiply(X0,multiply(sF0_fnc,X1)),double_divide(X1,X0)) = double_divide(sF0_fnc,double_divide(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f390,f14]) ).
fof(f412,plain,
! [X0] : double_divide(c3,sF1_fnc) = double_divide(sF0_fnc,double_divide(inverse(X0),X0)),
inference(forward_demodulation,[status(thm)],[f25,f411]) ).
fof(f414,plain,
! [X0,X1,X2] : double_divide(multiply(X0,multiply(sF3_fnc,X1)),double_divide(X1,X0)) = double_divide(sF3_fnc,double_divide(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f391,f14]) ).
fof(f415,plain,
! [X0] : double_divide(c3,b3) = double_divide(sF3_fnc,double_divide(inverse(X0),X0)),
inference(forward_demodulation,[status(thm)],[f24,f414]) ).
fof(f416,plain,
! [X0,X1] : multiply(double_divide(multiply(X0,X1),double_divide(X1,X0)),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f5,f393]) ).
fof(f417,plain,
! [X0,X1,X2] : double_divide(multiply(X0,multiply(sF1_fnc,X1)),double_divide(X1,X0)) = double_divide(sF1_fnc,double_divide(inverse(X2),X2)),
inference(paramodulation,[status(thm)],[f393,f14]) ).
fof(f418,plain,
! [X0] : double_divide(b3,a3) = double_divide(sF1_fnc,double_divide(inverse(X0),X0)),
inference(forward_demodulation,[status(thm)],[f27,f417]) ).
fof(f714,plain,
! [X0] : multiply(double_divide(sF3_fnc,double_divide(sF3_fnc,double_divide(inverse(X0),X0))),sF1_fnc) = sF1_fnc,
inference(paramodulation,[status(thm)],[f391,f416]) ).
fof(f766,plain,
multiply(double_divide(sF3_fnc,double_divide(c3,b3)),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f415,f714]) ).
fof(f1006,plain,
! [X0,X1,X2] : double_divide(multiply(multiply(X0,X1),inverse(X2)),X2) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f5,f392]) ).
fof(f1007,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),multiply(X1,X2)),double_divide(X2,X1)) = X0,
inference(paramodulation,[status(thm)],[f5,f392]) ).
fof(f1042,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X1,X2),inverse(X0))) = inverse(double_divide(X2,X1)),
inference(paramodulation,[status(thm)],[f5,f387]) ).
fof(f1075,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(inverse(X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f387,f13]) ).
fof(f1082,plain,
! [X0,X1,X2] : multiply(X0,multiply(multiply(X1,X2),inverse(X0))) = multiply(X1,X2),
inference(forward_demodulation,[status(thm)],[f5,f1042]) ).
fof(f1089,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(inverse(X2),X2)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f5,f1075]) ).
fof(f2551,plain,
! [X0,X1] : double_divide(multiply(sF0_fnc,inverse(X0)),X0) = double_divide(sF0_fnc,double_divide(inverse(X1),X1)),
inference(paramodulation,[status(thm)],[f390,f1006]) ).
fof(f2641,plain,
! [X0] : double_divide(multiply(sF0_fnc,inverse(X0)),X0) = double_divide(c3,sF1_fnc),
inference(forward_demodulation,[status(thm)],[f412,f2551]) ).
fof(f2810,plain,
! [X0] : multiply(X0,multiply(sF1_fnc,inverse(X0))) = multiply(double_divide(sF3_fnc,double_divide(c3,b3)),sF1_fnc),
inference(paramodulation,[status(thm)],[f766,f1082]) ).
fof(f2926,plain,
! [X0] : multiply(X0,multiply(sF1_fnc,inverse(X0))) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f766,f2810]) ).
fof(f3023,plain,
! [X0] : double_divide(sF1_fnc,double_divide(inverse(inverse(X0)),sF1_fnc)) = X0,
inference(paramodulation,[status(thm)],[f2926,f1007]) ).
fof(f5430,plain,
! [X0,X1] : X0 = double_divide(multiply(X1,inverse(X1)),inverse(X0)),
inference(paramodulation,[status(thm)],[f1007,f1089]) ).
fof(f5737,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,inverse(X1))) = inverse(X0),
inference(paramodulation,[status(thm)],[f5430,f5]) ).
fof(f5985,plain,
! [X0,X1,X2] : double_divide(inverse(X0),double_divide(inverse(X0),double_divide(multiply(X1,inverse(X1)),inverse(X2)))) = X2,
inference(paramodulation,[status(thm)],[f5737,f20]) ).
fof(f6050,plain,
! [X0,X1] : double_divide(inverse(X0),double_divide(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f5430,f5985]) ).
fof(f6074,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(inverse(double_divide(X1,X0)),X2)) = X2,
inference(paramodulation,[status(thm)],[f5,f6050]) ).
fof(f6129,plain,
! [X0,X1,X2] : double_divide(multiply(X0,X1),double_divide(multiply(X0,X1),X2)) = X2,
inference(forward_demodulation,[status(thm)],[f5,f6074]) ).
fof(f8347,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X0) = X1,
inference(paramodulation,[status(thm)],[f392,f6129]) ).
fof(f9640,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f5430,f8347]) ).
fof(f9741,plain,
! [X0] : double_divide(sF1_fnc,double_divide(X0,sF1_fnc)) = X0,
inference(backward_demodulation,[status(thm)],[f9640,f3023]) ).
fof(f9771,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f9640,f5737]) ).
fof(f9855,plain,
! [X0,X1] : multiply(X0,multiply(X1,inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f9640,f9771]) ).
fof(f10557,plain,
double_divide(b3,a3) = inverse(sF1_fnc),
inference(paramodulation,[status(thm)],[f418,f9741]) ).
fof(f10564,plain,
double_divide(sF1_fnc,double_divide(c3,sF1_fnc)) = multiply(sF0_fnc,inverse(sF1_fnc)),
inference(paramodulation,[status(thm)],[f2641,f9741]) ).
fof(f10638,plain,
c3 = multiply(sF0_fnc,inverse(sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f9741,f10564]) ).
fof(f11233,plain,
! [X0,X1] : double_divide(X0,double_divide(inverse(inverse(X1)),X0)) = X1,
inference(paramodulation,[status(thm)],[f9855,f13]) ).
fof(f11306,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f9640,f11233]) ).
fof(f11386,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f11306,f11306]) ).
fof(f14637,plain,
double_divide(inverse(sF1_fnc),b3) = a3,
inference(paramodulation,[status(thm)],[f10557,f11386]) ).
fof(f19852,plain,
multiply(a3,multiply(b3,multiply(sF0_fnc,inverse(sF1_fnc)))) = sF0_fnc,
inference(paramodulation,[status(thm)],[f14637,f79]) ).
fof(f19875,plain,
multiply(a3,multiply(b3,c3)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f10638,f19852]) ).
fof(f19876,plain,
multiply(a3,sF3_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f9,f19875]) ).
fof(f19877,plain,
sF2_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f10,f19876]) ).
fof(f19878,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f19877,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP615-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:20:28 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 7.98/1.43 % Refutation found
% 7.98/1.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.98/1.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.98/1.49 % Elapsed time: 1.109316 seconds
% 7.98/1.49 % CPU time: 8.548006 seconds
% 7.98/1.49 % Total memory used: 195.456 MB
% 7.98/1.49 % Net memory used: 189.960 MB
%------------------------------------------------------------------------------