%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP412-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:33:38 PM UTC 2026
% Result : Unsatisfiable 2.44s 0.70s
% Output : CNFRefutation 2.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 57 unt; 4 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 17 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : multiply(A,inverse(multiply(multiply(multiply(inverse(B),B),inverse(multiply(inverse(multiply(A,inverse(B))),C))),B))) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X0,inverse(X1))),X2))),X1))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f7,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f8,definition,
sF2_fnc = multiply(sF3_fnc,b1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f9,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f4,f8,f7,f6,f5]) ).
fof(f10,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(multiply(sF3_fnc,b1),inverse(multiply(inverse(multiply(X0,inverse(b1))),X1))),b1))) = X1,
inference(paramodulation,[status(thm)],[f7,f3]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(multiply(sF1_fnc,a1),inverse(multiply(inverse(multiply(X0,inverse(a1))),X1))),a1))) = X1,
inference(paramodulation,[status(thm)],[f5,f3]) ).
fof(f12,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1))) = inverse(multiply(multiply(multiply(inverse(X3),X3),inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),inverse(X3))),X2))),X3)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f16,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF2_fnc,inverse(multiply(inverse(multiply(X0,inverse(b1))),X1))),b1))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f10]) ).
fof(f17,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF2_fnc,inverse(multiply(inverse(multiply(X0,sF3_fnc)),X1))),b1))) = X1,
inference(forward_demodulation,[status(thm)],[f7,f16]) ).
fof(f18,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,inverse(a1))),X1))),a1))) = X1,
inference(forward_demodulation,[status(thm)],[f6,f11]) ).
fof(f19,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,sF1_fnc)),X1))),a1))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f18]) ).
fof(f24,plain,
! [X0,X1] : multiply(X0,inverse(multiply(multiply(sF2_fnc,inverse(X1)),b1))) = inverse(multiply(multiply(sF2_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X0,sF3_fnc)),sF3_fnc)),X1))),b1)),
inference(paramodulation,[status(thm)],[f17,f17]) ).
fof(f27,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(multiply(inverse(multiply(multiply(sF2_fnc,inverse(multiply(inverse(multiply(X0,sF3_fnc)),X1))),b1)),multiply(multiply(sF2_fnc,inverse(multiply(inverse(multiply(X0,sF3_fnc)),X1))),b1)),inverse(multiply(inverse(X1),X2))),multiply(multiply(sF2_fnc,inverse(multiply(inverse(multiply(X0,sF3_fnc)),X1))),b1)))) = X2,
inference(paramodulation,[status(thm)],[f17,f3]) ).
fof(f32,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1))) = inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(X1))),sF1_fnc)),X2))),a1)),
inference(paramodulation,[status(thm)],[f19,f3]) ).
fof(f37,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF3_fnc)),multiply(X0,inverse(multiply(multiply(sF2_fnc,inverse(X1)),b1)))) = X1,
inference(paramodulation,[status(thm)],[f24,f17]) ).
fof(f45,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF3_fnc)),multiply(X0,inverse(multiply(X1,b1)))) = multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(sF2_fnc,sF1_fnc)),X1))),a1),
inference(paramodulation,[status(thm)],[f19,f37]) ).
fof(f49,plain,
! [X0] : multiply(inverse(multiply(X0,sF3_fnc)),multiply(X0,inverse(multiply(multiply(sF2_fnc,sF3_fnc),b1)))) = b1,
inference(paramodulation,[status(thm)],[f7,f37]) ).
fof(f50,plain,
! [X0] : multiply(inverse(multiply(X0,sF3_fnc)),multiply(X0,inverse(multiply(multiply(sF2_fnc,sF1_fnc),b1)))) = a1,
inference(paramodulation,[status(thm)],[f5,f37]) ).
fof(f59,plain,
a1 = multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(sF2_fnc,sF1_fnc)),multiply(sF2_fnc,sF1_fnc)))),a1),
inference(paramodulation,[status(thm)],[f50,f45]) ).
fof(f60,plain,
b1 = multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(sF2_fnc,sF1_fnc)),multiply(sF2_fnc,sF3_fnc)))),a1),
inference(paramodulation,[status(thm)],[f49,f45]) ).
fof(f95,plain,
! [X0,X1,X2,X3] : X0 = inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(inverse(multiply(X2,inverse(X3))),inverse(X1))),multiply(inverse(multiply(X2,inverse(X3))),X0)))),X1)),
inference(paramodulation,[status(thm)],[f3,f12]) ).
fof(f149,plain,
! [X0,X1,X2] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(X2)),X1)))) = X2,
inference(paramodulation,[status(thm)],[f12,f3]) ).
fof(f511,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(multiply(multiply(multiply(inverse(a1),a1),inverse(X1)),a1)))) = X1,
inference(paramodulation,[status(thm)],[f5,f149]) ).
fof(f540,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(multiply(multiply(multiply(sF1_fnc,a1),inverse(X1)),a1)))) = X1,
inference(forward_demodulation,[status(thm)],[f5,f511]) ).
fof(f541,plain,
! [X0,X1] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(multiply(multiply(sF0_fnc,inverse(X1)),a1)))) = X1,
inference(forward_demodulation,[status(thm)],[f6,f540]) ).
fof(f556,plain,
! [X0] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(b1))) = multiply(inverse(multiply(sF2_fnc,sF1_fnc)),multiply(sF2_fnc,sF3_fnc)),
inference(paramodulation,[status(thm)],[f60,f541]) ).
fof(f557,plain,
! [X0] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,inverse(a1))) = multiply(inverse(multiply(sF2_fnc,sF1_fnc)),multiply(sF2_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f59,f541]) ).
fof(f572,plain,
! [X0] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF3_fnc)) = multiply(inverse(multiply(sF2_fnc,sF1_fnc)),multiply(sF2_fnc,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f7,f556]) ).
fof(f573,plain,
! [X0] : multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF1_fnc)) = multiply(inverse(multiply(sF2_fnc,sF1_fnc)),multiply(sF2_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f5,f557]) ).
fof(f694,plain,
! [X0] : b1 = multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF3_fnc)))),a1),
inference(paramodulation,[status(thm)],[f572,f60]) ).
fof(f1276,plain,
! [X0] : a1 = multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF1_fnc)))),a1),
inference(paramodulation,[status(thm)],[f573,f59]) ).
fof(f2548,plain,
! [X0,X1,X2] : X0 = inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(multiply(sF2_fnc,inverse(multiply(inverse(multiply(X1,sF3_fnc)),X2))),b1)))),sF1_fnc)),multiply(inverse(X2),X0)))),a1)),
inference(paramodulation,[status(thm)],[f27,f32]) ).
fof(f2727,plain,
! [X0,X1] : X0 = inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(inverse(X1),sF1_fnc)),multiply(inverse(X1),X0)))),a1)),
inference(forward_demodulation,[status(thm)],[f17,f2548]) ).
fof(f3178,plain,
! [X0,X1,X2] : X0 = inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X1,sF1_fnc)),multiply(inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(inverse(X2),sF1_fnc)),multiply(inverse(X2),X1)))),a1)),X0)))),a1)),
inference(paramodulation,[status(thm)],[f2727,f2727]) ).
fof(f3278,plain,
! [X0,X1] : X0 = inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X1,sF1_fnc)),multiply(X1,X0)))),a1)),
inference(forward_demodulation,[status(thm)],[f2727,f3178]) ).
fof(f3370,plain,
! [X0,X1] : X0 = inverse(multiply(inverse(multiply(X1,sF3_fnc)),multiply(X1,inverse(multiply(multiply(sF2_fnc,X0),b1))))),
inference(paramodulation,[status(thm)],[f45,f3278]) ).
fof(f4510,plain,
! [X0,X1,X2,X3,X4,X5] : X0 = inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(inverse(multiply(multiply(multiply(inverse(inverse(X3)),inverse(X3)),inverse(multiply(inverse(multiply(inverse(multiply(X4,inverse(X5))),inverse(inverse(X3)))),multiply(inverse(multiply(X4,inverse(X5))),X2)))),inverse(X3))),X0)))),X1)),
inference(paramodulation,[status(thm)],[f95,f95]) ).
fof(f4727,plain,
! [X0,X1,X2] : X0 = inverse(multiply(multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,X0)))),X1)),
inference(forward_demodulation,[status(thm)],[f95,f4510]) ).
fof(f8923,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,X2)) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f4727,f149]) ).
fof(f9265,plain,
! [X0,X1,X2,X3,X4] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,inverse(multiply(inverse(multiply(X4,sF3_fnc)),multiply(X4,inverse(multiply(multiply(sF2_fnc,X1),b1))))))),multiply(X3,X2)),
inference(paramodulation,[status(thm)],[f3370,f8923]) ).
fof(f9549,plain,
! [X0,X1,X2,X3] : multiply(inverse(multiply(X0,X1)),multiply(X0,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(forward_demodulation,[status(thm)],[f3370,f9265]) ).
fof(f9673,plain,
! [X0,X1] : multiply(inverse(sF0_fnc),multiply(sF1_fnc,X0)) = multiply(inverse(multiply(X1,a1)),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f6,f9549]) ).
fof(f11991,plain,
! [X0] : multiply(inverse(sF0_fnc),multiply(sF1_fnc,a1)) = multiply(inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF1_fnc)))),a1)),a1),
inference(paramodulation,[status(thm)],[f1276,f9673]) ).
fof(f11992,plain,
! [X0] : multiply(inverse(sF0_fnc),multiply(sF1_fnc,a1)) = multiply(inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF3_fnc)))),a1)),b1),
inference(paramodulation,[status(thm)],[f694,f9673]) ).
fof(f12117,plain,
! [X0] : multiply(inverse(sF0_fnc),sF0_fnc) = multiply(inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF1_fnc)))),a1)),a1),
inference(forward_demodulation,[status(thm)],[f6,f11991]) ).
fof(f12118,plain,
multiply(inverse(sF0_fnc),sF0_fnc) = multiply(sF1_fnc,a1),
inference(forward_demodulation,[status(thm)],[f3278,f12117]) ).
fof(f12119,plain,
multiply(inverse(sF0_fnc),sF0_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f6,f12118]) ).
fof(f12120,plain,
! [X0] : multiply(inverse(sF0_fnc),sF0_fnc) = multiply(inverse(multiply(multiply(sF0_fnc,inverse(multiply(inverse(multiply(X0,sF1_fnc)),multiply(X0,sF3_fnc)))),a1)),b1),
inference(forward_demodulation,[status(thm)],[f6,f11992]) ).
fof(f12121,plain,
multiply(inverse(sF0_fnc),sF0_fnc) = multiply(sF3_fnc,b1),
inference(forward_demodulation,[status(thm)],[f3278,f12120]) ).
fof(f12122,plain,
multiply(inverse(sF0_fnc),sF0_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f8,f12121]) ).
fof(f12242,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f12119,f12122]) ).
fof(f12243,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12242,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP412-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 20 20:12:22 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 % Drodi V4.1.1
% 2.44/0.70 % Refutation found
% 2.44/0.70 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.44/0.70 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.44/0.74 % Elapsed time: 0.415075 seconds
% 2.44/0.74 % CPU time: 3.136103 seconds
% 2.44/0.74 % Total memory used: 195.596 MB
% 2.44/0.74 % Net memory used: 194.629 MB
%------------------------------------------------------------------------------