%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP478-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:34:29 PM UTC 2026
% Result : Unsatisfiable 0.15s 6.04s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 59 unt; 4 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% 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 : 157 ( 157 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : divide(inverse(divide(divide(divide(A,A),B),divide(C,divide(B,D)))),D) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,inverse(B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X0),X1),divide(X2,divide(X1,X3)))),X3) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f8,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f9,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f10,definition,
sF2_fnc = multiply(sF3_fnc,b1),
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,X3,X4,X5] : divide(inverse(divide(divide(divide(X0,X0),X1),X2)),X3) = inverse(divide(divide(divide(X4,X4),X5),divide(X2,divide(X5,divide(X1,X3))))),
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f15,plain,
! [X0] : multiply(X0,b1) = divide(X0,sF3_fnc),
inference(paramodulation,[status(thm)],[f9,f5]) ).
fof(f16,plain,
! [X0] : multiply(X0,a1) = divide(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f24,plain,
sF2_fnc = divide(sF3_fnc,sF3_fnc),
inference(backward_demodulation,[status(thm)],[f15,f10]) ).
fof(f25,plain,
! [X0,X1] : divide(inverse(divide(divide(divide(X0,X0),sF3_fnc),divide(X1,sF2_fnc))),sF3_fnc) = X1,
inference(paramodulation,[status(thm)],[f24,f4]) ).
fof(f26,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(sF2_fnc,X0),divide(X1,divide(X0,X2)))),X2) = X1,
inference(paramodulation,[status(thm)],[f24,f4]) ).
fof(f27,plain,
sF0_fnc = divide(sF1_fnc,sF1_fnc),
inference(backward_demodulation,[status(thm)],[f16,f8]) ).
fof(f29,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(sF0_fnc,X0),divide(X1,divide(X0,X2)))),X2) = X1,
inference(paramodulation,[status(thm)],[f27,f4]) ).
fof(f32,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(sF2_fnc,X0),X1)),X2) = inverse(divide(divide(sF2_fnc,X3),divide(X1,divide(X3,divide(X0,X2))))),
inference(paramodulation,[status(thm)],[f26,f26]) ).
fof(f122,plain,
! [X0,X1,X2,X3,X4,X5,X6] : divide(inverse(divide(divide(divide(X0,X0),X1),inverse(divide(divide(sF0_fnc,X2),divide(X3,divide(X2,divide(X4,divide(X1,X5)))))))),X5) = inverse(divide(divide(divide(X6,X6),X4),X3)),
inference(paramodulation,[status(thm)],[f29,f12]) ).
fof(f151,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(divide(divide(X0,X0),X1),X2)),X3),divide(X1,X3)) = X2,
inference(paramodulation,[status(thm)],[f12,f4]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4,X5,X6] : divide(inverse(multiply(divide(divide(X0,X0),X1),divide(divide(sF0_fnc,X2),divide(X3,divide(X2,divide(X4,divide(X1,X5))))))),X5) = inverse(divide(divide(divide(X6,X6),X4),X3)),
inference(forward_demodulation,[status(thm)],[f5,f122]) ).
fof(f356,plain,
! [X0,X1,X2] : inverse(divide(divide(divide(X0,X0),X1),divide(divide(X2,sF2_fnc),divide(X1,divide(sF3_fnc,sF3_fnc))))) = X2,
inference(paramodulation,[status(thm)],[f12,f25]) ).
fof(f373,plain,
! [X0,X1,X2] : inverse(divide(divide(divide(X0,X0),X1),divide(divide(X2,sF2_fnc),divide(X1,sF2_fnc)))) = X2,
inference(forward_demodulation,[status(thm)],[f24,f356]) ).
fof(f789,plain,
! [X0,X1,X2] : divide(divide(inverse(divide(divide(sF2_fnc,X0),X1)),X2),divide(X0,X2)) = X1,
inference(paramodulation,[status(thm)],[f32,f26]) ).
fof(f839,plain,
! [X0,X1,X2] : divide(divide(inverse(divide(multiply(sF2_fnc,X0),X1)),X2),divide(inverse(X0),X2)) = X1,
inference(paramodulation,[status(thm)],[f5,f789]) ).
fof(f868,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(divide(divide(X0,X0),X1),divide(inverse(divide(divide(sF2_fnc,X2),X3)),divide(X1,X4)))),X4) = inverse(divide(divide(divide(X5,X5),X2),X3)),
inference(paramodulation,[status(thm)],[f789,f12]) ).
fof(f909,plain,
! [X0,X1,X2] : inverse(divide(divide(sF2_fnc,X0),X1)) = inverse(divide(divide(divide(X2,X2),X0),X1)),
inference(forward_demodulation,[status(thm)],[f4,f868]) ).
fof(f1068,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(X0,X1)),X2),divide(divide(X3,inverse(divide(divide(sF2_fnc,X3),X0))),X2)) = X1,
inference(paramodulation,[status(thm)],[f789,f151]) ).
fof(f1070,plain,
! [X0,X1,X2] : divide(divide(inverse(divide(divide(sF0_fnc,X0),X1)),X2),divide(X0,X2)) = X1,
inference(paramodulation,[status(thm)],[f27,f151]) ).
fof(f1122,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(X0,X1)),X2),divide(multiply(X3,divide(divide(sF2_fnc,X3),X0)),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f1068]) ).
fof(f1185,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(sF2_fnc,X0),divide(inverse(divide(divide(sF0_fnc,X1),X2)),divide(X0,X3)))),X3) = inverse(divide(divide(sF2_fnc,X1),X2)),
inference(paramodulation,[status(thm)],[f1070,f32]) ).
fof(f1227,plain,
! [X0,X1] : inverse(divide(divide(sF0_fnc,X0),X1)) = inverse(divide(divide(sF2_fnc,X0),X1)),
inference(forward_demodulation,[status(thm)],[f26,f1185]) ).
fof(f1309,plain,
! [X0,X1] : inverse(divide(divide(sF0_fnc,inverse(X0)),X1)) = inverse(divide(multiply(sF2_fnc,X0),X1)),
inference(paramodulation,[status(thm)],[f5,f1227]) ).
fof(f1315,plain,
! [X0,X1,X2] : multiply(X0,divide(divide(sF2_fnc,X1),X2)) = divide(X0,inverse(divide(divide(sF0_fnc,X1),X2))),
inference(paramodulation,[status(thm)],[f1227,f5]) ).
fof(f1318,plain,
! [X0,X1] : inverse(divide(multiply(sF0_fnc,X0),X1)) = inverse(divide(multiply(sF2_fnc,X0),X1)),
inference(forward_demodulation,[status(thm)],[f5,f1309]) ).
fof(f1319,plain,
! [X0,X1,X2] : multiply(X0,divide(divide(sF2_fnc,X1),X2)) = multiply(X0,divide(divide(sF0_fnc,X1),X2)),
inference(forward_demodulation,[status(thm)],[f5,f1315]) ).
fof(f1615,plain,
! [X0,X1,X2] : divide(divide(inverse(divide(multiply(sF0_fnc,X0),X1)),X2),divide(inverse(X0),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f1318,f839]) ).
fof(f1670,plain,
! [X0,X1,X2] : inverse(divide(divide(sF0_fnc,X0),X1)) = inverse(divide(divide(divide(X2,X2),X0),X1)),
inference(forward_demodulation,[status(thm)],[f1227,f909]) ).
fof(f1671,plain,
! [X0,X1,X2] : inverse(divide(divide(sF0_fnc,X0),inverse(X1))) = inverse(multiply(divide(divide(X2,X2),X0),X1)),
inference(paramodulation,[status(thm)],[f5,f1670]) ).
fof(f1685,plain,
! [X0,X1,X2] : inverse(multiply(divide(sF0_fnc,X0),X1)) = inverse(multiply(divide(divide(X2,X2),X0),X1)),
inference(forward_demodulation,[status(thm)],[f5,f1671]) ).
fof(f2750,plain,
! [X0,X1] : inverse(divide(divide(sF0_fnc,X0),divide(divide(X1,sF2_fnc),divide(X0,sF2_fnc)))) = X1,
inference(forward_demodulation,[status(thm)],[f1670,f373]) ).
fof(f2773,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,sF2_fnc),divide(X2,sF2_fnc)),
inference(paramodulation,[status(thm)],[f2750,f1070]) ).
fof(f3538,plain,
! [X0,X1,X2,X3] : divide(divide(X0,X1),divide(X2,X1)) = divide(divide(X0,X3),divide(X2,X3)),
inference(paramodulation,[status(thm)],[f2773,f2773]) ).
fof(f3756,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(divide(sF0_fnc,X0),divide(X1,X0))),X2),divide(X3,X2)) = divide(X1,X3),
inference(paramodulation,[status(thm)],[f3538,f1070]) ).
fof(f5951,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(multiply(divide(sF0_fnc,X0),divide(divide(sF0_fnc,X1),divide(X2,divide(X1,divide(X3,divide(X0,X4))))))),X4) = inverse(divide(divide(divide(X5,X5),X3),X2)),
inference(forward_demodulation,[status(thm)],[f1685,f156]) ).
fof(f5952,plain,
! [X0,X1,X2,X3,X4] : divide(inverse(multiply(divide(sF0_fnc,X0),divide(divide(sF0_fnc,X1),divide(X2,divide(X1,divide(X3,divide(X0,X4))))))),X4) = inverse(divide(divide(sF0_fnc,X3),X2)),
inference(forward_demodulation,[status(thm)],[f1670,f5951]) ).
fof(f8769,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(X0,X1)),X2),divide(multiply(X3,divide(divide(sF0_fnc,X3),X0)),X2)) = X1,
inference(forward_demodulation,[status(thm)],[f1319,f1122]) ).
fof(f10616,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(X0,multiply(X2,divide(divide(sF0_fnc,X2),divide(sF0_fnc,X1)))),
inference(paramodulation,[status(thm)],[f8769,f3756]) ).
fof(f10885,plain,
! [X0,X1,X2,X3] : divide(divide(inverse(divide(multiply(sF0_fnc,X0),X1)),X2),divide(inverse(X0),X2)) = multiply(X3,divide(divide(sF0_fnc,X3),divide(sF0_fnc,X1))),
inference(paramodulation,[status(thm)],[f10616,f1615]) ).
fof(f11039,plain,
! [X0,X1] : X0 = multiply(X1,divide(divide(sF0_fnc,X1),divide(sF0_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f1615,f10885]) ).
fof(f11171,plain,
! [X0,X1,X2] : divide(inverse(divide(divide(sF0_fnc,X0),divide(X1,divide(X0,X2)))),X2) = inverse(divide(divide(sF0_fnc,X1),sF0_fnc)),
inference(paramodulation,[status(thm)],[f11039,f5952]) ).
fof(f11195,plain,
! [X0] : X0 = inverse(divide(divide(sF0_fnc,X0),sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f29,f11171]) ).
fof(f11205,plain,
! [X0,X1] : divide(divide(X0,X1),divide(X0,X1)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f11195,f1070]) ).
fof(f11575,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(divide(multiply(sF0_fnc,X1),X0)),X2),divide(inverse(X1),X2))) = sF0_fnc,
inference(paramodulation,[status(thm)],[f1615,f11205]) ).
fof(f11767,plain,
! [X0] : divide(X0,X0) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f1615,f11575]) ).
fof(f12204,plain,
sF2_fnc = sF0_fnc,
inference(backward_demodulation,[status(thm)],[f11767,f24]) ).
fof(f12401,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f12204,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP478-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n014.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sun Sep 20 20:14:10 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Drodi V4.1.1
% 0.15/6.04 % Refutation found
% 0.15/6.04 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/6.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.28/6.09 % Elapsed time: 0.707360 seconds
% 4.28/6.09 % CPU time: 5.499176 seconds
% 4.28/6.09 % Total memory used: 157.136 MB
% 4.28/6.09 % Net memory used: 151.983 MB
%------------------------------------------------------------------------------