%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO067-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:06:38 PM UTC 2026
% Result : Unsatisfiable 16.72s 2.51s
% Output : CNFRefutation 16.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 63 unt; 5 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-3 aty)
% Number of variables : 179 ( 179 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D,E,F,G] : multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
sF1_fnc = multiply(d,e,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f6,definition,
sF2_fnc = multiply(d,e,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f7,definition,
sF0_fnc = multiply(sF1_fnc,b,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f8,definition,
sF4_fnc = multiply(a,b,c),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f9,definition,
sF3_fnc = multiply(d,e,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f10,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f4,f9,f8,f7,f6,f5]) ).
fof(f11,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X8)),X8),X0),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(d,e,X2),X3,sF2_fnc)),multiply(e,multiply(c,X3,X2),d)) = X1,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f24,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,multiply(X4,multiply(X5,X6,X7),X8)),inverse(multiply(multiply(X8,X4,X7),X6,multiply(X8,X4,X5))),multiply(X2,X3,multiply(X9,inverse(X9),X10)))),multiply(X3,X10,X2)) = X1,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,c),b,multiply(X2,X3,a))),multiply(X3,sF4_fnc,X2)) = X1,
inference(paramodulation,[status(thm)],[f8,f3]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,c),e,multiply(X2,X3,d))),multiply(X3,sF2_fnc,X2)) = X1,
inference(paramodulation,[status(thm)],[f6,f3]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,multiply(X4,sF4_fnc,X5)),inverse(multiply(multiply(X5,X4,c),b,multiply(X5,X4,a))),multiply(X2,X3,multiply(X6,inverse(X6),X7)))),multiply(X3,X7,X2)) = X1,
inference(paramodulation,[status(thm)],[f25,f3]) ).
fof(f56,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,multiply(X4,sF2_fnc,X5)),inverse(multiply(multiply(X5,X4,c),e,multiply(X5,X4,d))),multiply(X2,X3,multiply(X6,inverse(X6),X7)))),multiply(X3,X7,X2)) = X1,
inference(paramodulation,[status(thm)],[f28,f3]) ).
fof(f452,plain,
! [X0,X1,X2] : X0 = multiply(inverse(X1),multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),X1),
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f4153,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,multiply(multiply(X3,inverse(X3),inverse(X2)),inverse(multiply(multiply(X4,X5,c),b,multiply(X4,X5,a))),multiply(X5,sF4_fnc,X4)),multiply(X6,inverse(X6),X7))),multiply(inverse(X2),X7,X2)) = X1,
inference(paramodulation,[status(thm)],[f34,f24]) ).
fof(f4522,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = X1,
inference(forward_demodulation,[status(thm)],[f25,f4153]) ).
fof(f4949,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = multiply(inverse(X5),X1,X5),
inference(paramodulation,[status(thm)],[f4522,f4522]) ).
fof(f5092,plain,
! [X0,X1] : X0 = multiply(inverse(X1),X0,X1),
inference(forward_demodulation,[status(thm)],[f4522,f4949]) ).
fof(f5171,plain,
! [X0,X1,X2] : X0 = multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),
inference(backward_demodulation,[status(thm)],[f5092,f452]) ).
fof(f7846,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(X1,inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f5092,f5171]) ).
fof(f8153,plain,
! [X0,X1] : X0 = multiply(X0,inverse(X1),X1),
inference(backward_demodulation,[status(thm)],[f7846,f5171]) ).
fof(f10720,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,multiply(multiply(X3,inverse(X3),inverse(X2)),inverse(multiply(multiply(X4,X5,c),e,multiply(X4,X5,d))),multiply(X5,sF2_fnc,X4)),multiply(X6,inverse(X6),X7))),multiply(inverse(X2),X7,X2)) = X1,
inference(paramodulation,[status(thm)],[f56,f24]) ).
fof(f10818,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = X1,
inference(forward_demodulation,[status(thm)],[f28,f10720]) ).
fof(f10819,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),X3)),multiply(inverse(X4),X3,X4)) = X1,
inference(forward_demodulation,[status(thm)],[f7846,f10818]) ).
fof(f10820,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0),X1),inverse(X2),multiply(inverse(X3),X2,X3)) = X1,
inference(forward_demodulation,[status(thm)],[f7846,f10819]) ).
fof(f10821,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X0),X1),inverse(X2),X2) = X1,
inference(forward_demodulation,[status(thm)],[f5092,f10820]) ).
fof(f10822,plain,
! [X0,X1] : multiply(X0,inverse(X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f8153,f10821]) ).
fof(f11361,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(multiply(d,e,X1),X2,sF2_fnc)),multiply(e,multiply(c,X2,X1),d)) = X0,
inference(backward_demodulation,[status(thm)],[f10822,f22]) ).
fof(f11395,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,inverse(multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))),multiply(X2,multiply(X5,X4,X3),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f10822,f3]) ).
fof(f11397,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f5092,f10822]) ).
fof(f11536,plain,
! [X0,X1] : multiply(inverse(X0),X0,X1) = X1,
inference(paramodulation,[status(thm)],[f11397,f10822]) ).
fof(f11538,plain,
! [X0,X1] : X0 = multiply(X1,X0,inverse(X1)),
inference(paramodulation,[status(thm)],[f11397,f5092]) ).
fof(f11539,plain,
! [X0,X1,X2,X3] : multiply(X0,X1,X2) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X3)),X3),X0),
inference(backward_demodulation,[status(thm)],[f11395,f11]) ).
fof(f11573,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(X1,X2,multiply(X3,inverse(X3),X4))),multiply(inverse(X3),multiply(X4,X2,X1),X3)) = X0,
inference(paramodulation,[status(thm)],[f10822,f11395]) ).
fof(f11657,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(X1,X2,X3)),multiply(inverse(X4),multiply(X3,X2,X1),X4)) = X0,
inference(forward_demodulation,[status(thm)],[f10822,f11573]) ).
fof(f11658,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,X2,X3)),multiply(X3,X2,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f5092,f11657]) ).
fof(f12636,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = inverse(inverse(multiply(X2,X1,X0))),
inference(paramodulation,[status(thm)],[f11536,f11658]) ).
fof(f12653,plain,
! [X0] : multiply(X0,inverse(sF4_fnc),multiply(c,b,a)) = X0,
inference(paramodulation,[status(thm)],[f8,f11658]) ).
fof(f12655,plain,
! [X0] : multiply(X0,inverse(sF3_fnc),multiply(sF4_fnc,e,d)) = X0,
inference(paramodulation,[status(thm)],[f9,f11658]) ).
fof(f12740,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X2,X1,X0),
inference(forward_demodulation,[status(thm)],[f11397,f12636]) ).
fof(f13489,plain,
multiply(c,b,a) = inverse(inverse(sF4_fnc)),
inference(paramodulation,[status(thm)],[f11536,f12653]) ).
fof(f13537,plain,
multiply(c,b,a) = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f11397,f13489]) ).
fof(f13550,plain,
! [X0] : multiply(X0,inverse(multiply(multiply(d,e,a),b,sF2_fnc)),multiply(e,sF4_fnc,d)) = X0,
inference(paramodulation,[status(thm)],[f13537,f11361]) ).
fof(f13577,plain,
! [X0] : multiply(X0,inverse(multiply(sF1_fnc,b,sF2_fnc)),multiply(e,sF4_fnc,d)) = X0,
inference(forward_demodulation,[status(thm)],[f5,f13550]) ).
fof(f13578,plain,
! [X0] : multiply(X0,inverse(sF0_fnc),multiply(e,sF4_fnc,d)) = X0,
inference(forward_demodulation,[status(thm)],[f7,f13577]) ).
fof(f13798,plain,
multiply(sF4_fnc,e,d) = inverse(inverse(sF3_fnc)),
inference(paramodulation,[status(thm)],[f11536,f12655]) ).
fof(f13847,plain,
multiply(sF4_fnc,e,d) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f11397,f13798]) ).
fof(f17100,plain,
multiply(e,sF4_fnc,d) = inverse(inverse(sF0_fnc)),
inference(paramodulation,[status(thm)],[f11536,f13578]) ).
fof(f17168,plain,
multiply(e,sF4_fnc,d) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f11397,f17100]) ).
fof(f17184,plain,
multiply(d,sF4_fnc,e) = sF0_fnc,
inference(paramodulation,[status(thm)],[f12740,f17168]) ).
fof(f17975,plain,
! [X0,X1,X2] : multiply(X0,X1,inverse(inverse(multiply(X0,X1,X2)))) = multiply(X1,X2,X0),
inference(paramodulation,[status(thm)],[f11536,f11539]) ).
fof(f18137,plain,
! [X0,X1,X2] : multiply(X0,X1,multiply(X0,X1,X2)) = multiply(X1,X2,X0),
inference(forward_demodulation,[status(thm)],[f11397,f17975]) ).
fof(f18711,plain,
! [X0,X1] : multiply(X0,X1,X1) = multiply(X1,inverse(X0),X0),
inference(paramodulation,[status(thm)],[f11538,f18137]) ).
fof(f18804,plain,
! [X0,X1] : multiply(X0,X1,X1) = X1,
inference(forward_demodulation,[status(thm)],[f8153,f18711]) ).
fof(f18911,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X1,multiply(X2,inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f18804,f11539]) ).
fof(f18954,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X1,X2,X0),
inference(forward_demodulation,[status(thm)],[f8153,f18911]) ).
fof(f19628,plain,
multiply(d,sF4_fnc,e) = sF3_fnc,
inference(paramodulation,[status(thm)],[f13847,f18954]) ).
fof(f19982,plain,
sF0_fnc = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f17184,f19628]) ).
fof(f19983,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f19982,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO067-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:51:19 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 16.72/2.51 % Refutation found
% 16.72/2.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 16.72/2.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.86/3.77 % Elapsed time: 3.186965 seconds
% 13.86/3.77 % CPU time: 13.967490 seconds
% 13.86/3.77 % Total memory used: 322.503 MB
% 13.86/3.77 % Net memory used: 310.560 MB
%------------------------------------------------------------------------------