%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:06:35 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 41 ( 41 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 75 ( 75 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V,W,X,Y,Z] : multiply(multiply(V,W,X),Y,multiply(V,W,Z)) = multiply(V,W,multiply(X,Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Y,X] : multiply(Y,X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : multiply(X,X,Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Y,X] : multiply(inverse(Y),Y,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : multiply(X,Y,inverse(Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
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(f7,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X0,X1,multiply(X2,X3,X4)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] : multiply(X0,X1,X1) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : multiply(X0,X0,X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : multiply(inverse(X0),X0,X1) = X1,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1,inverse(X1)) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
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,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
multiply(multiply(a,inverse(a),b),inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(forward_demodulation,[status(thm)],[f7,f12]) ).
fof(f37,plain,
! [X0,X1,X2,X3] : multiply(X0,X1,multiply(X0,X0,X2)) = multiply(X0,X0,multiply(X3,X1,X2)),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f43,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1,X2),X3,X1) = multiply(X0,X1,multiply(X2,X3,X1)),
inference(paramodulation,[status(thm)],[f8,f7]) ).
fof(f47,plain,
! [X0,X1,X2,X3] : multiply(X0,X1,X0) = multiply(X0,X0,multiply(X2,X1,X3)),
inference(forward_demodulation,[status(thm)],[f9,f37]) ).
fof(f48,plain,
! [X0,X1] : multiply(X0,X1,X0) = X0,
inference(forward_demodulation,[status(thm)],[f9,f47]) ).
fof(f60,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1,X2),X3,X0) = multiply(X0,X1,multiply(X2,X3,X0)),
inference(paramodulation,[status(thm)],[f48,f7]) ).
fof(f71,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X0,X2,multiply(inverse(X2),X1,X2)),
inference(paramodulation,[status(thm)],[f11,f43]) ).
fof(f111,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),X1,X2),X1,X0) = multiply(inverse(X0),X1,multiply(X2,X0,X0)),
inference(paramodulation,[status(thm)],[f7,f71]) ).
fof(f120,plain,
! [X0,X1] : multiply(X0,inverse(X1),X1) = multiply(X0,X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f9,f71]) ).
fof(f132,plain,
! [X0,X1,X2] : multiply(multiply(inverse(X0),X1,X2),X1,X0) = multiply(inverse(X0),X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f111]) ).
fof(f136,plain,
! [X0,X1] : multiply(X0,inverse(X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f11,f120]) ).
fof(f145,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f10,f136]) ).
fof(f165,plain,
! [X0,X1] : multiply(X0,inverse(X0),X1) = X1,
inference(paramodulation,[status(thm)],[f145,f10]) ).
fof(f166,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,f,e),c)) != b,
inference(backward_demodulation,[status(thm)],[f165,f23]) ).
fof(f833,plain,
! [X0,X1] : multiply(X0,X0,X1) = multiply(inverse(X1),X0,X1),
inference(paramodulation,[status(thm)],[f8,f132]) ).
fof(f864,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X0,X2,X1),
inference(backward_demodulation,[status(thm)],[f881,f71]) ).
fof(f881,plain,
! [X0,X1] : X0 = multiply(inverse(X1),X0,X1),
inference(forward_demodulation,[status(thm)],[f9,f833]) ).
fof(f921,plain,
multiply(b,inverse(multiply(c,d,multiply(e,f,g))),multiply(d,multiply(g,e,f),c)) != b,
inference(backward_demodulation,[status(thm)],[f864,f166]) ).
fof(f945,plain,
multiply(b,multiply(d,multiply(g,e,f),c),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(forward_demodulation,[status(thm)],[f864,f921]) ).
fof(f946,plain,
multiply(b,multiply(d,c,multiply(g,e,f)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(forward_demodulation,[status(thm)],[f864,f945]) ).
fof(f959,plain,
! [X0,X1] : X0 = multiply(X1,X0,inverse(X1)),
inference(paramodulation,[status(thm)],[f145,f881]) ).
fof(f1011,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X2,X0,multiply(inverse(X2),X1,X2)),
inference(paramodulation,[status(thm)],[f959,f60]) ).
fof(f1029,plain,
multiply(b,multiply(d,c,multiply(f,g,e)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(backward_demodulation,[status(thm)],[f1038,f946]) ).
fof(f1038,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X2,X0,X1),
inference(forward_demodulation,[status(thm)],[f881,f1011]) ).
fof(f1047,plain,
multiply(b,multiply(c,multiply(f,g,e),d),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(forward_demodulation,[status(thm)],[f1038,f1029]) ).
fof(f1048,plain,
multiply(b,multiply(c,d,multiply(f,g,e)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(forward_demodulation,[status(thm)],[f864,f1047]) ).
fof(f1049,plain,
multiply(b,multiply(c,d,multiply(e,f,g)),inverse(multiply(c,d,multiply(e,f,g)))) != b,
inference(forward_demodulation,[status(thm)],[f1038,f1048]) ).
fof(f1050,plain,
b != b,
inference(forward_demodulation,[status(thm)],[f11,f1049]) ).
fof(f1051,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1050]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO034-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:48:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.48/1.67 % Elapsed time: 1.088214 seconds
% 1.48/1.67 % CPU time: 0.328610 seconds
% 1.48/1.67 % Total memory used: 9.634 MB
% 1.48/1.67 % Net memory used: 9.340 MB
%------------------------------------------------------------------------------