%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO025-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 12:06:34 PM UTC 2026
% Result : Unsatisfiable 0.15s 1.01s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 7
% Syntax : Number of formulae : 89 ( 89 unt; 0 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 145 ( 145 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : multiply(add(X,Y),Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : add(X,inverse(X)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : pixley(X,Y,Z) = add(multiply(X,inverse(Y)),add(multiply(X,Z),multiply(inverse(Y),Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : pixley(X,X,Y) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : pixley(X,Y,Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X1,X0),multiply(X2,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0] : add(X0,inverse(X0)) = n1,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1,X2] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),add(multiply(X0,X2),multiply(inverse(X1),X2))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1] : pixley(X0,X0,X1) = X1,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] : pixley(X0,X1,X1) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0,X1,X2] : pixley(X0,X1,X2) = add(multiply(X0,inverse(X1)),multiply(X2,add(X0,inverse(X1)))),
inference(forward_demodulation,[status(thm)],[f10,f12]) ).
fof(f29,plain,
! [X0,X1,X2] : multiply(X0,add(add(X1,X0),X2)) = add(X0,multiply(X2,X0)),
inference(paramodulation,[status(thm)],[f9,f10]) ).
fof(f30,plain,
! [X0,X1,X2] : multiply(X0,add(X1,add(X2,X0))) = add(multiply(X1,X0),X0),
inference(paramodulation,[status(thm)],[f9,f10]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(multiply(X0,add(X1,X2)),multiply(X2,X0)) = multiply(X2,X0),
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f32,plain,
! [X0] : multiply(n1,inverse(X0)) = inverse(X0),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f40,plain,
! [X0,X1] : multiply(X0,n1) = add(X0,multiply(inverse(add(X1,X0)),X0)),
inference(paramodulation,[status(thm)],[f11,f29]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(add(X0,X1),multiply(X1,add(X2,add(X0,X1)))) = multiply(X1,add(X2,add(X0,X1))),
inference(paramodulation,[status(thm)],[f9,f31]) ).
fof(f70,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(multiply(X2,X1),X1)) = multiply(X1,add(X2,add(X0,X1))),
inference(forward_demodulation,[status(thm)],[f30,f57]) ).
fof(f71,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(multiply(X2,X1),X1)) = add(multiply(X2,X1),X1),
inference(forward_demodulation,[status(thm)],[f30,f70]) ).
fof(f114,plain,
! [X0,X1,X2] : multiply(add(X0,X1),add(X1,X1)) = add(multiply(add(X2,X1),X1),X1),
inference(paramodulation,[status(thm)],[f9,f71]) ).
fof(f138,plain,
! [X0,X1] : multiply(add(X0,X1),add(X1,X1)) = add(X1,X1),
inference(forward_demodulation,[status(thm)],[f9,f114]) ).
fof(f144,plain,
! [X0] : multiply(n1,add(inverse(X0),inverse(X0))) = add(inverse(X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f11,f138]) ).
fof(f146,plain,
! [X0,X1] : multiply(add(X0,X0),multiply(X0,add(X1,X0))) = multiply(X0,add(X1,X0)),
inference(paramodulation,[status(thm)],[f138,f31]) ).
fof(f167,plain,
! [X0,X1] : pixley(X0,X0,X1) = add(multiply(X0,inverse(X0)),multiply(X1,n1)),
inference(paramodulation,[status(thm)],[f11,f22]) ).
fof(f174,plain,
! [X0,X1,X2] : multiply(pixley(X0,X1,X2),multiply(X2,add(X0,inverse(X1)))) = multiply(X2,add(X0,inverse(X1))),
inference(paramodulation,[status(thm)],[f22,f9]) ).
fof(f176,plain,
! [X0,X1] : X0 = add(multiply(X1,inverse(X1)),multiply(X0,n1)),
inference(forward_demodulation,[status(thm)],[f13,f167]) ).
fof(f201,plain,
! [X0] : X0 = add(inverse(n1),multiply(X0,n1)),
inference(paramodulation,[status(thm)],[f32,f176]) ).
fof(f208,plain,
! [X0,X1] : multiply(multiply(X0,n1),add(X1,X0)) = add(multiply(X1,multiply(X0,n1)),multiply(X0,n1)),
inference(paramodulation,[status(thm)],[f176,f30]) ).
fof(f209,plain,
! [X0] : multiply(X0,multiply(X0,n1)) = multiply(X0,n1),
inference(paramodulation,[status(thm)],[f176,f9]) ).
fof(f215,plain,
! [X0] : add(X0,n1) = add(inverse(n1),n1),
inference(paramodulation,[status(thm)],[f9,f201]) ).
fof(f231,plain,
! [X0,X1] : multiply(add(X0,multiply(X1,n1)),add(multiply(X1,n1),multiply(X1,n1))) = add(multiply(X1,multiply(X1,n1)),multiply(X1,n1)),
inference(paramodulation,[status(thm)],[f209,f71]) ).
fof(f236,plain,
! [X0] : add(multiply(X0,n1),multiply(X0,n1)) = add(multiply(X0,multiply(X0,n1)),multiply(X0,n1)),
inference(forward_demodulation,[status(thm)],[f138,f231]) ).
fof(f237,plain,
! [X0] : multiply(n1,add(X0,X0)) = add(multiply(X0,multiply(X0,n1)),multiply(X0,n1)),
inference(forward_demodulation,[status(thm)],[f10,f236]) ).
fof(f238,plain,
! [X0] : multiply(n1,add(X0,X0)) = multiply(multiply(X0,n1),add(X0,X0)),
inference(forward_demodulation,[status(thm)],[f208,f237]) ).
fof(f240,plain,
! [X0,X1] : add(X0,n1) = add(X1,n1),
inference(paramodulation,[status(thm)],[f215,f215]) ).
fof(f264,plain,
! [X0,X1] : multiply(X0,add(X1,n1)) = add(X0,multiply(n1,X0)),
inference(paramodulation,[status(thm)],[f240,f29]) ).
fof(f267,plain,
! [X0,X1] : multiply(add(X0,n1),add(X1,n1)) = add(n1,n1),
inference(paramodulation,[status(thm)],[f240,f138]) ).
fof(f294,plain,
! [X0,X1,X2] : multiply(X0,add(X1,n1)) = multiply(X0,add(X2,n1)),
inference(paramodulation,[status(thm)],[f264,f264]) ).
fof(f295,plain,
! [X0,X1] : multiply(inverse(X0),add(X1,n1)) = add(inverse(X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f32,f264]) ).
fof(f341,plain,
! [X0,X1,X2] : multiply(add(X0,n1),add(add(X1,n1),X2)) = add(add(n1,n1),multiply(X2,add(X0,n1))),
inference(paramodulation,[status(thm)],[f267,f10]) ).
fof(f380,plain,
! [X0,X1] : multiply(add(X0,X0),add(X1,multiply(X0,n1))) = add(multiply(X1,add(X0,X0)),multiply(n1,add(X0,X0))),
inference(paramodulation,[status(thm)],[f238,f10]) ).
fof(f389,plain,
! [X0,X1] : multiply(add(X0,X0),add(X1,multiply(X0,n1))) = multiply(add(X0,X0),add(X1,n1)),
inference(forward_demodulation,[status(thm)],[f10,f380]) ).
fof(f439,plain,
! [X0,X1] : multiply(add(inverse(X0),inverse(X0)),add(X1,n1)) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(paramodulation,[status(thm)],[f144,f264]) ).
fof(f483,plain,
! [X0,X1,X2] : multiply(add(X0,n1),add(X1,n1)) = add(add(X0,n1),multiply(n1,add(X2,n1))),
inference(paramodulation,[status(thm)],[f294,f264]) ).
fof(f520,plain,
! [X0,X1] : add(n1,n1) = add(add(X0,n1),multiply(n1,add(X1,n1))),
inference(forward_demodulation,[status(thm)],[f267,f483]) ).
fof(f576,plain,
! [X0,X1] : multiply(X0,multiply(X1,add(X0,inverse(X1)))) = multiply(X1,add(X0,inverse(X1))),
inference(paramodulation,[status(thm)],[f14,f174]) ).
fof(f775,plain,
! [X0] : multiply(add(n1,n1),add(n1,multiply(n1,n1))) = multiply(n1,add(X0,n1)),
inference(paramodulation,[status(thm)],[f264,f146]) ).
fof(f798,plain,
! [X0] : multiply(add(n1,n1),add(n1,n1)) = multiply(n1,add(X0,n1)),
inference(forward_demodulation,[status(thm)],[f389,f775]) ).
fof(f803,plain,
! [X0] : add(n1,n1) = add(add(X0,n1),add(n1,n1)),
inference(backward_demodulation,[status(thm)],[f804,f520]) ).
fof(f804,plain,
! [X0] : add(n1,n1) = multiply(n1,add(X0,n1)),
inference(forward_demodulation,[status(thm)],[f267,f798]) ).
fof(f862,plain,
! [X0,X1] : multiply(add(X0,n1),add(n1,X1)) = add(add(n1,n1),multiply(X1,add(X0,n1))),
inference(paramodulation,[status(thm)],[f804,f10]) ).
fof(f871,plain,
! [X0,X1,X2] : multiply(add(X0,n1),add(add(X1,n1),X2)) = multiply(add(X0,n1),add(n1,X2)),
inference(backward_demodulation,[status(thm)],[f862,f341]) ).
fof(f964,plain,
! [X0,X1] : add(n1,n1) = add(add(X0,n1),add(X1,n1)),
inference(paramodulation,[status(thm)],[f240,f803]) ).
fof(f1021,plain,
! [X0] : multiply(add(X0,n1),n1) = add(add(X0,n1),multiply(inverse(add(n1,n1)),add(X0,n1))),
inference(paramodulation,[status(thm)],[f964,f40]) ).
fof(f1022,plain,
! [X0,X1] : multiply(add(X0,n1),add(add(n1,n1),X1)) = add(add(X0,n1),multiply(X1,add(X0,n1))),
inference(paramodulation,[status(thm)],[f964,f29]) ).
fof(f1049,plain,
! [X0] : n1 = add(add(X0,n1),multiply(inverse(add(n1,n1)),add(X0,n1))),
inference(forward_demodulation,[status(thm)],[f9,f1021]) ).
fof(f1050,plain,
! [X0] : n1 = multiply(add(X0,n1),add(n1,inverse(add(n1,n1)))),
inference(backward_demodulation,[status(thm)],[f1051,f1049]) ).
fof(f1051,plain,
! [X0,X1] : multiply(add(X0,n1),add(n1,X1)) = add(add(X0,n1),multiply(X1,add(X0,n1))),
inference(forward_demodulation,[status(thm)],[f871,f1022]) ).
fof(f1457,plain,
multiply(n1,n1) = multiply(add(n1,n1),add(n1,inverse(add(n1,n1)))),
inference(paramodulation,[status(thm)],[f1050,f576]) ).
fof(f1483,plain,
multiply(n1,n1) = n1,
inference(forward_demodulation,[status(thm)],[f1050,f1457]) ).
fof(f1512,plain,
n1 = add(inverse(n1),n1),
inference(paramodulation,[status(thm)],[f1483,f201]) ).
fof(f1534,plain,
! [X0] : n1 = add(X0,n1),
inference(paramodulation,[status(thm)],[f240,f1512]) ).
fof(f1543,plain,
! [X0] : multiply(inverse(X0),n1) = add(inverse(X0),inverse(X0)),
inference(paramodulation,[status(thm)],[f1512,f295]) ).
fof(f1632,plain,
! [X0] : multiply(add(inverse(X0),inverse(X0)),n1) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(backward_demodulation,[status(thm)],[f1534,f439]) ).
fof(f1836,plain,
! [X0] : multiply(multiply(inverse(X0),n1),n1) = add(add(inverse(X0),inverse(X0)),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f1543,f1632]) ).
fof(f1837,plain,
! [X0] : multiply(multiply(inverse(X0),n1),n1) = add(multiply(inverse(X0),n1),add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f1543,f1836]) ).
fof(f1838,plain,
! [X0] : multiply(multiply(inverse(X0),n1),n1) = add(multiply(inverse(X0),n1),multiply(inverse(X0),n1)),
inference(forward_demodulation,[status(thm)],[f1543,f1837]) ).
fof(f1839,plain,
! [X0] : multiply(multiply(inverse(X0),n1),n1) = multiply(n1,add(inverse(X0),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f10,f1838]) ).
fof(f1840,plain,
! [X0] : multiply(multiply(inverse(X0),n1),n1) = add(inverse(X0),inverse(X0)),
inference(forward_demodulation,[status(thm)],[f144,f1839]) ).
fof(f1842,plain,
! [X0] : multiply(multiply(inverse(X0),n1),n1) = multiply(inverse(X0),n1),
inference(forward_demodulation,[status(thm)],[f1543,f1840]) ).
fof(f2208,plain,
! [X0] : multiply(inverse(X0),n1) = add(inverse(n1),multiply(inverse(X0),n1)),
inference(paramodulation,[status(thm)],[f1842,f201]) ).
fof(f2259,plain,
! [X0] : multiply(inverse(X0),n1) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f201,f2208]) ).
fof(f2341,plain,
! [X0] : inverse(X0) = add(inverse(n1),inverse(X0)),
inference(paramodulation,[status(thm)],[f2259,f201]) ).
fof(f2342,plain,
! [X0,X1] : inverse(X0) = add(multiply(X1,inverse(X1)),inverse(X0)),
inference(paramodulation,[status(thm)],[f2259,f176]) ).
fof(f2841,plain,
inverse(inverse(n1)) = n1,
inference(paramodulation,[status(thm)],[f11,f2341]) ).
fof(f2926,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = add(multiply(X0,inverse(inverse(n1))),multiply(X1,add(X0,n1))),
inference(paramodulation,[status(thm)],[f2841,f22]) ).
fof(f2975,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = add(multiply(X0,n1),multiply(X1,add(X0,n1))),
inference(forward_demodulation,[status(thm)],[f2841,f2926]) ).
fof(f2976,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = add(multiply(X0,n1),multiply(X1,n1)),
inference(forward_demodulation,[status(thm)],[f1534,f2975]) ).
fof(f2980,plain,
! [X0,X1] : pixley(X0,inverse(n1),X1) = multiply(n1,add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f10,f2976]) ).
fof(f4150,plain,
! [X0] : X0 = multiply(n1,add(X0,inverse(n1))),
inference(paramodulation,[status(thm)],[f14,f2980]) ).
fof(f4341,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(n1,inverse(n1)),
inference(paramodulation,[status(thm)],[f2342,f4150]) ).
fof(f4372,plain,
multiply(b,inverse(b)) != inverse(n1),
inference(backward_demodulation,[status(thm)],[f4393,f16]) ).
fof(f4393,plain,
! [X0] : multiply(X0,inverse(X0)) = inverse(n1),
inference(forward_demodulation,[status(thm)],[f32,f4341]) ).
fof(f4469,plain,
inverse(n1) != inverse(n1),
inference(forward_demodulation,[status(thm)],[f4393,f4372]) ).
fof(f4470,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f4469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO025-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.53 % Computer : n013.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.54 % CPULimit : 300
% 0.11/0.54 % WCLimit : 300
% 0.11/0.54 % DateTime : Mon Sep 21 13:48:23 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.54 % Drodi V4.1.1
% 0.15/1.01 % Refutation found
% 0.15/1.01 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/1.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/1.05 % Elapsed time: 0.506522 seconds
% 0.15/1.05 % CPU time: 3.871031 seconds
% 0.15/1.05 % Total memory used: 146.136 MB
% 0.15/1.05 % Net memory used: 143.470 MB
%------------------------------------------------------------------------------