%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP756-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:35:17 PM UTC 2026
% Result : Unsatisfiable 4.79s 1.09s
% Output : CNFRefutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 46 unt; 4 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : mult(A,mult(mult(B,B),C)) = mult(mult(A,B),mult(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] : mult(X0,mult(mult(X1,X1),X2)) = mult(mult(X0,X1),mult(X1,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
sF1_fnc = mult(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f14,definition,
sF0_fnc = mult(sF1_fnc,c),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f15,definition,
sF3_fnc = mult(b,c),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f16,definition,
sF2_fnc = mult(a,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f17,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f12,f16,f15,f14,f13]) ).
fof(f21,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f30,plain,
rd(sF3_fnc,c) = b,
inference(paramodulation,[status(thm)],[f15,f10]) ).
fof(f31,plain,
rd(sF0_fnc,c) = sF1_fnc,
inference(paramodulation,[status(thm)],[f14,f10]) ).
fof(f35,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f7,f10]) ).
fof(f68,plain,
! [X0,X1,X2] : rd(mult(X0,mult(mult(X1,X1),X2)),mult(X1,X2)) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f176,plain,
! [X0,X1,X2] : rd(X0,mult(X1,X2)) = mult(rd(X0,mult(mult(X1,X1),X2)),X1),
inference(paramodulation,[status(thm)],[f9,f68]) ).
fof(f237,plain,
! [X0,X1,X2] : rd(X0,mult(X1,ld(mult(X1,X1),X2))) = mult(rd(X0,X2),X1),
inference(paramodulation,[status(thm)],[f7,f176]) ).
fof(f333,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X1),X2),X0) = mult(X2,ld(mult(X2,X2),X1)),
inference(paramodulation,[status(thm)],[f237,f21]) ).
fof(f488,plain,
! [X0,X1] : ld(X0,X0) = mult(X1,ld(mult(X1,X1),X1)),
inference(paramodulation,[status(thm)],[f9,f333]) ).
fof(f492,plain,
! [X0] : ld(mult(sF1_fnc,X0),sF0_fnc) = mult(X0,ld(mult(X0,X0),c)),
inference(paramodulation,[status(thm)],[f31,f333]) ).
fof(f493,plain,
! [X0] : ld(mult(b,X0),sF3_fnc) = mult(X0,ld(mult(X0,X0),c)),
inference(paramodulation,[status(thm)],[f30,f333]) ).
fof(f499,plain,
! [X0,X1,X2] : ld(mult(X0,X1),X2) = mult(X1,ld(mult(X1,X1),ld(X0,X2))),
inference(paramodulation,[status(thm)],[f35,f333]) ).
fof(f530,plain,
! [X0] : ld(mult(sF1_fnc,X0),sF0_fnc) = ld(mult(b,X0),sF3_fnc),
inference(backward_demodulation,[status(thm)],[f493,f492]) ).
fof(f586,plain,
! [X0,X1,X2] : rd(X0,ld(X1,X1)) = mult(rd(X0,X2),X2),
inference(paramodulation,[status(thm)],[f488,f237]) ).
fof(f631,plain,
! [X0,X1] : rd(X0,ld(X1,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f9,f586]) ).
fof(f693,plain,
! [X0,X1,X2] : ld(mult(X0,X1),X0) = mult(X1,ld(mult(X1,X1),ld(X2,X2))),
inference(paramodulation,[status(thm)],[f631,f333]) ).
fof(f707,plain,
! [X0,X1,X2] : ld(mult(X0,X1),X0) = ld(mult(X2,X1),X2),
inference(forward_demodulation,[status(thm)],[f499,f693]) ).
fof(f3509,plain,
! [X0] : mult(mult(sF1_fnc,X0),ld(mult(b,X0),sF3_fnc)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f530,f7]) ).
fof(f4248,plain,
! [X0] : mult(mult(sF1_fnc,ld(mult(b,b),b)),ld(ld(X0,X0),sF3_fnc)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f488,f3509]) ).
fof(f5312,plain,
! [X0] : ld(sF1_fnc,a) = ld(mult(X0,b),X0),
inference(paramodulation,[status(thm)],[f13,f707]) ).
fof(f5327,plain,
! [X0,X1,X2] : ld(X0,X1) = ld(mult(X2,ld(X1,X0)),X2),
inference(paramodulation,[status(thm)],[f7,f707]) ).
fof(f5363,plain,
! [X0,X1,X2] : ld(mult(X0,ld(mult(X1,X1),X1)),X0) = ld(ld(X2,X2),X1),
inference(paramodulation,[status(thm)],[f488,f707]) ).
fof(f5408,plain,
! [X0] : mult(mult(sF1_fnc,ld(sF1_fnc,a)),ld(ld(X0,X0),sF3_fnc)) = sF0_fnc,
inference(backward_demodulation,[status(thm)],[f5312,f4248]) ).
fof(f5442,plain,
! [X0,X1] : ld(X0,mult(X0,X0)) = ld(ld(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f5327,f5363]) ).
fof(f5473,plain,
! [X0,X1] : X0 = ld(ld(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f8,f5442]) ).
fof(f5525,plain,
! [X0] : mult(a,ld(ld(X0,X0),sF3_fnc)) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f7,f5408]) ).
fof(f5526,plain,
sF2_fnc = sF0_fnc,
inference(backward_demodulation,[status(thm)],[f5527,f16]) ).
fof(f5527,plain,
mult(a,sF3_fnc) = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f5473,f5525]) ).
fof(f5553,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5526,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP756-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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 : Sun Sep 20 20:37:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 4.79/1.09 % Refutation found
% 4.79/1.09 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.79/1.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.36/1.16 % Elapsed time: 0.774698 seconds
% 3.36/1.16 % CPU time: 5.891547 seconds
% 3.36/1.16 % Total memory used: 146.847 MB
% 3.36/1.16 % Net memory used: 145.540 MB
%------------------------------------------------------------------------------