%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP665-10 : TPTP v9.3.1. Released v8.1.0.
% 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 12:35:04 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 27 ( 27 unt; 4 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : mult(op_c,A) = mult(A,op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
mult(op_c,mult(x0,x1)) != mult(mult(op_c,x0),x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),ld(X2,mult(X1,X2))),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
mult(op_c,mult(x0,x1)) != mult(mult(op_c,x0),x1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f21,definition,
sF1_fnc = mult(x0,x1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f22,definition,
sF0_fnc = mult(op_c,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f23,definition,
sF3_fnc = mult(op_c,x0),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f24,definition,
sF2_fnc = mult(sF3_fnc,x1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f25,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f20,f24,f23,f22,f21]) ).
fof(f41,plain,
! [X0] : ld(op_c,mult(X0,op_c)) = X0,
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f45,plain,
! [X0] : ld(X0,mult(op_c,X0)) = op_c,
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f109,plain,
ld(x0,sF3_fnc) = op_c,
inference(paramodulation,[status(thm)],[f23,f45]) ).
fof(f110,plain,
ld(sF1_fnc,sF0_fnc) = op_c,
inference(paramodulation,[status(thm)],[f22,f45]) ).
fof(f211,plain,
mult(x0,op_c) = sF3_fnc,
inference(paramodulation,[status(thm)],[f109,f11]) ).
fof(f213,plain,
mult(sF1_fnc,op_c) = sF0_fnc,
inference(paramodulation,[status(thm)],[f110,f11]) ).
fof(f221,plain,
! [X0] : mult(mult(x0,X0),op_c) = mult(sF3_fnc,ld(op_c,mult(X0,op_c))),
inference(paramodulation,[status(thm)],[f211,f18]) ).
fof(f227,plain,
! [X0] : mult(mult(x0,X0),op_c) = mult(sF3_fnc,X0),
inference(forward_demodulation,[status(thm)],[f41,f221]) ).
fof(f345,plain,
mult(sF1_fnc,op_c) = mult(sF3_fnc,x1),
inference(paramodulation,[status(thm)],[f21,f227]) ).
fof(f358,plain,
sF0_fnc = mult(sF3_fnc,x1),
inference(forward_demodulation,[status(thm)],[f213,f345]) ).
fof(f359,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f24,f358]) ).
fof(f360,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f359,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP665-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n019.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 20 20:30:51 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.54 % Elapsed time: 0.060420 seconds
% 0.19/0.54 % CPU time: 0.109431 seconds
% 0.19/0.54 % Total memory used: 3.729 MB
% 0.19/0.54 % Net memory used: 3.662 MB
%------------------------------------------------------------------------------