%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP700-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:35:09 PM UTC 2026
% Result : Unsatisfiable 1.53s 0.74s
% Output : CNFRefutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 42 ( 42 unt; 4 def)
% Number of atoms : 42 ( 41 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : mult(mult(mult(A,B),A),mult(A,C)) = mult(A,mult(mult(mult(B,A),A),C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [X1] : tuple(mult(X1,x0),mult(x0,X1)) != tuple(unit,unit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X0),mult(X0,X2)) = mult(X0,mult(mult(mult(X1,X0),X0),X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0] : tuple(mult(X0,x0),mult(x0,X0)) != tuple(unit,unit),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
! [X0] : sF1_fnc(X0) = mult(X0,x0),
introduced(definition,[new_symbols(definition,[sF1_fnc(X0)])],[function_definition]) ).
fof(f20,definition,
! [X0] : sF2_fnc(X0) = mult(x0,X0),
introduced(definition,[new_symbols(definition,[sF2_fnc(X0)])],[function_definition]) ).
fof(f21,definition,
! [X0] : sF0_fnc(X0) = tuple(sF1_fnc(X0),sF2_fnc(X0)),
introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition]) ).
fof(f22,definition,
sF3_fnc = tuple(unit,unit),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f23,plain,
! [X0] : sF0_fnc(X0) != sF3_fnc,
inference(definition_folding,[],[f18,f22,f21,f20,f19]) ).
fof(f26,plain,
sF2_fnc(unit) = x0,
inference(paramodulation,[status(thm)],[f20,f14]) ).
fof(f29,plain,
sF1_fnc(unit) = x0,
inference(paramodulation,[status(thm)],[f19,f15]) ).
fof(f37,plain,
! [X0,X1] : mult(sF1_fnc(mult(x0,X0)),mult(x0,X1)) = mult(x0,mult(mult(mult(X0,x0),x0),X1)),
inference(paramodulation,[status(thm)],[f19,f16]) ).
fof(f52,plain,
! [X0,X1] : mult(sF1_fnc(sF2_fnc(X0)),mult(x0,X1)) = mult(x0,mult(mult(mult(X0,x0),x0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f53,plain,
! [X0,X1] : mult(sF1_fnc(sF2_fnc(X0)),sF2_fnc(X1)) = mult(x0,mult(mult(mult(X0,x0),x0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f52]) ).
fof(f54,plain,
! [X0,X1] : mult(sF1_fnc(sF2_fnc(X0)),sF2_fnc(X1)) = sF2_fnc(mult(mult(mult(X0,x0),x0),X1)),
inference(forward_demodulation,[status(thm)],[f20,f53]) ).
fof(f55,plain,
! [X0,X1] : mult(sF1_fnc(sF2_fnc(X0)),sF2_fnc(X1)) = sF2_fnc(mult(sF1_fnc(mult(X0,x0)),X1)),
inference(forward_demodulation,[status(thm)],[f19,f54]) ).
fof(f56,plain,
! [X0,X1] : mult(sF1_fnc(sF2_fnc(X0)),sF2_fnc(X1)) = sF2_fnc(mult(sF1_fnc(sF1_fnc(X0)),X1)),
inference(forward_demodulation,[status(thm)],[f19,f55]) ).
fof(f161,plain,
! [X0] : sF1_fnc(rd(X0,x0)) = X0,
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f174,plain,
! [X0] : rd(X0,X0) = unit,
inference(paramodulation,[status(thm)],[f15,f13]) ).
fof(f175,plain,
! [X0] : rd(sF2_fnc(X0),X0) = x0,
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f178,plain,
! [X0] : rd(sF1_fnc(X0),x0) = X0,
inference(paramodulation,[status(thm)],[f19,f13]) ).
fof(f195,plain,
! [X0] : mult(sF1_fnc(sF2_fnc(X0)),x0) = sF2_fnc(mult(sF1_fnc(sF1_fnc(X0)),unit)),
inference(paramodulation,[status(thm)],[f26,f56]) ).
fof(f203,plain,
! [X0] : sF1_fnc(sF1_fnc(sF2_fnc(X0))) = sF2_fnc(mult(sF1_fnc(sF1_fnc(X0)),unit)),
inference(forward_demodulation,[status(thm)],[f19,f195]) ).
fof(f204,plain,
! [X0] : sF1_fnc(sF1_fnc(sF2_fnc(X0))) = sF2_fnc(sF1_fnc(sF1_fnc(X0))),
inference(forward_demodulation,[status(thm)],[f14,f203]) ).
fof(f217,plain,
! [X0] : sF0_fnc(rd(X0,x0)) = tuple(X0,sF2_fnc(rd(X0,x0))),
inference(paramodulation,[status(thm)],[f161,f21]) ).
fof(f903,plain,
! [X0] : sF1_fnc(sF1_fnc(sF2_fnc(rd(X0,x0)))) = sF2_fnc(sF1_fnc(X0)),
inference(paramodulation,[status(thm)],[f161,f204]) ).
fof(f1763,plain,
! [X0] : rd(sF2_fnc(sF1_fnc(X0)),x0) = sF1_fnc(sF2_fnc(rd(X0,x0))),
inference(paramodulation,[status(thm)],[f903,f178]) ).
fof(f3941,plain,
rd(sF2_fnc(x0),x0) = sF1_fnc(sF2_fnc(rd(unit,x0))),
inference(paramodulation,[status(thm)],[f29,f1763]) ).
fof(f3954,plain,
x0 = sF1_fnc(sF2_fnc(rd(unit,x0))),
inference(forward_demodulation,[status(thm)],[f175,f3941]) ).
fof(f3974,plain,
rd(x0,x0) = sF2_fnc(rd(unit,x0)),
inference(paramodulation,[status(thm)],[f3954,f178]) ).
fof(f4002,plain,
unit = sF2_fnc(rd(unit,x0)),
inference(forward_demodulation,[status(thm)],[f174,f3974]) ).
fof(f4005,plain,
sF0_fnc(rd(unit,x0)) = tuple(unit,unit),
inference(paramodulation,[status(thm)],[f4002,f217]) ).
fof(f4019,plain,
sF0_fnc(rd(unit,x0)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f22,f4005]) ).
fof(f4020,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4019,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP700-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:36:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 1.53/0.74 % Refutation found
% 1.53/0.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.53/0.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.35/0.77 % Elapsed time: 0.398490 seconds
% 0.35/0.77 % CPU time: 3.017005 seconds
% 0.35/0.77 % Total memory used: 74.077 MB
% 0.35/0.77 % Net memory used: 72.924 MB
%------------------------------------------------------------------------------