%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:35:06 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 72 ( 72 unt; 5 def)
% Number of atoms : 72 ( 71 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 71 ( 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : ld(A,mult(A,A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(A,ld(A,B)) = ld(A,mult(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C,D] : ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : ld(X0,mult(X0,X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
ld(ld(x0,x1),mult(ld(x0,x1),x2)) != ld(x0,mult(x0,x2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f17,definition,
sF1_fnc = ld(x0,x1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f18,definition,
sF2_fnc = mult(sF1_fnc,x2),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f19,definition,
sF0_fnc = ld(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f20,definition,
sF4_fnc = mult(x0,x2),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f21,definition,
sF3_fnc = ld(x0,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f22,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f16,f21,f20,f19,f18,f17]) ).
fof(f24,plain,
mult(x0,sF3_fnc) = ld(x0,mult(x0,sF4_fnc)),
inference(paramodulation,[status(thm)],[f21,f11]) ).
fof(f40,plain,
! [X0,X1] : ld(sF0_fnc,mult(ld(sF1_fnc,sF2_fnc),mult(X0,X1))) = mult(ld(sF1_fnc,mult(sF1_fnc,X0)),X1),
inference(paramodulation,[status(thm)],[f19,f13]) ).
fof(f46,plain,
! [X0,X1] : ld(sF1_fnc,mult(ld(x0,x1),mult(X0,X1))) = mult(ld(x0,mult(x0,X0)),X1),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f49,plain,
! [X0,X1,X2] : ld(X0,mult(ld(X0,mult(X0,X0)),mult(X1,X2))) = mult(ld(X0,mult(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f53,plain,
! [X0,X1] : ld(ld(sF1_fnc,sF2_fnc),mult(sF0_fnc,mult(X0,X1))) = mult(ld(sF1_fnc,mult(sF1_fnc,X0)),X1),
inference(paramodulation,[status(thm)],[f19,f13]) ).
fof(f74,plain,
! [X0,X1] : ld(sF0_fnc,mult(sF0_fnc,mult(X0,X1))) = mult(ld(sF1_fnc,mult(sF1_fnc,X0)),X1),
inference(forward_demodulation,[status(thm)],[f19,f40]) ).
fof(f80,plain,
! [X0,X1] : ld(sF1_fnc,mult(sF1_fnc,mult(X0,X1))) = mult(ld(x0,mult(x0,X0)),X1),
inference(forward_demodulation,[status(thm)],[f17,f46]) ).
fof(f83,plain,
! [X0,X1,X2] : ld(X0,mult(X0,mult(X1,X2))) = mult(ld(X0,mult(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f9,f49]) ).
fof(f87,plain,
! [X0,X1] : ld(sF0_fnc,mult(sF0_fnc,mult(X0,X1))) = mult(ld(sF1_fnc,mult(sF1_fnc,X0)),X1),
inference(forward_demodulation,[status(thm)],[f19,f53]) ).
fof(f111,plain,
! [X0,X1] : ld(X0,mult(X0,mult(X0,X1))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f9,f83]) ).
fof(f113,plain,
! [X0] : ld(x0,mult(x0,mult(x2,X0))) = mult(ld(x0,sF4_fnc),X0),
inference(paramodulation,[status(thm)],[f20,f83]) ).
fof(f114,plain,
! [X0] : ld(sF1_fnc,mult(sF1_fnc,mult(x2,X0))) = mult(ld(sF1_fnc,sF2_fnc),X0),
inference(paramodulation,[status(thm)],[f18,f83]) ).
fof(f125,plain,
! [X0] : ld(x0,mult(x0,mult(x2,X0))) = mult(sF3_fnc,X0),
inference(forward_demodulation,[status(thm)],[f21,f113]) ).
fof(f126,plain,
! [X0] : ld(sF1_fnc,mult(sF1_fnc,mult(x2,X0))) = mult(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f19,f114]) ).
fof(f151,plain,
ld(x0,mult(x0,sF4_fnc)) = mult(x0,x2),
inference(paramodulation,[status(thm)],[f20,f111]) ).
fof(f160,plain,
mult(x0,sF3_fnc) = mult(x0,x2),
inference(forward_demodulation,[status(thm)],[f24,f151]) ).
fof(f161,plain,
mult(x0,sF3_fnc) = sF4_fnc,
inference(forward_demodulation,[status(thm)],[f20,f160]) ).
fof(f271,plain,
! [X0] : mult(x0,mult(sF3_fnc,X0)) = ld(x0,mult(x0,mult(x0,mult(x2,X0)))),
inference(paramodulation,[status(thm)],[f125,f11]) ).
fof(f274,plain,
! [X0] : mult(x0,mult(sF3_fnc,X0)) = mult(x0,mult(x2,X0)),
inference(forward_demodulation,[status(thm)],[f111,f271]) ).
fof(f279,plain,
! [X0] : mult(sF1_fnc,mult(sF0_fnc,X0)) = ld(sF1_fnc,mult(sF1_fnc,mult(sF1_fnc,mult(x2,X0)))),
inference(paramodulation,[status(thm)],[f126,f11]) ).
fof(f282,plain,
! [X0] : mult(sF1_fnc,mult(sF0_fnc,X0)) = mult(sF1_fnc,mult(x2,X0)),
inference(forward_demodulation,[status(thm)],[f111,f279]) ).
fof(f349,plain,
! [X0] : ld(X0,ld(X0,mult(X0,X0))) = rd(mult(rd(X0,X0),X0),X0),
inference(paramodulation,[status(thm)],[f11,f15]) ).
fof(f355,plain,
! [X0] : ld(X0,X0) = rd(mult(rd(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f9,f349]) ).
fof(f356,plain,
! [X0] : ld(X0,X0) = rd(rd(mult(X0,X0),X0),X0),
inference(forward_demodulation,[status(thm)],[f12,f355]) ).
fof(f357,plain,
! [X0] : ld(X0,X0) = rd(X0,X0),
inference(forward_demodulation,[status(thm)],[f10,f356]) ).
fof(f363,plain,
! [X0] : ld(sF0_fnc,mult(sF0_fnc,mult(x2,X0))) = mult(sF0_fnc,X0),
inference(backward_demodulation,[status(thm)],[f364,f126]) ).
fof(f364,plain,
! [X0,X1] : ld(sF0_fnc,mult(sF0_fnc,mult(X0,X1))) = ld(sF1_fnc,mult(sF1_fnc,mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f83,f74]) ).
fof(f494,plain,
! [X0] : mult(X0,rd(X0,X0)) = ld(X0,mult(X0,X0)),
inference(paramodulation,[status(thm)],[f357,f11]) ).
fof(f497,plain,
! [X0] : mult(X0,rd(X0,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f9,f494]) ).
fof(f502,plain,
mult(x0,sF3_fnc) = mult(x0,mult(x2,rd(sF3_fnc,sF3_fnc))),
inference(paramodulation,[status(thm)],[f497,f274]) ).
fof(f504,plain,
ld(x0,mult(x0,x2)) = mult(sF3_fnc,rd(x2,x2)),
inference(paramodulation,[status(thm)],[f497,f125]) ).
fof(f516,plain,
sF4_fnc = mult(x0,mult(x2,rd(sF3_fnc,sF3_fnc))),
inference(forward_demodulation,[status(thm)],[f161,f502]) ).
fof(f517,plain,
ld(x0,sF4_fnc) = mult(sF3_fnc,rd(x2,x2)),
inference(forward_demodulation,[status(thm)],[f20,f504]) ).
fof(f518,plain,
sF3_fnc = mult(sF3_fnc,rd(x2,x2)),
inference(forward_demodulation,[status(thm)],[f21,f517]) ).
fof(f625,plain,
! [X0,X1] : ld(sF0_fnc,mult(sF0_fnc,mult(X0,X1))) = mult(ld(x0,mult(x0,X0)),X1),
inference(forward_demodulation,[status(thm)],[f364,f80]) ).
fof(f627,plain,
! [X0] : ld(x0,mult(x0,mult(x2,X0))) = mult(sF0_fnc,X0),
inference(backward_demodulation,[status(thm)],[f630,f363]) ).
fof(f630,plain,
! [X0,X1] : ld(sF0_fnc,mult(sF0_fnc,mult(X0,X1))) = ld(x0,mult(x0,mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f83,f625]) ).
fof(f651,plain,
! [X0] : mult(sF3_fnc,X0) = mult(sF0_fnc,X0),
inference(forward_demodulation,[status(thm)],[f125,f627]) ).
fof(f685,plain,
sF3_fnc = mult(sF0_fnc,rd(x2,x2)),
inference(backward_demodulation,[status(thm)],[f651,f518]) ).
fof(f690,plain,
sF3_fnc = mult(sF0_fnc,rd(sF3_fnc,sF3_fnc)),
inference(paramodulation,[status(thm)],[f497,f651]) ).
fof(f748,plain,
mult(sF1_fnc,sF3_fnc) = mult(sF1_fnc,mult(x2,rd(x2,x2))),
inference(paramodulation,[status(thm)],[f685,f282]) ).
fof(f755,plain,
mult(sF1_fnc,sF3_fnc) = mult(sF1_fnc,x2),
inference(forward_demodulation,[status(thm)],[f497,f748]) ).
fof(f756,plain,
mult(sF1_fnc,sF3_fnc) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f18,f755]) ).
fof(f786,plain,
mult(sF1_fnc,sF3_fnc) = mult(sF1_fnc,mult(x2,rd(sF3_fnc,sF3_fnc))),
inference(paramodulation,[status(thm)],[f690,f282]) ).
fof(f793,plain,
sF2_fnc = mult(sF1_fnc,mult(x2,rd(sF3_fnc,sF3_fnc))),
inference(forward_demodulation,[status(thm)],[f756,f786]) ).
fof(f876,plain,
! [X0,X1] : ld(x0,mult(x0,mult(X0,X1))) = mult(ld(sF1_fnc,mult(sF1_fnc,X0)),X1),
inference(forward_demodulation,[status(thm)],[f630,f87]) ).
fof(f877,plain,
! [X0,X1] : ld(x0,mult(x0,mult(X0,X1))) = ld(sF1_fnc,mult(sF1_fnc,mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f83,f876]) ).
fof(f879,plain,
ld(x0,mult(x0,mult(x2,rd(sF3_fnc,sF3_fnc)))) = ld(sF1_fnc,sF2_fnc),
inference(paramodulation,[status(thm)],[f793,f877]) ).
fof(f906,plain,
ld(x0,sF4_fnc) = ld(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f516,f879]) ).
fof(f907,plain,
sF3_fnc = ld(sF1_fnc,sF2_fnc),
inference(forward_demodulation,[status(thm)],[f21,f906]) ).
fof(f908,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f19,f907]) ).
fof(f909,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f908,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP682-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.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 20:33:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.42/1.62 % Elapsed time: 1.035780 seconds
% 1.42/1.62 % CPU time: 0.088048 seconds
% 1.42/1.62 % Total memory used: 4.074 MB
% 1.42/1.62 % Net memory used: 4.022 MB
%------------------------------------------------------------------------------