%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP687-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:35:08 PM UTC 2026
% Result : Unsatisfiable 25.66s 3.66s
% Output : CNFRefutation 13.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 13
% Syntax : Number of formulae : 100 ( 100 unt; 6 def)
% Number of atoms : 100 ( 99 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 157 ( 157 !; 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(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(f7,axiom,
! [A,B,C] : mult(mult(A,A),mult(B,C)) = mult(mult(A,mult(A,B)),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
mult(a,mult(b,mult(b,c))) != mult(mult(a,mult(b,b)),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f11,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1,X2] : mult(mult(X0,X0),mult(X1,X2)) = mult(mult(X0,mult(X0,X1)),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
mult(a,mult(b,mult(b,c))) != mult(mult(a,mult(b,b)),c),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f17,definition,
sF2_fnc = mult(b,c),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f18,definition,
sF1_fnc = mult(b,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f19,definition,
sF0_fnc = mult(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f20,definition,
sF5_fnc = mult(b,b),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f21,definition,
sF4_fnc = mult(a,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f22,definition,
sF3_fnc = mult(sF4_fnc,c),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f23,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f16,f22,f21,f20,f19,f18,f17]) ).
fof(f33,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f11,f10]) ).
fof(f42,plain,
! [X0] : ld(X0,X0) = unit,
inference(paramodulation,[status(thm)],[f13,f10]) ).
fof(f62,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f75,plain,
! [X0,X1] : mult(mult(X0,X0),mult(X1,unit)) = mult(X0,mult(X0,X1)),
inference(paramodulation,[status(thm)],[f13,f15]) ).
fof(f76,plain,
! [X0,X1,X2,X3] : mult(mult(mult(X0,mult(X0,X1)),mult(X0,mult(X0,X1))),mult(X2,X3)) = mult(mult(mult(X0,X0),mult(X1,mult(mult(X0,mult(X0,X1)),X2))),X3),
inference(paramodulation,[status(thm)],[f15,f15]) ).
fof(f85,plain,
! [X0] : mult(mult(b,b),mult(c,X0)) = mult(mult(b,sF2_fnc),X0),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f87,plain,
! [X0,X1,X2] : mult(mult(X0,X0),mult(ld(X0,X1),X2)) = mult(mult(X0,X1),X2),
inference(paramodulation,[status(thm)],[f9,f15]) ).
fof(f91,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X0),mult(X1,X2)),X2) = mult(X0,mult(X0,X1)),
inference(paramodulation,[status(thm)],[f15,f12]) ).
fof(f95,plain,
! [X0,X1] : mult(mult(X0,X0),X1) = mult(X0,mult(X0,X1)),
inference(forward_demodulation,[status(thm)],[f13,f75]) ).
fof(f96,plain,
! [X0,X1,X2,X3] : mult(mult(X0,mult(X0,X1)),mult(mult(X0,mult(X0,X1)),mult(X2,X3))) = mult(mult(mult(X0,X0),mult(X1,mult(mult(X0,mult(X0,X1)),X2))),X3),
inference(forward_demodulation,[status(thm)],[f95,f76]) ).
fof(f97,plain,
! [X0,X1,X2,X3] : mult(mult(X0,X0),mult(X1,mult(mult(X0,mult(X0,X1)),mult(X2,X3)))) = mult(mult(mult(X0,X0),mult(X1,mult(mult(X0,mult(X0,X1)),X2))),X3),
inference(forward_demodulation,[status(thm)],[f15,f96]) ).
fof(f98,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(mult(X0,mult(X0,X1)),mult(X2,X3))))) = mult(mult(mult(X0,X0),mult(X1,mult(mult(X0,mult(X0,X1)),X2))),X3),
inference(forward_demodulation,[status(thm)],[f95,f97]) ).
fof(f99,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(mult(X0,X0),mult(X1,mult(X2,X3)))))) = mult(mult(mult(X0,X0),mult(X1,mult(mult(X0,mult(X0,X1)),X2))),X3),
inference(forward_demodulation,[status(thm)],[f15,f98]) ).
fof(f100,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(X0,mult(X0,mult(X1,mult(X2,X3))))))) = mult(mult(mult(X0,X0),mult(X1,mult(mult(X0,mult(X0,X1)),X2))),X3),
inference(forward_demodulation,[status(thm)],[f95,f99]) ).
fof(f101,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(X0,mult(X0,mult(X1,mult(X2,X3))))))) = mult(mult(X0,mult(X0,mult(X1,mult(mult(X0,mult(X0,X1)),X2)))),X3),
inference(forward_demodulation,[status(thm)],[f95,f100]) ).
fof(f102,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(X0,mult(X0,mult(X1,mult(X2,X3))))))) = mult(mult(X0,X0),mult(mult(X1,mult(mult(X0,mult(X0,X1)),X2)),X3)),
inference(forward_demodulation,[status(thm)],[f15,f101]) ).
fof(f103,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(X0,mult(X0,mult(X1,mult(X2,X3))))))) = mult(X0,mult(X0,mult(mult(X1,mult(mult(X0,mult(X0,X1)),X2)),X3))),
inference(forward_demodulation,[status(thm)],[f95,f102]) ).
fof(f104,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(X0,mult(X0,mult(X1,mult(X2,X3))))))) = mult(X0,mult(X0,mult(mult(X1,mult(mult(X0,X0),mult(X1,X2))),X3))),
inference(forward_demodulation,[status(thm)],[f15,f103]) ).
fof(f105,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(X0,mult(X0,mult(X1,mult(X2,X3))))))) = mult(X0,mult(X0,mult(mult(X1,mult(X0,mult(X0,mult(X1,X2)))),X3))),
inference(forward_demodulation,[status(thm)],[f95,f104]) ).
fof(f125,plain,
! [X0] : mult(b,mult(b,mult(c,X0))) = mult(mult(b,sF2_fnc),X0),
inference(forward_demodulation,[status(thm)],[f95,f85]) ).
fof(f126,plain,
! [X0] : mult(b,mult(b,mult(c,X0))) = mult(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f18,f125]) ).
fof(f130,plain,
! [X0,X1,X2] : mult(X0,mult(X0,mult(ld(X0,X1),X2))) = mult(mult(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f95,f87]) ).
fof(f134,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X0,mult(X1,X2))),X2) = mult(X0,mult(X0,X1)),
inference(forward_demodulation,[status(thm)],[f95,f91]) ).
fof(f161,plain,
! [X0,X1] : X0 = mult(X1,mult(X1,ld(mult(X1,X1),X0))),
inference(paramodulation,[status(thm)],[f9,f95]) ).
fof(f164,plain,
! [X0] : mult(sF5_fnc,X0) = mult(b,mult(b,X0)),
inference(paramodulation,[status(thm)],[f20,f95]) ).
fof(f173,plain,
! [X0] : mult(sF5_fnc,mult(c,X0)) = mult(sF1_fnc,X0),
inference(backward_demodulation,[status(thm)],[f164,f126]) ).
fof(f181,plain,
mult(sF5_fnc,c) = mult(sF1_fnc,unit),
inference(paramodulation,[status(thm)],[f13,f173]) ).
fof(f184,plain,
mult(sF5_fnc,c) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f13,f181]) ).
fof(f190,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,mult(X1,mult(X0,mult(X0,mult(X1,mult(X2,ld(mult(X1,mult(X0,mult(X0,mult(X1,X2)))),X3)))))))) = mult(X0,mult(X0,X3)),
inference(paramodulation,[status(thm)],[f9,f105]) ).
fof(f327,plain,
ld(sF5_fnc,sF1_fnc) = c,
inference(paramodulation,[status(thm)],[f184,f10]) ).
fof(f341,plain,
! [X0] : mult(sF5_fnc,ld(b,X0)) = mult(b,X0),
inference(paramodulation,[status(thm)],[f9,f164]) ).
fof(f549,plain,
! [X0] : ld(sF5_fnc,mult(b,X0)) = ld(b,X0),
inference(paramodulation,[status(thm)],[f341,f10]) ).
fof(f719,plain,
! [X0] : ld(sF5_fnc,X0) = ld(b,ld(b,X0)),
inference(paramodulation,[status(thm)],[f9,f549]) ).
fof(f808,plain,
! [X0,X1] : mult(b,mult(b,mult(ld(sF5_fnc,X0),X1))) = mult(mult(b,ld(b,X0)),X1),
inference(paramodulation,[status(thm)],[f719,f130]) ).
fof(f837,plain,
! [X0,X1,X2] : ld(X0,mult(mult(X0,X1),X2)) = mult(X0,mult(ld(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f130,f10]) ).
fof(f861,plain,
! [X0,X1] : mult(sF5_fnc,mult(ld(sF5_fnc,X0),X1)) = mult(mult(b,ld(b,X0)),X1),
inference(forward_demodulation,[status(thm)],[f164,f808]) ).
fof(f862,plain,
! [X0,X1] : mult(sF5_fnc,mult(ld(sF5_fnc,X0),X1)) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f9,f861]) ).
fof(f892,plain,
! [X0,X1] : ld(sF5_fnc,mult(mult(sF5_fnc,X0),X1)) = mult(X0,X1),
inference(backward_demodulation,[status(thm)],[f837,f862]) ).
fof(f1041,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X0,X1)),X2) = mult(X0,mult(X0,rd(X1,X2))),
inference(paramodulation,[status(thm)],[f11,f134]) ).
fof(f1196,plain,
! [X0,X1] : ld(X0,X1) = mult(X0,ld(mult(X0,X0),X1)),
inference(paramodulation,[status(thm)],[f161,f10]) ).
fof(f1431,plain,
! [X0,X1] : ld(X0,ld(X0,X1)) = ld(mult(X0,X0),X1),
inference(paramodulation,[status(thm)],[f1196,f10]) ).
fof(f1481,plain,
! [X0,X1] : rd(X0,ld(X1,ld(X1,X0))) = mult(X1,X1),
inference(paramodulation,[status(thm)],[f1431,f62]) ).
fof(f1519,plain,
! [X0,X1] : rd(mult(X0,X1),ld(X0,X1)) = mult(X0,X0),
inference(paramodulation,[status(thm)],[f10,f1481]) ).
fof(f1871,plain,
! [X0,X1] : ld(sF5_fnc,mult(X0,X1)) = mult(ld(sF5_fnc,X0),X1),
inference(paramodulation,[status(thm)],[f9,f892]) ).
fof(f1913,plain,
! [X0,X1] : rd(ld(sF5_fnc,mult(X0,X1)),X1) = ld(sF5_fnc,X0),
inference(paramodulation,[status(thm)],[f1871,f12]) ).
fof(f3979,plain,
! [X0,X1] : rd(ld(sF5_fnc,X0),X1) = ld(sF5_fnc,rd(X0,X1)),
inference(paramodulation,[status(thm)],[f11,f1913]) ).
fof(f4298,plain,
! [X0,X1,X2,X3] : rd(mult(X0,mult(X0,X1)),mult(X0,mult(X2,mult(X0,mult(X0,mult(X2,mult(X3,ld(mult(X2,mult(X0,mult(X0,mult(X2,X3)))),X1)))))))) = X0,
inference(paramodulation,[status(thm)],[f190,f12]) ).
fof(f4299,plain,
! [X0,X1,X2,X3] : ld(X0,mult(X0,mult(X0,X1))) = mult(X0,mult(X2,mult(X0,mult(X0,mult(X2,mult(X3,ld(mult(X2,mult(X0,mult(X0,mult(X2,X3)))),X1))))))),
inference(paramodulation,[status(thm)],[f190,f10]) ).
fof(f4958,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X0,rd(X1,mult(X0,mult(X2,mult(X0,mult(X0,mult(X2,mult(X3,ld(mult(X2,mult(X0,mult(X0,mult(X2,X3)))),X1)))))))))) = X0,
inference(forward_demodulation,[status(thm)],[f1041,f4298]) ).
fof(f4967,plain,
! [X0,X1] : mult(X0,mult(X0,rd(X1,mult(X0,X1)))) = X0,
inference(backward_demodulation,[status(thm)],[f4971,f4958]) ).
fof(f4971,plain,
! [X0,X1,X2,X3] : mult(X0,X1) = mult(X0,mult(X2,mult(X0,mult(X0,mult(X2,mult(X3,ld(mult(X2,mult(X0,mult(X0,mult(X2,X3)))),X1))))))),
inference(forward_demodulation,[status(thm)],[f10,f4299]) ).
fof(f5295,plain,
! [X0] : rd(c,X0) = ld(sF5_fnc,rd(sF1_fnc,X0)),
inference(paramodulation,[status(thm)],[f327,f3979]) ).
fof(f5297,plain,
! [X0] : rd(unit,X0) = ld(sF5_fnc,rd(sF5_fnc,X0)),
inference(paramodulation,[status(thm)],[f42,f3979]) ).
fof(f22179,plain,
mult(sF4_fnc,mult(sF4_fnc,rd(c,sF3_fnc))) = sF4_fnc,
inference(paramodulation,[status(thm)],[f22,f4967]) ).
fof(f22182,plain,
mult(a,mult(a,rd(sF5_fnc,sF4_fnc))) = a,
inference(paramodulation,[status(thm)],[f21,f4967]) ).
fof(f22183,plain,
mult(a,mult(a,rd(sF1_fnc,sF0_fnc))) = a,
inference(paramodulation,[status(thm)],[f19,f4967]) ).
fof(f22195,plain,
! [X0] : mult(X0,mult(X0,rd(unit,X0))) = X0,
inference(paramodulation,[status(thm)],[f13,f4967]) ).
fof(f22552,plain,
ld(sF4_fnc,sF4_fnc) = mult(sF4_fnc,rd(c,sF3_fnc)),
inference(paramodulation,[status(thm)],[f22179,f10]) ).
fof(f22560,plain,
unit = mult(sF4_fnc,rd(c,sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f42,f22552]) ).
fof(f23285,plain,
ld(sF4_fnc,unit) = rd(c,sF3_fnc),
inference(paramodulation,[status(thm)],[f22560,f10]) ).
fof(f23305,plain,
ld(ld(sF4_fnc,unit),c) = sF3_fnc,
inference(paramodulation,[status(thm)],[f23285,f33]) ).
fof(f23326,plain,
ld(a,a) = mult(a,rd(sF5_fnc,sF4_fnc)),
inference(paramodulation,[status(thm)],[f22182,f10]) ).
fof(f23334,plain,
unit = mult(a,rd(sF5_fnc,sF4_fnc)),
inference(forward_demodulation,[status(thm)],[f42,f23326]) ).
fof(f23339,plain,
ld(a,unit) = rd(sF5_fnc,sF4_fnc),
inference(paramodulation,[status(thm)],[f23334,f10]) ).
fof(f24046,plain,
rd(unit,sF4_fnc) = ld(sF5_fnc,ld(a,unit)),
inference(paramodulation,[status(thm)],[f23339,f5297]) ).
fof(f24077,plain,
ld(a,a) = mult(a,rd(sF1_fnc,sF0_fnc)),
inference(paramodulation,[status(thm)],[f22183,f10]) ).
fof(f24085,plain,
unit = mult(a,rd(sF1_fnc,sF0_fnc)),
inference(forward_demodulation,[status(thm)],[f42,f24077]) ).
fof(f24090,plain,
ld(a,unit) = rd(sF1_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f24085,f10]) ).
fof(f24108,plain,
rd(c,sF0_fnc) = ld(sF5_fnc,ld(a,unit)),
inference(paramodulation,[status(thm)],[f24090,f5295]) ).
fof(f24123,plain,
rd(c,sF0_fnc) = rd(unit,sF4_fnc),
inference(forward_demodulation,[status(thm)],[f24046,f24108]) ).
fof(f24296,plain,
ld(rd(unit,sF4_fnc),c) = sF0_fnc,
inference(paramodulation,[status(thm)],[f24123,f33]) ).
fof(f25121,plain,
! [X0] : rd(X0,ld(X0,mult(X0,rd(unit,X0)))) = mult(X0,X0),
inference(paramodulation,[status(thm)],[f22195,f1519]) ).
fof(f25297,plain,
! [X0] : rd(X0,rd(unit,X0)) = mult(X0,X0),
inference(forward_demodulation,[status(thm)],[f10,f25121]) ).
fof(f25373,plain,
! [X0] : ld(mult(X0,X0),X0) = rd(unit,X0),
inference(paramodulation,[status(thm)],[f25297,f33]) ).
fof(f25528,plain,
! [X0] : ld(X0,ld(X0,X0)) = rd(unit,X0),
inference(forward_demodulation,[status(thm)],[f1431,f25373]) ).
fof(f25531,plain,
ld(ld(sF4_fnc,unit),c) = sF0_fnc,
inference(backward_demodulation,[status(thm)],[f25616,f24296]) ).
fof(f25616,plain,
! [X0] : ld(X0,unit) = rd(unit,X0),
inference(forward_demodulation,[status(thm)],[f42,f25528]) ).
fof(f25631,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f23305,f25531]) ).
fof(f25632,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f25631,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP687-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:37:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 25.66/3.66 % Refutation found
% 25.66/3.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 25.66/3.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.52/4.90 % Elapsed time: 4.324800 seconds
% 19.52/4.90 % CPU time: 21.594722 seconds
% 19.52/4.90 % Total memory used: 394.424 MB
% 19.52/4.90 % Net memory used: 385.352 MB
%------------------------------------------------------------------------------