%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:32:23 PM UTC 2026
% Result : Unsatisfiable 9.41s 1.74s
% Output : CNFRefutation 9.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 84 unt; 3 def)
% Number of atoms : 84 ( 83 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(identity,X,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,W,Z] : ifeq(product(X,Y,W),true,ifeq(product(X,Y,Z),true,equalish(Z,W),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U,Z,W,Y,V,X] : ifeq(product(U,Z,W),true,ifeq(product(Y,Z,V),true,ifeq(product(X,Y,U),true,product(X,V,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,W,Z] : ifeq(equalish(X,Y),true,ifeq(product(W,Z,X),true,product(W,Z,Y),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
equalish(a,b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0] : product(identity,X0,X0) = true,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
! [X0] : product(inverse(X0),X0,identity) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X3,X2),true),true) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f16,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X1,X4),true,ifeq(product(X5,X3,X0),true,product(X5,X4,X2),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : ifeq(equalish(X0,X1),true,ifeq(product(X2,X3,X0),true,product(X2,X3,X1),true),true) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f19,plain,
equalish(a,b) = true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f20,plain,
equalish(inverse(a),inverse(b)) != true,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f21,definition,
sF1_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f22,definition,
sF2_fnc = inverse(b),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f23,definition,
sF0_fnc = equalish(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f24,plain,
sF0_fnc != true,
inference(definition_folding,[],[f20,f23,f22,f21]) ).
fof(f26,plain,
! [X0,X1] : ifeq(product(X0,X1,sF2_fnc),true,ifeq(product(X0,X1,sF1_fnc),true,sF0_fnc,true),true) = true,
inference(paramodulation,[status(thm)],[f23,f15]) ).
fof(f27,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(X0,X1,a),true,product(X0,X1,b),true),true) = true,
inference(paramodulation,[status(thm)],[f19,f18]) ).
fof(f29,plain,
! [X0,X1] : ifeq(product(X0,X1,a),true,product(X0,X1,b),true) = true,
inference(backward_demodulation,[status(thm)],[f11,f27]) ).
fof(f78,plain,
product(sF2_fnc,b,identity) = true,
inference(paramodulation,[status(thm)],[f22,f13]) ).
fof(f79,plain,
product(sF1_fnc,a,identity) = true,
inference(paramodulation,[status(thm)],[f21,f13]) ).
fof(f83,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(inverse(X0),X0,X1),true,equalish(X1,identity),true),true) = true,
inference(paramodulation,[status(thm)],[f13,f15]) ).
fof(f86,plain,
! [X0,X1] : ifeq(product(inverse(X0),X0,X1),true,equalish(X1,identity),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f83]) ).
fof(f90,plain,
! [X0,X1,X2] : ifeq(equalish(multiply(X0,X1),X2),true,ifeq(true,true,product(X0,X1,X2),true),true) = true,
inference(paramodulation,[status(thm)],[f14,f18]) ).
fof(f94,plain,
! [X0,X1,X2] : ifeq(equalish(multiply(X0,X1),X2),true,product(X0,X1,X2),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f90]) ).
fof(f153,plain,
! [X0,X1,X2,X3] : ifeq(true,true,ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,identity),true,product(X3,X2,X1),true),true),true) = true,
inference(paramodulation,[status(thm)],[f12,f16]) ).
fof(f178,plain,
! [X0,X1,X2,X3] : ifeq(product(X0,X1,X2),true,ifeq(product(X3,X0,identity),true,product(X3,X2,X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f153]) ).
fof(f1970,plain,
! [X0] : ifeq(true,true,ifeq(product(X0,sF1_fnc,identity),true,product(X0,identity,a),true),true) = true,
inference(paramodulation,[status(thm)],[f79,f178]) ).
fof(f1979,plain,
! [X0,X1] : ifeq(true,true,ifeq(product(X0,inverse(X1),identity),true,product(X0,identity,X1),true),true) = true,
inference(paramodulation,[status(thm)],[f13,f178]) ).
fof(f1995,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(X0,X1,identity),true,product(X0,multiply(X1,X2),X2),true),true) = true,
inference(paramodulation,[status(thm)],[f14,f178]) ).
fof(f1997,plain,
! [X0,X1] : ifeq(product(a,X0,X1),true,ifeq(true,true,product(sF1_fnc,X1,X0),true),true) = true,
inference(paramodulation,[status(thm)],[f79,f178]) ).
fof(f1998,plain,
! [X0,X1] : ifeq(product(b,X0,X1),true,ifeq(true,true,product(sF2_fnc,X1,X0),true),true) = true,
inference(paramodulation,[status(thm)],[f78,f178]) ).
fof(f1999,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,ifeq(true,true,product(inverse(X0),X2,X1),true),true) = true,
inference(paramodulation,[status(thm)],[f13,f178]) ).
fof(f2039,plain,
! [X0] : ifeq(product(X0,sF1_fnc,identity),true,product(X0,identity,a),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f1970]) ).
fof(f2048,plain,
! [X0,X1] : ifeq(product(X0,inverse(X1),identity),true,product(X0,identity,X1),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f1979]) ).
fof(f2064,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,identity),true,product(X0,multiply(X1,X2),X2),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f1995]) ).
fof(f2065,plain,
! [X0,X1] : ifeq(product(a,X0,X1),true,product(sF1_fnc,X1,X0),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f1997]) ).
fof(f2066,plain,
! [X0,X1] : ifeq(product(b,X0,X1),true,product(sF2_fnc,X1,X0),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f1998]) ).
fof(f2067,plain,
! [X0,X1,X2] : ifeq(product(X0,X1,X2),true,product(inverse(X0),X2,X1),true) = true,
inference(forward_demodulation,[status(thm)],[f11,f1999]) ).
fof(f10393,plain,
! [X0] : ifeq(true,true,product(sF1_fnc,multiply(a,X0),X0),true) = true,
inference(paramodulation,[status(thm)],[f14,f2065]) ).
fof(f10412,plain,
! [X0] : product(sF1_fnc,multiply(a,X0),X0) = true,
inference(forward_demodulation,[status(thm)],[f11,f10393]) ).
fof(f27704,plain,
! [X0,X1] : ifeq(true,true,product(inverse(X0),multiply(X0,X1),X1),true) = true,
inference(paramodulation,[status(thm)],[f13,f2064]) ).
fof(f27772,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1) = true,
inference(forward_demodulation,[status(thm)],[f11,f27704]) ).
fof(f27802,plain,
! [X0] : ifeq(true,true,product(inverse(sF1_fnc),X0,multiply(a,X0)),true) = true,
inference(paramodulation,[status(thm)],[f10412,f2067]) ).
fof(f28002,plain,
! [X0] : product(inverse(sF1_fnc),X0,multiply(a,X0)) = true,
inference(forward_demodulation,[status(thm)],[f11,f27802]) ).
fof(f29370,plain,
! [X0,X1] : ifeq(true,true,product(inverse(inverse(X0)),X1,multiply(X0,X1)),true) = true,
inference(paramodulation,[status(thm)],[f27772,f2067]) ).
fof(f29471,plain,
! [X0,X1] : product(inverse(inverse(X0)),X1,multiply(X0,X1)) = true,
inference(forward_demodulation,[status(thm)],[f11,f29370]) ).
fof(f29997,plain,
ifeq(true,true,equalish(multiply(a,sF1_fnc),identity),true) = true,
inference(paramodulation,[status(thm)],[f28002,f86]) ).
fof(f30098,plain,
equalish(multiply(a,sF1_fnc),identity) = true,
inference(forward_demodulation,[status(thm)],[f11,f29997]) ).
fof(f30173,plain,
ifeq(true,true,product(a,sF1_fnc,identity),true) = true,
inference(paramodulation,[status(thm)],[f30098,f94]) ).
fof(f30186,plain,
product(a,sF1_fnc,identity) = true,
inference(forward_demodulation,[status(thm)],[f11,f30173]) ).
fof(f30198,plain,
ifeq(true,true,product(a,identity,a),true) = true,
inference(paramodulation,[status(thm)],[f30186,f2039]) ).
fof(f30283,plain,
product(a,identity,a) = true,
inference(forward_demodulation,[status(thm)],[f11,f30198]) ).
fof(f30511,plain,
ifeq(true,true,product(a,identity,b),true) = true,
inference(paramodulation,[status(thm)],[f30283,f29]) ).
fof(f30592,plain,
product(a,identity,b) = true,
inference(forward_demodulation,[status(thm)],[f11,f30511]) ).
fof(f30652,plain,
ifeq(true,true,product(sF1_fnc,b,identity),true) = true,
inference(paramodulation,[status(thm)],[f30592,f2065]) ).
fof(f30735,plain,
product(sF1_fnc,b,identity) = true,
inference(forward_demodulation,[status(thm)],[f11,f30652]) ).
fof(f30813,plain,
! [X0] : ifeq(true,true,product(sF1_fnc,multiply(b,X0),X0),true) = true,
inference(paramodulation,[status(thm)],[f30735,f2064]) ).
fof(f30898,plain,
! [X0] : product(sF1_fnc,multiply(b,X0),X0) = true,
inference(forward_demodulation,[status(thm)],[f11,f30813]) ).
fof(f31716,plain,
! [X0] : ifeq(true,true,product(inverse(sF1_fnc),X0,multiply(b,X0)),true) = true,
inference(paramodulation,[status(thm)],[f30898,f2067]) ).
fof(f31818,plain,
! [X0] : product(inverse(sF1_fnc),X0,multiply(b,X0)) = true,
inference(forward_demodulation,[status(thm)],[f11,f31716]) ).
fof(f35852,plain,
! [X0] : ifeq(true,true,equalish(multiply(X0,inverse(X0)),identity),true) = true,
inference(paramodulation,[status(thm)],[f29471,f86]) ).
fof(f35959,plain,
! [X0] : equalish(multiply(X0,inverse(X0)),identity) = true,
inference(forward_demodulation,[status(thm)],[f11,f35852]) ).
fof(f36043,plain,
! [X0] : ifeq(true,true,product(X0,inverse(X0),identity),true) = true,
inference(paramodulation,[status(thm)],[f35959,f94]) ).
fof(f36056,plain,
! [X0] : product(X0,inverse(X0),identity) = true,
inference(forward_demodulation,[status(thm)],[f11,f36043]) ).
fof(f36113,plain,
! [X0] : ifeq(true,true,product(X0,identity,X0),true) = true,
inference(paramodulation,[status(thm)],[f36056,f2048]) ).
fof(f36245,plain,
! [X0] : product(X0,identity,X0) = true,
inference(forward_demodulation,[status(thm)],[f11,f36113]) ).
fof(f42641,plain,
ifeq(true,true,equalish(multiply(b,sF1_fnc),identity),true) = true,
inference(paramodulation,[status(thm)],[f31818,f86]) ).
fof(f42752,plain,
equalish(multiply(b,sF1_fnc),identity) = true,
inference(forward_demodulation,[status(thm)],[f11,f42641]) ).
fof(f42836,plain,
ifeq(true,true,product(b,sF1_fnc,identity),true) = true,
inference(paramodulation,[status(thm)],[f42752,f94]) ).
fof(f42849,plain,
product(b,sF1_fnc,identity) = true,
inference(forward_demodulation,[status(thm)],[f11,f42836]) ).
fof(f42857,plain,
ifeq(true,true,product(sF2_fnc,identity,sF1_fnc),true) = true,
inference(paramodulation,[status(thm)],[f42849,f2066]) ).
fof(f42947,plain,
product(sF2_fnc,identity,sF1_fnc) = true,
inference(forward_demodulation,[status(thm)],[f11,f42857]) ).
fof(f43121,plain,
ifeq(product(sF2_fnc,identity,sF2_fnc),true,ifeq(true,true,sF0_fnc,true),true) = true,
inference(paramodulation,[status(thm)],[f42947,f26]) ).
fof(f43205,plain,
ifeq(true,true,ifeq(true,true,sF0_fnc,true),true) = true,
inference(forward_demodulation,[status(thm)],[f36245,f43121]) ).
fof(f43206,plain,
ifeq(true,true,sF0_fnc,true) = true,
inference(forward_demodulation,[status(thm)],[f11,f43205]) ).
fof(f43207,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f11,f43206]) ).
fof(f43208,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f43207,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP048-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n020.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 19:56:32 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 9.41/1.74 % Refutation found
% 9.41/1.74 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.41/1.74 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.42/2.70 % Elapsed time: 2.321520 seconds
% 9.42/2.70 % CPU time: 12.378959 seconds
% 9.42/2.70 % Total memory used: 287.811 MB
% 9.42/2.70 % Net memory used: 277.702 MB
%------------------------------------------------------------------------------