%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG006-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:04:38 PM UTC 2026
% Result : Unsatisfiable 102.33s 13.33s
% Output : CNFRefutation 78.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 18
% Syntax : Number of formulae : 91 ( 91 unt; 1 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 155 ( 155 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : sum(additive_identity,X,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : sum(X,additive_identity,X) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : sum(X,Y,add(X,Y)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,Z,W,Y,V,X] : ifeq(sum(U,Z,W),true,ifeq(sum(Y,Z,V),true,ifeq(sum(X,Y,U),true,sum(X,V,W),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] : ifeq(sum(X,Y,Z),true,sum(Y,X,Z),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,V3,V4,Z,V2,Y,V1] : ifeq(product(X,V3,V4),true,ifeq(product(X,Z,V2),true,ifeq(product(X,Y,V1),true,ifeq(sum(Y,Z,V3),true,sum(V1,V2,V4),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,V,U] : ifeq2(sum(X,Y,V),true,ifeq2(sum(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,V,U] : ifeq2(product(X,Y,V),true,ifeq2(product(X,Y,U),true,U,V),V) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
sum(b,additive_inverse(c),bS_Ic) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(a,b,aPb) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
product(a,c,aPc) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
product(a,bS_Ic,aPb_S_IaPc) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0] : sum(additive_identity,X0,X0) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0] : sum(X0,additive_identity,X0) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f29,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X1,X4),true,ifeq(sum(X5,X3,X0),true,sum(X5,X4,X2),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(X1,X0,X2),true) = true,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4,X5,X6] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(product(X0,X5,X6),true,ifeq(sum(X5,X3,X1),true,sum(X6,X4,X2),true),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f42,plain,
! [X0,X1,X2,X3] : ifeq2(sum(X0,X1,X2),true,ifeq2(sum(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
! [X0,X1,X2,X3] : ifeq2(product(X0,X1,X2),true,ifeq2(product(X0,X1,X3),true,X3,X2),X2) = X2,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
sum(b,additive_inverse(c),bS_Ic) = true,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f45,plain,
product(a,b,aPb) = true,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f46,plain,
product(a,c,aPc) = true,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f48,plain,
product(a,bS_Ic,aPb_S_IaPc) != true,
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f49,definition,
sF0_fnc = product(a,bS_Ic,aPb_S_IaPc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f50,plain,
sF0_fnc != true,
inference(definition_folding,[],[f48,f49]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(true,true,ifeq(sum(X5,X3,X1),true,sum(multiply(X0,X5),X4,X2),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f29,f38]) ).
fof(f137,plain,
! [X0,X1,X2,X3,X4,X5] : ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X5,X3,X1),true,sum(multiply(X0,X5),X4,X2),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f115]) ).
fof(f229,plain,
ifeq(true,true,sum(additive_inverse(aPc),aPb,aPb_S_IaPc),true) = true,
inference(paramodulation,[status(thm)],[f47,f35]) ).
fof(f230,plain,
ifeq(true,true,sum(additive_inverse(c),b,bS_Ic),true) = true,
inference(paramodulation,[status(thm)],[f44,f35]) ).
fof(f233,plain,
! [X0,X1] : ifeq(true,true,sum(X0,X1,add(X1,X0)),true) = true,
inference(paramodulation,[status(thm)],[f30,f35]) ).
fof(f244,plain,
sum(additive_inverse(aPc),aPb,aPb_S_IaPc) = true,
inference(forward_demodulation,[status(thm)],[f26,f229]) ).
fof(f245,plain,
sum(additive_inverse(c),b,bS_Ic) = true,
inference(forward_demodulation,[status(thm)],[f26,f230]) ).
fof(f248,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)) = true,
inference(forward_demodulation,[status(thm)],[f26,f233]) ).
fof(f292,plain,
! [X0,X1,X2,X3] : ifeq(true,true,ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true),true) = true,
inference(paramodulation,[status(thm)],[f27,f33]) ).
fof(f333,plain,
! [X0,X1,X2,X3] : ifeq(sum(X0,X1,X2),true,ifeq(sum(X3,X0,additive_identity),true,sum(X3,X2,X1),true),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f292]) ).
fof(f585,plain,
! [X0,X1,X2] : ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X1,X0)),add(X1,X0)) = add(X1,X0),
inference(paramodulation,[status(thm)],[f248,f42]) ).
fof(f586,plain,
! [X0,X1,X2] : ifeq2(true,true,ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)),add(X0,X1)) = add(X0,X1),
inference(paramodulation,[status(thm)],[f30,f42]) ).
fof(f594,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,ifeq2(true,true,X0,X1),X1) = X1,
inference(paramodulation,[status(thm)],[f28,f42]) ).
fof(f595,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,ifeq2(true,true,add(X1,X0),X2),X2) = X2,
inference(paramodulation,[status(thm)],[f248,f42]) ).
fof(f605,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,X2,add(X1,X0)) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f25,f585]) ).
fof(f606,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,X2,add(X0,X1)) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f586]) ).
fof(f614,plain,
! [X0,X1] : ifeq2(sum(X0,additive_identity,X1),true,X0,X1) = X1,
inference(forward_demodulation,[status(thm)],[f25,f594]) ).
fof(f615,plain,
! [X0,X1,X2] : ifeq2(sum(X0,X1,X2),true,add(X1,X0),X2) = X2,
inference(forward_demodulation,[status(thm)],[f25,f595]) ).
fof(f701,plain,
ifeq2(true,true,add(b,additive_inverse(c)),bS_Ic) = bS_Ic,
inference(paramodulation,[status(thm)],[f245,f615]) ).
fof(f702,plain,
ifeq2(true,true,add(aPb,additive_inverse(aPc)),aPb_S_IaPc) = aPb_S_IaPc,
inference(paramodulation,[status(thm)],[f244,f615]) ).
fof(f710,plain,
! [X0,X1] : ifeq2(true,true,add(X0,X1),add(X1,X0)) = add(X1,X0),
inference(paramodulation,[status(thm)],[f30,f615]) ).
fof(f716,plain,
add(b,additive_inverse(c)) = bS_Ic,
inference(forward_demodulation,[status(thm)],[f25,f701]) ).
fof(f717,plain,
add(aPb,additive_inverse(aPc)) = aPb_S_IaPc,
inference(forward_demodulation,[status(thm)],[f25,f702]) ).
fof(f724,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f25,f710]) ).
fof(f754,plain,
! [X0] : ifeq2(product(a,c,X0),true,ifeq2(true,true,aPc,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f46,f43]) ).
fof(f761,plain,
! [X0] : ifeq2(product(a,c,X0),true,aPc,X0) = X0,
inference(forward_demodulation,[status(thm)],[f25,f754]) ).
fof(f963,plain,
ifeq2(true,true,aPc,multiply(a,c)) = multiply(a,c),
inference(paramodulation,[status(thm)],[f29,f761]) ).
fof(f965,plain,
aPc = multiply(a,c),
inference(forward_demodulation,[status(thm)],[f25,f963]) ).
fof(f3793,plain,
! [X0,X1,X2] : ifeq(true,true,ifeq(product(a,X0,X1),true,ifeq(sum(X2,X0,b),true,sum(multiply(a,X2),X1,aPb),true),true),true) = true,
inference(paramodulation,[status(thm)],[f45,f137]) ).
fof(f3854,plain,
! [X0,X1,X2] : ifeq(product(a,X0,X1),true,ifeq(sum(X2,X0,b),true,sum(multiply(a,X2),X1,aPb),true),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f3793]) ).
fof(f11752,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,ifeq(true,true,sum(additive_inverse(X0),X2,X1),true),true) = true,
inference(paramodulation,[status(thm)],[f31,f333]) ).
fof(f11779,plain,
! [X0,X1,X2] : ifeq(sum(X0,X1,X2),true,sum(additive_inverse(X0),X2,X1),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f11752]) ).
fof(f12149,plain,
! [X0] : ifeq(true,true,sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),true) = true,
inference(paramodulation,[status(thm)],[f31,f11779]) ).
fof(f12155,plain,
! [X0,X1] : ifeq(true,true,sum(additive_inverse(X0),add(X1,X0),X1),true) = true,
inference(paramodulation,[status(thm)],[f248,f11779]) ).
fof(f12180,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0) = true,
inference(forward_demodulation,[status(thm)],[f26,f12149]) ).
fof(f12187,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1) = true,
inference(forward_demodulation,[status(thm)],[f26,f12155]) ).
fof(f12204,plain,
! [X0] : ifeq2(true,true,additive_inverse(additive_inverse(X0)),X0) = X0,
inference(paramodulation,[status(thm)],[f12180,f614]) ).
fof(f12302,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f25,f12204]) ).
fof(f12425,plain,
sum(additive_inverse(additive_inverse(c)),bS_Ic,b) = true,
inference(paramodulation,[status(thm)],[f716,f12187]) ).
fof(f12499,plain,
! [X0,X1] : ifeq2(true,true,X0,add(add(X0,X1),additive_inverse(X1))) = add(add(X0,X1),additive_inverse(X1)),
inference(paramodulation,[status(thm)],[f12187,f605]) ).
fof(f12530,plain,
sum(c,bS_Ic,b) = true,
inference(forward_demodulation,[status(thm)],[f12302,f12425]) ).
fof(f12591,plain,
! [X0,X1] : X0 = add(add(X0,X1),additive_inverse(X1)),
inference(forward_demodulation,[status(thm)],[f25,f12499]) ).
fof(f13481,plain,
! [X0,X1] : X0 = add(add(X1,X0),additive_inverse(X1)),
inference(paramodulation,[status(thm)],[f724,f12591]) ).
fof(f143543,plain,
! [X0] : ifeq(product(a,bS_Ic,X0),true,ifeq(true,true,sum(multiply(a,c),X0,aPb),true),true) = true,
inference(paramodulation,[status(thm)],[f12530,f3854]) ).
fof(f143585,plain,
! [X0] : ifeq(product(a,bS_Ic,X0),true,sum(multiply(a,c),X0,aPb),true) = true,
inference(forward_demodulation,[status(thm)],[f26,f143543]) ).
fof(f143586,plain,
! [X0] : ifeq(product(a,bS_Ic,X0),true,sum(aPc,X0,aPb),true) = true,
inference(forward_demodulation,[status(thm)],[f965,f143585]) ).
fof(f148690,plain,
ifeq(true,true,sum(aPc,multiply(a,bS_Ic),aPb),true) = true,
inference(paramodulation,[status(thm)],[f29,f143586]) ).
fof(f148703,plain,
sum(aPc,multiply(a,bS_Ic),aPb) = true,
inference(forward_demodulation,[status(thm)],[f26,f148690]) ).
fof(f148935,plain,
ifeq2(true,true,aPb,add(aPc,multiply(a,bS_Ic))) = add(aPc,multiply(a,bS_Ic)),
inference(paramodulation,[status(thm)],[f148703,f606]) ).
fof(f149223,plain,
aPb = add(aPc,multiply(a,bS_Ic)),
inference(forward_demodulation,[status(thm)],[f25,f148935]) ).
fof(f149428,plain,
multiply(a,bS_Ic) = add(aPb,additive_inverse(aPc)),
inference(paramodulation,[status(thm)],[f149223,f13481]) ).
fof(f149450,plain,
multiply(a,bS_Ic) = aPb_S_IaPc,
inference(forward_demodulation,[status(thm)],[f717,f149428]) ).
fof(f150051,plain,
product(a,bS_Ic,aPb_S_IaPc) = true,
inference(paramodulation,[status(thm)],[f149450,f29]) ).
fof(f150057,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f49,f150051]) ).
fof(f150058,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f150057,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 04:09:50 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 102.33/13.33 % Refutation found
% 102.33/13.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 102.33/13.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 60.86/14.62 % Elapsed time: 14.048856 seconds
% 60.86/14.62 % CPU time: 94.561752 seconds
% 60.86/14.62 % Total memory used: 853.001 MB
% 60.86/14.62 % Net memory used: 840.106 MB
%------------------------------------------------------------------------------