%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 26.79s 3.84s
% Output : CNFRefutation 26.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 91 ( 57 unt; 0 def)
% Number of atoms : 161 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 142 ( 72 ~; 70 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 182 ( 182 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X,V,W] :
( sum(X,V,W)
| ! [U,Z] :
( ~ sum(U,Z,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X,V3,V4] :
( product(X,V3,V4)
| ! [V1,V2] :
( ~ sum(V1,V2,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f46,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f51,plain,
product(a,b,aPb),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f52,plain,
product(a,c,aPc),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f53,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(multiply(X0,X3),X2,X5)
| ~ product(X0,X4,X5)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f39]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( product(a,X2,X3)
| ~ sum(aPb,X1,X3)
| ~ sum(b,X0,X2)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[f51,f41]) ).
fof(f88,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( sum(additive_inverse(X0),X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f27]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,X2,X3)
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f23]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( sum(X2,X1,X3)
| ~ sum(X2,X0,X3)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f30,f24]) ).
fof(f115,plain,
! [X0,X1] :
( additive_identity = X1
| ~ sum(additive_inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f47,f27]) ).
fof(f116,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f47,f23]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f47,f24]) ).
fof(f121,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f88]) ).
fof(f122,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f26]) ).
fof(f158,plain,
! [X0,X1,X2] :
( sum(multiply(a,X0),aPc,X2)
| ~ product(a,X1,X2)
| ~ sum(X0,c,X1) ),
inference(resolution,[status(thm)],[f58,f52]) ).
fof(f165,plain,
additive_inverse(additive_identity) = additive_identity,
inference(resolution,[status(thm)],[f116,f28]) ).
fof(f168,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(resolution,[status(thm)],[f116,f26]) ).
fof(f184,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(resolution,[status(thm)],[f115,f88]) ).
fof(f211,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f121,f26]) ).
fof(f250,plain,
! [X0,X1,X2] :
( product(a,X1,X2)
| ~ sum(aPb,multiply(a,X0),X2)
| ~ sum(b,X0,X1) ),
inference(resolution,[status(thm)],[f68,f25]) ).
fof(f449,plain,
! [X0,X1,X2] :
( sum(additive_identity,add(X1,X0),X2)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f100,f88]) ).
fof(f478,plain,
! [X0,X1] : sum(additive_identity,add(X0,X1),add(X1,X0)),
inference(resolution,[status(thm)],[f449,f26]) ).
fof(f727,plain,
! [X0,X1,X2,X3] :
( sum(X0,add(X2,X1),X3)
| ~ sum(X0,add(X1,X2),X3) ),
inference(resolution,[status(thm)],[f104,f478]) ).
fof(f804,plain,
! [X0,X1] :
( sum(additive_inverse(additive_inverse(X0)),additive_identity,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f99,f27]) ).
fof(f811,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X0,X2),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f99,f88]) ).
fof(f1304,plain,
! [X0,X1,X2] : sum(X0,add(X1,X2),add(add(X2,X1),X0)),
inference(resolution,[status(thm)],[f727,f88]) ).
fof(f1417,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X2,X1),X0),
inference(resolution,[status(thm)],[f1304,f122]) ).
fof(f2588,plain,
! [X0] :
( sum(multiply(a,additive_inverse(c)),aPc,X0)
| ~ product(a,additive_identity,X0) ),
inference(resolution,[status(thm)],[f158,f27]) ).
fof(f2589,plain,
! [X0] :
( sum(multiply(a,additive_identity),aPc,X0)
| ~ product(a,c,X0) ),
inference(resolution,[status(thm)],[f158,f23]) ).
fof(f3296,plain,
! [X0] :
( product(a,bS_Ic,X0)
| ~ sum(aPb,multiply(a,additive_inverse(c)),X0) ),
inference(resolution,[status(thm)],[f250,f50]) ).
fof(f4147,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(resolution,[status(thm)],[f804,f23]) ).
fof(f4448,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(resolution,[status(thm)],[f4147,f120]) ).
fof(f4539,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f811,f23]) ).
fof(f4900,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f4539,f122]) ).
fof(f4901,plain,
! [X0,X1] : add(add(X0,X1),additive_inverse(X1)) = X0,
inference(resolution,[status(thm)],[f4539,f121]) ).
fof(f4934,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f1417,f4901]) ).
fof(f5009,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X0) = additive_inverse(X1),
inference(paramodulation,[status(thm)],[f4900,f4900]) ).
fof(f5068,plain,
! [X0,X1] : add(X0,additive_inverse(add(X0,X1))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f211,f5009]) ).
fof(f5164,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X1) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f4934,f4900]) ).
fof(f5212,plain,
! [X0,X1] : add(X0,additive_inverse(add(X1,X0))) = additive_inverse(X1),
inference(forward_demodulation,[status(thm)],[f211,f5164]) ).
fof(f22414,plain,
sum(multiply(a,additive_identity),aPc,aPc),
inference(resolution,[status(thm)],[f2589,f52]) ).
fof(f22462,plain,
add(multiply(a,additive_identity),aPc) = aPc,
inference(resolution,[status(thm)],[f22414,f122]) ).
fof(f22474,plain,
add(aPc,multiply(a,additive_identity)) = aPc,
inference(forward_demodulation,[status(thm)],[f211,f22462]) ).
fof(f22526,plain,
add(aPc,additive_inverse(aPc)) = additive_inverse(multiply(a,additive_identity)),
inference(paramodulation,[status(thm)],[f22474,f5068]) ).
fof(f22570,plain,
additive_identity = additive_inverse(multiply(a,additive_identity)),
inference(forward_demodulation,[status(thm)],[f184,f22526]) ).
fof(f22642,plain,
additive_inverse(additive_identity) = multiply(a,additive_identity),
inference(paramodulation,[status(thm)],[f22570,f4448]) ).
fof(f22674,plain,
additive_identity = multiply(a,additive_identity),
inference(forward_demodulation,[status(thm)],[f165,f22642]) ).
fof(f22715,plain,
product(a,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f22674,f25]) ).
fof(f22734,plain,
sum(multiply(a,additive_inverse(c)),aPc,additive_identity),
inference(resolution,[status(thm)],[f22715,f2588]) ).
fof(f23746,plain,
add(multiply(a,additive_inverse(c)),aPc) = additive_identity,
inference(resolution,[status(thm)],[f22734,f122]) ).
fof(f23759,plain,
add(aPc,multiply(a,additive_inverse(c))) = additive_identity,
inference(forward_demodulation,[status(thm)],[f211,f23746]) ).
fof(f24119,plain,
add(multiply(a,additive_inverse(c)),additive_inverse(additive_identity)) = additive_inverse(aPc),
inference(paramodulation,[status(thm)],[f23759,f5212]) ).
fof(f24190,plain,
add(additive_inverse(additive_identity),multiply(a,additive_inverse(c))) = additive_inverse(aPc),
inference(forward_demodulation,[status(thm)],[f211,f24119]) ).
fof(f24191,plain,
add(additive_identity,multiply(a,additive_inverse(c))) = additive_inverse(aPc),
inference(forward_demodulation,[status(thm)],[f165,f24190]) ).
fof(f24192,plain,
multiply(a,additive_inverse(c)) = additive_inverse(aPc),
inference(forward_demodulation,[status(thm)],[f168,f24191]) ).
fof(f24236,plain,
! [X0] :
( product(a,bS_Ic,X0)
| ~ sum(aPb,additive_inverse(aPc),X0) ),
inference(backward_demodulation,[status(thm)],[f24192,f3296]) ).
fof(f32412,plain,
product(a,bS_Ic,aPb_S_IaPc),
inference(resolution,[status(thm)],[f24236,f53]) ).
fof(f32415,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f32412,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 04:12:00 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 26.79/3.84 % Refutation found
% 26.79/3.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 26.79/3.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.79/3.88 % Elapsed time: 3.483264 seconds
% 26.79/3.88 % CPU time: 27.345965 seconds
% 26.79/3.88 % Total memory used: 176.033 MB
% 26.79/3.88 % Net memory used: 148.405 MB
%------------------------------------------------------------------------------