%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN055+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 : Tue Sep 29 12:26:39 PM UTC 2026
% Result : Theorem 3.75s 1.51s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 134 ( 17 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 181 ( 83 ~; 66 |; 32 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 0 con; 1-2 aty)
% Number of variables : 121 ( 98 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( ~ r3(X0,X1,X3)
& X3 != X2 )
| ( r3(X0,X1,X3)
& X3 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) )
& X3 = X2 )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f8,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r3(X0,X2,X1) )
& X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f12,conjecture,
? [X0] :
( ? [X1] :
( ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& r3(X4,X1,X0) ) )
& ? [X5] :
( X0 = X5
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplustwoeqtwo) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( ? [X2] :
( r2(X2,X1)
& ? [X3] :
( r1(X3)
& r2(X3,X2) ) )
& ? [X4] :
( r1(X4)
& r3(X4,X1,X0) ) )
& ? [X5] :
( X0 = X5
& ? [X6] :
( r2(X6,X5)
& ? [X7] :
( r1(X7)
& r2(X7,X6) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r2(X2,X1)
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X2) ) )
| ! [X4] :
( ~ r1(X4)
| ~ r3(X4,X1,X0) ) )
| ! [X5] :
( X0 != X5
| ! [X6] :
( ~ r2(X6,X5)
| ! [X7] :
( ~ r1(X7)
| ~ r2(X7,X6) ) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f18,plain,
! [X0] :
( r1(sK6(X0))
& r3(X0,sK6(X0),sK5(X0))
& sK5(X0) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f8]) ).
fof(f19,plain,
! [X0,X1] :
( r2(X1,sK9(X0,X1))
& r3(X0,sK9(X0,X1),sK8(X0,X1))
& sK7(X0,X1) = sK8(X0,X1)
& r2(sK10(X0,X1),sK7(X0,X1))
& r3(X0,X1,sK10(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1)),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f5]) ).
fof(f20,plain,
! [X0,X1,X3] :
( ( ~ r3(X0,X1,X3)
& sK11(X0,X1) != X3 )
| ( r3(X0,X1,X3)
& sK11(X0,X1) = X3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f3]) ).
fof(f21,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ r2(X2,X1)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r3(X4,X1,X0)
| X0 != X5
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X0] : sK5(X0) = X0,
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
! [X0] : r3(X0,sK6(X0),sK5(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0] : r1(sK6(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f39,plain,
! [X0,X1] : r3(X0,X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] : r2(sK10(X0,X1),sK7(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
! [X0,X1] : sK7(X0,X1) = sK8(X0,X1),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0,X1] : r3(X0,sK9(X0,X1),sK8(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : r2(X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f19]) ).
fof(f46,plain,
! [X3,X0,X1] :
( sK11(X0,X1) = X3
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f20]) ).
fof(f48,plain,
! [X0,X1] : r2(sK10(X0,X1),sK8(X0,X1)),
inference(definition_unfolding,[],[f40,f41]) ).
fof(f49,plain,
! [X2,X3,X1,X6,X7,X4,X5] :
( ~ r3(X4,X1,X5)
| ~ r1(X3)
| ~ r2(X3,X2)
| ~ r1(X4)
| ~ r2(X2,X1)
| ~ r2(X6,X5)
| ~ r1(X7)
| ~ r2(X7,X6) ),
inference(equality_resolution,[],[f21]) ).
fof(f62,plain,
! [X0] : r3(X0,sK6(X0),X0),
inference(forward_demodulation,[],[f37,f36]) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X4,sK8(X2,X3))
| ~ r2(X0,X1)
| ~ r1(X2)
| ~ r2(X1,sK9(X2,X3))
| ~ r1(X0)
| ~ r1(X5)
| ~ r2(X5,X4) ),
inference(resolution,[],[f42,f49]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X4,sK10(X2,X3))
| ~ r1(X2)
| ~ r2(X1,sK9(X2,X3))
| ~ r1(X0)
| ~ r1(X4)
| ~ r2(X0,X1) ),
inference(resolution,[],[f78,f48]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ r3(X1,X2,X3)
| X0 = X3
| ~ r3(X1,X2,X0) ),
inference(superposition,[],[f46,f46]) ).
fof(f161,plain,
! [X2,X0,X1] :
( sK10(X1,X2) = X0
| ~ r3(X1,X2,X0) ),
inference(resolution,[],[f88,f39]) ).
fof(f270,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r2(X4,sK9(X2,X3))
| ~ r1(X2)
| ~ r2(X1,X0)
| ~ r1(X5)
| ~ r1(X1)
| ~ r2(X5,X4)
| ~ r3(X2,X3,X0) ),
inference(superposition,[],[f79,f161]) ).
fof(f712,plain,
! [X2,X3,X0,X1,X4] :
( ~ r3(X0,X4,X2)
| ~ r2(X1,X2)
| ~ r1(X3)
| ~ r1(X1)
| ~ r2(X3,X4)
| ~ r1(X0) ),
inference(resolution,[],[f270,f43]) ).
fof(f721,plain,
! [X2,X3,X0,X1] :
( ~ r2(X3,sK9(X1,X2))
| ~ r1(X3)
| ~ r1(X0)
| ~ r2(X0,sK8(X1,X2))
| ~ r1(X1) ),
inference(resolution,[],[f712,f42]) ).
fof(f744,plain,
! [X2,X0,X1] :
( ~ r2(X1,sK8(X2,X0))
| ~ r1(X1)
| ~ r1(X0)
| ~ r1(X2) ),
inference(resolution,[],[f721,f43]) ).
fof(f748,plain,
! [X0,X1] :
( ~ r1(sK10(X0,X1))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[],[f744,f48]) ).
fof(f751,plain,
! [X2,X0,X1] :
( ~ r3(X1,X2,X0)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X0) ),
inference(superposition,[],[f748,f161]) ).
fof(f752,plain,
! [X0] :
( ~ r1(sK6(X0))
| ~ r1(X0)
| ~ r1(X0) ),
inference(resolution,[],[f751,f62]) ).
fof(f756,plain,
! [X0] :
( ~ r1(sK6(X0))
| ~ r1(X0) ),
inference(duplicate_literal_removal,[],[f752]) ).
fof(f757,plain,
! [X0] : ~ r1(X0),
inference(forward_subsumption_resolution,[],[f756,f38]) ).
fof(f769,plain,
$false,
inference(resolution,[],[f757,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN055+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n018.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 21:54:09 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.75/1.51 % (2767543)Detected formulas, will run a generic FOF schedule.
% 3.75/1.51 % (2767651)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3756874887:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.75/1.51 % (2767649)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2325909215:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.75/1.51 % (2767650)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=680319325:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.75/1.51 % (2767655)dis-21_1_sil=8000:lcm=predicate:random_seed=4189690270:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.75/1.51 % (2767653)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=779977495:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.75/1.51 % (2767654)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4168633340:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.75/1.51 % (2767652)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2766558262:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.75/1.51 % (2767652)Refutation not found, incomplete strategy
% 3.75/1.51 % (2767652)------------------------------
% 3.75/1.51 % (2767652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.51 % (2767652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.51 % (2767652)CaDiCaL version: 2.1.3
% 3.75/1.51 % (2767652)Termination reason: Refutation not found, incomplete strategy
% 3.75/1.51 % (2767652)Time elapsed: 0.003 s
% 3.75/1.51 % (2767652)Peak memory usage: 88 MB
% 3.75/1.51 % (2767652)Instructions burned: 3 (million)
% 3.75/1.51 % (2767653)First to succeed.
% 3.75/1.51 % (2767654)Also succeeded, but the first one will report.
% 3.75/1.51 % (2767653)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2767543"
% 3.75/1.51 % (2767655)Instruction limit reached!
% 3.75/1.51 % (2767655)------------------------------
% 3.75/1.51 % (2767655)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.51 % (2767655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.51 % (2767655)CaDiCaL version: 2.1.3
% 3.75/1.51 % (2767655)Termination reason: Instruction limit
% 3.75/1.51 % (2767655)Termination phase: Saturation
% 3.75/1.51 % (2767655)Time elapsed: 0.066 s
% 3.75/1.51 % (2767655)Peak memory usage: 88 MB
% 3.75/1.51 % (2767655)Instructions burned: 131 (million)
% 3.75/1.51 % (2767652)------------------------------
% 3.75/1.51 % (2767652)------------------------------
% 3.75/1.51 % (2767653)Refutation found. Thanks to Tanya!
% 3.75/1.51 % SZS status Theorem for theBenchmark
% 3.75/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.51 % (2767653)------------------------------
% 3.75/1.51 % (2767653)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.51 % (2767653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.51 % (2767653)CaDiCaL version: 2.1.3
% 3.75/1.51 % (2767653)Termination reason: Refutation
% 3.75/1.51 % (2767653)Time elapsed: 0.027 s
% 3.75/1.51 % (2767653)Peak memory usage: 88 MB
% 3.75/1.51 % (2767653)Instructions burned: 41 (million)
% 3.75/1.51 % (2767653)------------------------------
% 3.75/1.51 % (2767653)------------------------------
% 3.75/1.51 % (2767543)Success in time 0.442 s
% 3.75/1.51 % Vampire exiting
%------------------------------------------------------------------------------