%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 2.60s 1.39s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 13 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 200 ( 93 ~; 71 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 124 ( 104 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f3,axiom,
! [X0,X1] :
? [X2] :
! [X3] :
( ( id(X3,X2)
& r3(X0,X1,X3) )
| ( ~ r3(X0,X1,X3)
& ~ id(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f6,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
fof(f8,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| ( ~ r1(X0)
& ~ r1(X1) )
| ( r1(X0)
& r1(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ~ id(X0,X2)
| ~ id(X1,X3)
| ( ~ r2(X0,X1)
& ~ r2(X2,X3) )
| ( r2(X0,X1)
& r2(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
fof(f12,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( id(X3,X2)
& ? [X4] :
( r2(X1,X4)
& r3(X0,X4,X3) ) )
& ? [X5] :
( r2(X5,X2)
& r3(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
fof(f15,axiom,
! [X0] :
? [X1] :
( id(X1,X0)
& ? [X2] :
( r1(X2)
& r3(X0,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
fof(f19,conjecture,
? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r3(X2,X1,X0) )
& ? [X3] :
( r1(X3)
& r2(X3,X1) ) )
& ? [X4] :
( id(X0,X4)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneidone) ).
fof(f20,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r3(X2,X1,X0) )
& ? [X3] :
( r1(X3)
& r2(X3,X1) ) )
& ? [X4] :
( id(X0,X4)
& ? [X5] :
( r1(X5)
& r2(X5,X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r3(X2,X1,X0) )
| ! [X3] :
( ~ r1(X3)
| ~ r2(X3,X1) ) )
| ! [X4] :
( ~ id(X0,X4)
| ! [X5] :
( ~ r1(X5)
| ~ r2(X5,X4) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f23,plain,
! [X1] :
( ( id(X1,sK3)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f1]) ).
fof(f25,plain,
! [X0] :
( id(sK5(X0),X0)
& r1(sK6(X0))
& r3(X0,sK6(X0),sK5(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X1,sK5(X0)),skolemize(X2,sK6(X0))],[f15]) ).
fof(f26,plain,
! [X0,X1] :
( id(sK8(X0,X1),sK7(X0,X1))
& r2(X1,sK9(X0,X1))
& r3(X0,sK9(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))],[f12]) ).
fof(f27,plain,
! [X0,X1,X3] :
( ( id(X3,sK11(X0,X1))
& r3(X0,X1,X3) )
| ( ~ r3(X0,X1,X3)
& ~ id(X3,sK11(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f3]) ).
fof(f28,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r3(X2,X1,X0)
| ~ r1(X2)
| ~ r1(X3)
| ~ r2(X3,X1)
| ~ id(X0,X4)
| ~ r1(X5)
| ~ r2(X5,X4) ),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f31,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f39,plain,
! [X0,X1] :
( ~ id(X0,X1)
| ~ r1(X0)
| r1(X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f41,plain,
! [X1] :
( ~ id(X1,sK3)
| r1(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( r2(X0,X1)
| ~ id(X1,X3)
| ~ r2(X2,X3)
| ~ id(X0,X2) ),
inference(cnf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0] : r3(X0,sK6(X0),sK5(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f55,plain,
! [X0] : r1(sK6(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f56,plain,
! [X0] : id(sK5(X0),X0),
inference(cnf_transformation,[],[f25]) ).
fof(f57,plain,
! [X0,X1] : r3(X0,X1,sK10(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f58,plain,
! [X0,X1] : r2(sK10(X0,X1),sK7(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f59,plain,
! [X0,X1] : r3(X0,sK9(X0,X1),sK8(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f60,plain,
! [X0,X1] : r2(X1,sK9(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f61,plain,
! [X0,X1] : id(sK8(X0,X1),sK7(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f69,plain,
! [X3,X0,X1] :
( id(X3,sK11(X0,X1))
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f71,plain,
r1(sK5(sK3)),
inference(resolution,[],[f41,f56]) ).
fof(f96,plain,
! [X0] :
( ~ r1(sK5(X0))
| r1(X0) ),
inference(resolution,[],[f39,f56]) ).
fof(f134,plain,
! [X2,X3,X0,X1,X4] :
( ~ r2(X1,sK9(X0,X2))
| ~ r1(X1)
| ~ r1(X0)
| ~ id(sK8(X0,X2),X3)
| ~ r1(X4)
| ~ r2(X4,X3) ),
inference(resolution,[],[f59,f28]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ id(sK8(X1,X0),X2)
| ~ r1(X1)
| ~ r1(X0)
| ~ r1(X3)
| ~ r2(X3,X2) ),
inference(resolution,[],[f134,f60]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ~ r2(X2,sK7(X0,X1))
| ~ r1(X1)
| ~ r1(X2)
| ~ r1(X0) ),
inference(resolution,[],[f135,f61]) ).
fof(f165,plain,
! [X2,X0,X1] :
( r1(sK11(X0,X1))
| ~ r1(X2)
| ~ r3(X0,X1,X2) ),
inference(resolution,[],[f69,f39]) ).
fof(f192,plain,
! [X2,X3,X0,X1,X4] :
( ~ id(sK7(X0,X1),X2)
| ~ r2(X3,X2)
| ~ id(X4,X3)
| ~ r1(X1)
| ~ r1(X4)
| ~ r1(X0) ),
inference(resolution,[],[f47,f154]) ).
fof(f676,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,sK7(X1,X2))
| ~ id(X3,X0)
| ~ r1(X2)
| ~ r1(X3)
| ~ r1(X1) ),
inference(resolution,[],[f192,f31]) ).
fof(f694,plain,
! [X2,X0,X1] :
( ~ id(X0,sK10(X1,X2))
| ~ r1(X2)
| ~ r1(X0)
| ~ r1(X1) ),
inference(resolution,[],[f676,f58]) ).
fof(f699,plain,
! [X2,X0,X1] :
( ~ id(sK10(X2,X0),X1)
| ~ r1(X1)
| ~ r1(X2)
| ~ r1(X0) ),
inference(resolution,[],[f694,f30]) ).
fof(f737,plain,
! [X2,X3,X0,X1] :
( ~ r3(X0,X1,sK10(X2,X3))
| ~ r1(X2)
| ~ r1(X3)
| ~ r1(sK11(X0,X1)) ),
inference(resolution,[],[f699,f69]) ).
fof(f1002,plain,
! [X0,X1] :
( ~ r1(sK11(X0,X1))
| ~ r1(X1)
| ~ r1(X0) ),
inference(resolution,[],[f737,f57]) ).
fof(f1012,plain,
! [X2,X0,X1] :
( ~ r3(X1,X0,X2)
| ~ r1(X1)
| ~ r1(X2)
| ~ r1(X0) ),
inference(resolution,[],[f1002,f165]) ).
fof(f1026,plain,
! [X0] :
( ~ r1(X0)
| ~ r1(sK5(X0))
| ~ r1(sK6(X0)) ),
inference(resolution,[],[f1012,f54]) ).
fof(f1033,plain,
! [X0] :
( ~ r1(sK5(X0))
| ~ r1(sK6(X0)) ),
inference(forward_subsumption_resolution,[],[f1026,f96]) ).
fof(f1034,plain,
! [X0] : ~ r1(sK5(X0)),
inference(forward_subsumption_resolution,[],[f1033,f55]) ).
fof(f1035,plain,
$false,
inference(resolution,[],[f1034,f71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 21:54:09 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.60/1.39 % (2767673)Detected formulas, will run a generic FOF schedule.
% 2.60/1.39 % (2767684)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3113344905:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.60/1.39 % (2767684)First to succeed.
% 2.60/1.39 % (2767684)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2767673"
% 2.60/1.39 % (2767685)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3126797949:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.60/1.39 % (2767683)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=716877534:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.60/1.39 % (2767686)dis-21_1_sil=8000:lcm=predicate:random_seed=2907436489: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)
% 2.60/1.39 % (2767681)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=412106627:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.60/1.39 % (2767680)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=2365422758:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.60/1.39 % (2767682)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=1144036228:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.60/1.39 % (2767683)Instruction limit reached!
% 2.60/1.39 % (2767683)------------------------------
% 2.60/1.39 % (2767683)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.39 % (2767683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.39 % (2767683)CaDiCaL version: 2.1.3
% 2.60/1.39 % (2767683)Termination reason: Instruction limit
% 2.60/1.39 % (2767683)Termination phase: Saturation
% 2.60/1.39 % (2767683)Time elapsed: 0.060 s
% 2.60/1.39 % (2767683)Peak memory usage: 88 MB
% 2.60/1.39 % (2767683)Instructions burned: 110 (million)
% 2.60/1.39 % (2767686)Instruction limit reached!
% 2.60/1.39 % (2767686)------------------------------
% 2.60/1.39 % (2767686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.39 % (2767686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.39 % (2767686)CaDiCaL version: 2.1.3
% 2.60/1.39 % (2767686)Termination reason: Instruction limit
% 2.60/1.39 % (2767686)Termination phase: Saturation
% 2.60/1.39 % (2767686)Time elapsed: 0.067 s
% 2.60/1.39 % (2767686)Peak memory usage: 88 MB
% 2.60/1.39 % (2767686)Instructions burned: 130 (million)
% 2.60/1.39 % (2767685)Instruction limit reached!
% 2.60/1.39 % (2767685)------------------------------
% 2.60/1.39 % (2767685)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.39 % (2767685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.39 % (2767685)CaDiCaL version: 2.1.3
% 2.60/1.39 % (2767685)Termination reason: Instruction limit
% 2.60/1.39 % (2767685)Termination phase: Saturation
% 2.60/1.39 % (2767685)Time elapsed: 0.091 s
% 2.60/1.39 % (2767685)Peak memory usage: 89 MB
% 2.60/1.39 % (2767685)Instructions burned: 139 (million)
% 2.60/1.39 % (2767684)Refutation found. Thanks to Tanya!
% 2.60/1.39 % SZS status Theorem for theBenchmark
% 2.60/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 2.60/1.39 % (2767684)------------------------------
% 2.60/1.39 % (2767684)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.60/1.39 % (2767684)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.60/1.39 % (2767684)CaDiCaL version: 2.1.3
% 2.60/1.39 % (2767684)Termination reason: Refutation
% 2.60/1.39 % (2767684)Time elapsed: 0.020 s
% 2.60/1.39 % (2767684)Peak memory usage: 88 MB
% 2.60/1.39 % (2767684)Instructions burned: 60 (million)
% 2.60/1.39 % (2767684)------------------------------
% 2.60/1.39 % (2767684)------------------------------
% 2.60/1.39 % (2767673)Success in time 0.27 s
% 2.60/1.39 % Vampire exiting
%------------------------------------------------------------------------------