%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:26:41 PM UTC 2026
% Result : Theorem 5.20s 1.86s
% Output : Refutation 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 31 ~; 21 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 77 ( 61 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f13,axiom,
! [X0,X1] :
? [X2] :
( ? [X3] :
( id(X3,X2)
& ? [X4] :
( r2(X1,X4)
& r4(X0,X4,X3) ) )
& ? [X5] :
( r3(X5,X0,X2)
& r4(X0,X1,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
fof(f18,axiom,
! [X0,X1] :
( ! [X2] :
( ~ id(X2,X1)
| ~ r1(X2) )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
fof(f19,conjecture,
! [X0] :
? [X1,X2] :
( ! [X3] :
( ~ id(X2,X3)
| ~ r1(X3) )
& ? [X4] :
( id(X4,X1)
& r3(X0,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infiniteNumbersid) ).
fof(f20,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ! [X3] :
( ~ id(X2,X3)
| ~ r1(X3) )
& ? [X4] :
( id(X4,X1)
& r3(X0,X2,X4) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
? [X0] :
! [X1,X2] :
( ? [X3] :
( id(X2,X3)
& r1(X3) )
| ! [X4] :
( ~ id(X4,X1)
| ~ r3(X0,X2,X4) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f22,plain,
! [X1,X2] :
( ( id(X2,sK1(X2))
& r1(sK1(X2)) )
| ! [X4] :
( ~ id(X4,X1)
| ~ r3(sK0,X2,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1(X2))],[f21]) ).
fof(f26,plain,
! [X0,X1] :
( id(sK11(X0,X1),sK10(X0,X1))
& r2(X1,sK12(X0,X1))
& r4(X0,sK12(X0,X1),sK11(X0,X1))
& r3(sK13(X0,X1),X0,sK10(X0,X1))
& r4(X0,X1,sK13(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X2,sK10(X0,X1)),skolemize(X3,sK11(X0,X1)),skolemize(X4,sK12(X0,X1)),skolemize(X5,sK13(X0,X1))],[f13]) ).
fof(f27,plain,
! [X0,X1] :
( id(sK15(X0,X1),sK14(X0,X1))
& r2(X1,sK16(X0,X1))
& r3(X0,sK16(X0,X1),sK15(X0,X1))
& r2(sK17(X0,X1),sK14(X0,X1))
& r3(X0,X1,sK17(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X2,sK14(X0,X1)),skolemize(X3,sK15(X0,X1)),skolemize(X4,sK16(X0,X1)),skolemize(X5,sK17(X0,X1))],[f12]) ).
fof(f32,plain,
! [X2,X1,X4] :
( ~ r3(sK0,X2,X4)
| ~ id(X4,X1)
| r1(sK1(X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X2,X1,X4] :
( ~ r3(sK0,X2,X4)
| ~ id(X4,X1)
| id(X2,sK1(X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| ~ id(X2,X1)
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f50,plain,
! [X0,X1] : r2(X1,sK12(X0,X1)),
inference(cnf_transformation,[],[f26]) ).
fof(f52,plain,
! [X0,X1] : r3(X0,X1,sK17(X0,X1)),
inference(cnf_transformation,[],[f27]) ).
fof(f74,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f75,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f114,plain,
! [X0,X1] :
( id(X0,sK1(X0))
| ~ id(sK17(sK0,X0),X1) ),
inference(resolution,[],[f52,f33]) ).
fof(f115,plain,
! [X0,X1] :
( r1(sK1(X0))
| ~ id(sK17(sK0,X0),X1) ),
inference(resolution,[],[f52,f32]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ r2(X2,X1)
| ~ id(sK1(X0),X1)
| ~ id(sK17(sK0,X0),X3) ),
inference(resolution,[],[f34,f115]) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ~ id(sK1(X0),sK12(X1,X2))
| ~ id(sK17(sK0,X0),X3) ),
inference(resolution,[],[f131,f50]) ).
fof(f233,plain,
! [X2,X0,X1] : ~ id(sK1(X0),sK12(X1,X2)),
inference(resolution,[],[f163,f75]) ).
fof(f258,plain,
! [X2,X0,X1] : ~ id(sK12(X0,X1),sK1(X2)),
inference(resolution,[],[f233,f74]) ).
fof(f270,plain,
! [X2,X0,X1] : ~ id(sK17(sK0,sK12(X0,X1)),X2),
inference(resolution,[],[f258,f114]) ).
fof(f272,plain,
$false,
inference(resolution,[],[f270,f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN062+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 % Computer : n013.cluster.edu
% 0.13/0.42 % Model : x86_64 x86_64
% 0.13/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42 % Memory : 8046.5625MB
% 0.13/0.42 % OS : Linux 6.8.0-71-generic
% 0.13/0.42 % CPULimit : 300
% 0.13/0.42 % WCLimit : 300
% 0.13/0.42 % DateTime : Sun Sep 27 21:51:51 UTC 2026
% 0.13/0.42 % CPUTime :
% 0.13/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 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
% 5.20/1.86 % (591559)Detected formulas, will run a generic FOF schedule.
% 5.20/1.86 % (591567)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=916428495:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.20/1.86 % (591570)dis-21_1_sil=8000:lcm=predicate:random_seed=3189578696: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)
% 5.20/1.86 % (591567)Refutation not found, incomplete strategy
% 5.20/1.86 % (591567)------------------------------
% 5.20/1.86 % (591567)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.86 % (591567)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.86 % (591567)CaDiCaL version: 2.1.3
% 5.20/1.86 % (591567)Termination reason: Refutation not found, incomplete strategy
% 5.20/1.86 % (591567)Time elapsed: 0.006 s
% 5.20/1.86 % (591567)Peak memory usage: 88 MB
% 5.20/1.86 % (591567)Instructions burned: 9 (million)
% 5.20/1.86 % (591570)First to succeed.
% 5.20/1.86 % (591570)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-591559"
% 5.20/1.86 % (591568)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3674542387:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.20/1.86 % (591569)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3725516906:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.20/1.86 % (591566)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=786503351:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.20/1.86 % (591565)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=4118135199:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.20/1.86 % (591564)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=820894828:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.20/1.86 % (591568)Also succeeded, but the first one will report.
% 5.20/1.86 % (591569)Instruction limit reached!
% 5.20/1.86 % (591569)------------------------------
% 5.20/1.86 % (591569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.86 % (591569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.86 % (591569)CaDiCaL version: 2.1.3
% 5.20/1.86 % (591569)Termination reason: Instruction limit
% 5.20/1.86 % (591569)Termination phase: Saturation
% 5.20/1.86 % (591569)Time elapsed: 0.131 s
% 5.20/1.86 % (591569)Peak memory usage: 89 MB
% 5.20/1.86 % (591569)Instructions burned: 139 (million)
% 5.20/1.86 % (591567)------------------------------
% 5.20/1.86 % (591567)------------------------------
% 5.20/1.86 % (591578)lrs+10_1_sil=8000:sp=occurrence:random_seed=2393538813:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.20/1.86 % (591578)Also succeeded, but the first one will report.
% 5.20/1.86 % (591570)Refutation found. Thanks to Tanya!
% 5.20/1.86 % SZS status Theorem for theBenchmark
% 5.20/1.86 % SZS output start Proof for theBenchmark
% See solution above
% 5.20/1.86 % (591570)------------------------------
% 5.20/1.86 % (591570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.20/1.86 % (591570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.20/1.86 % (591570)CaDiCaL version: 2.1.3
% 5.20/1.86 % (591570)Termination reason: Refutation
% 5.20/1.86 % (591570)Time elapsed: 0.009 s
% 5.20/1.86 % (591570)Peak memory usage: 89 MB
% 5.20/1.86 % (591570)Instructions burned: 6 (million)
% 5.20/1.86 % (591570)------------------------------
% 5.20/1.86 % (591570)------------------------------
% 5.20/1.86 % (591559)Success in time 0.635 s
% 5.20/1.86 % Vampire exiting
%------------------------------------------------------------------------------