%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN087+1 : 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 : n001.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 12:26:47 PM UTC 2026
% Result : Theorem 3.85s 1.51s
% Output : Refutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 9 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 140 ( 69 ~; 51 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 72 ( 62 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( id(X1,X0)
& r1(X1) )
| ( ~ r1(X1)
& ~ id(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f5,axiom,
! [X0] : id(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f6,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| id(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f8,axiom,
! [X0,X1] :
( ~ id(X0,X1)
| ( ~ r1(X0)
& ~ r1(X1) )
| ( r1(X0)
& r1(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ~ id(X0,X3)
| ~ id(X1,X4)
| ~ id(X2,X5)
| ( ~ r4(X0,X1,X2)
& ~ r4(X3,X4,X5) )
| ( r4(X0,X1,X2)
& r4(X3,X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
fof(f16,axiom,
! [X0] :
? [X1] :
( ? [X2] :
( r1(X2)
& r4(X0,X2,X1) )
& ? [X3] :
( id(X1,X3)
& r1(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
fof(f19,conjecture,
? [X0] :
( ? [X1] :
( r1(X1)
& r4(X1,X1,X0) )
& ? [X2] :
( id(X0,X2)
& r1(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimeszeroeqzero) ).
fof(f20,negated_conjecture,
~ ? [X0] :
( ? [X1] :
( r1(X1)
& r4(X1,X1,X0) )
& ? [X2] :
( id(X0,X2)
& r1(X2) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0] :
( ! [X1] :
( ~ r1(X1)
| ~ r4(X1,X1,X0) )
| ! [X2] :
( ~ id(X0,X2)
| ~ r1(X2) ) ),
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(f24,plain,
! [X0] :
( r1(sK5(X0))
& r4(X0,sK5(X0),sK4(X0))
& id(sK4(X0),sK6(X0))
& r1(sK6(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X1,sK4(X0)),skolemize(X2,sK5(X0)),skolemize(X3,sK6(X0))],[f16]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ r4(X1,X1,X0)
| ~ r1(X1)
| ~ id(X0,X2)
| ~ r1(X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1] :
( id(X1,X0)
| ~ id(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0] : id(X0,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f41,plain,
! [X0,X1] :
( ~ id(X0,X1)
| ~ r1(X1)
| r1(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f47,plain,
! [X1] :
( id(X1,sK3)
| ~ r1(X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f48,plain,
! [X0] : r1(sK6(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f49,plain,
! [X0] : id(sK4(X0),sK6(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f50,plain,
! [X0] : r4(X0,sK5(X0),sK4(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f51,plain,
! [X0] : r1(sK5(X0)),
inference(cnf_transformation,[],[f24]) ).
fof(f58,plain,
! [X2,X3,X0,X1,X4,X5] :
( r4(X0,X1,X2)
| ~ id(X1,X4)
| ~ id(X2,X5)
| ~ r4(X3,X4,X5)
| ~ id(X0,X3) ),
inference(cnf_transformation,[],[f11]) ).
fof(f112,plain,
! [X0] :
( ~ r1(sK6(X0))
| r1(sK4(X0)) ),
inference(resolution,[],[f41,f49]) ).
fof(f113,plain,
! [X0] : r1(sK4(X0)),
inference(forward_subsumption_resolution,[],[f112,f48]) ).
fof(f280,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ r4(X4,X1,X3)
| ~ id(X2,X3)
| ~ id(X0,X1)
| ~ id(X0,X4)
| ~ r1(X0)
| ~ id(X2,X5)
| ~ r1(X5) ),
inference(resolution,[],[f58,f31]) ).
fof(f315,plain,
! [X2,X3,X0,X1] :
( ~ id(X2,sK5(X1))
| ~ id(X0,sK4(X1))
| ~ id(X2,X1)
| ~ r1(X2)
| ~ id(X0,X3)
| ~ r1(X3) ),
inference(resolution,[],[f280,f50]) ).
fof(f993,plain,
! [X0,X1] :
( ~ id(X0,sK5(X1))
| ~ id(X0,sK4(X1))
| ~ id(X0,X1)
| ~ r1(X0)
| ~ r1(sK5(X1)) ),
inference(factoring,[],[f315]) ).
fof(f994,plain,
! [X0,X1] :
( ~ id(X0,sK5(X1))
| ~ id(X0,sK4(X1))
| ~ id(X0,X1)
| ~ r1(sK5(X1)) ),
inference(forward_subsumption_resolution,[],[f993,f41]) ).
fof(f996,plain,
! [X0,X1] :
( ~ id(X0,sK5(X1))
| ~ id(X0,sK4(X1))
| ~ id(X0,X1) ),
inference(forward_subsumption_resolution,[],[f994,f51]) ).
fof(f1001,plain,
! [X0,X1] :
( ~ id(sK5(X1),X0)
| ~ id(X0,X1)
| ~ id(X0,sK4(X1)) ),
inference(resolution,[],[f996,f33]) ).
fof(f1047,plain,
! [X0] :
( ~ id(sK3,X0)
| ~ id(sK3,sK4(X0))
| ~ r1(sK5(X0)) ),
inference(resolution,[],[f1001,f47]) ).
fof(f1051,plain,
! [X0] :
( ~ id(sK3,sK4(X0))
| ~ id(sK3,X0) ),
inference(forward_subsumption_resolution,[],[f1047,f51]) ).
fof(f1073,plain,
! [X0] :
( ~ id(sK4(X0),sK3)
| ~ id(sK3,X0) ),
inference(resolution,[],[f1051,f33]) ).
fof(f1090,plain,
! [X0] :
( ~ id(sK3,X0)
| ~ r1(sK4(X0)) ),
inference(resolution,[],[f1073,f47]) ).
fof(f1094,plain,
! [X0] : ~ id(sK3,X0),
inference(forward_subsumption_resolution,[],[f1090,f113]) ).
fof(f1095,plain,
$false,
inference(resolution,[],[f1094,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN087+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:06:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.85/1.51 % (4005265)Detected formulas, will run a generic FOF schedule.
% 3.85/1.51 % (4005271)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=2974656801:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.85/1.51 % (4005272)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=1864469989:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.85/1.51 % (4005274)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1427115261:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.85/1.51 % (4005273)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1466285884:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.85/1.51 % (4005276)dis-21_1_sil=8000:lcm=predicate:random_seed=2809040627: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)
% 3.85/1.51 % (4005270)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=3935457822:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.85/1.51 % (4005275)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3315057230:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.85/1.51 % (4005273)Refutation not found, incomplete strategy
% 3.85/1.51 % (4005273)------------------------------
% 3.85/1.51 % (4005273)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.51 % (4005273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.51 % (4005273)CaDiCaL version: 2.1.3
% 3.85/1.51 % (4005273)Termination reason: Refutation not found, incomplete strategy
% 3.85/1.51 % (4005273)Time elapsed: 0.003 s
% 3.85/1.51 % (4005273)Peak memory usage: 88 MB
% 3.85/1.51 % (4005273)Instructions burned: 3 (million)
% 3.85/1.51 % (4005274)First to succeed.
% 3.85/1.51 % (4005274)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4005265"
% 3.85/1.51 % (4005276)Instruction limit reached!
% 3.85/1.51 % (4005276)------------------------------
% 3.85/1.51 % (4005276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.51 % (4005276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.51 % (4005276)CaDiCaL version: 2.1.3
% 3.85/1.51 % (4005276)Termination reason: Instruction limit
% 3.85/1.51 % (4005276)Termination phase: Saturation
% 3.85/1.51 % (4005276)Time elapsed: 0.080 s
% 3.85/1.51 % (4005276)Peak memory usage: 89 MB
% 3.85/1.51 % (4005276)Instructions burned: 129 (million)
% 3.85/1.51 % (4005275)Instruction limit reached!
% 3.85/1.51 % (4005275)------------------------------
% 3.85/1.51 % (4005275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.51 % (4005275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.51 % (4005275)CaDiCaL version: 2.1.3
% 3.85/1.51 % (4005275)Termination reason: Instruction limit
% 3.85/1.51 % (4005275)Termination phase: Saturation
% 3.85/1.51 % (4005275)Time elapsed: 0.094 s
% 3.85/1.51 % (4005275)Peak memory usage: 89 MB
% 3.85/1.51 % (4005275)Instructions burned: 140 (million)
% 3.85/1.51 % (4005273)------------------------------
% 3.85/1.51 % (4005273)------------------------------
% 3.85/1.51 % (4005284)lrs+10_1_sil=8000:sp=occurrence:random_seed=3337742533:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.85/1.51 % (4005285)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3929997160:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.85/1.51 % (4005274)Refutation found. Thanks to Tanya!
% 3.85/1.51 % SZS status Theorem for theBenchmark
% 3.85/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.85/1.51 % (4005274)------------------------------
% 3.85/1.51 % (4005274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.85/1.51 % (4005274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.85/1.51 % (4005274)CaDiCaL version: 2.1.3
% 3.85/1.51 % (4005274)Termination reason: Refutation
% 3.85/1.51 % (4005274)Time elapsed: 0.023 s
% 3.85/1.51 % (4005274)Peak memory usage: 88 MB
% 3.85/1.51 % (4005274)Instructions burned: 34 (million)
% 3.85/1.51 % (4005274)------------------------------
% 3.85/1.51 % (4005274)------------------------------
% 3.85/1.51 % (4005265)Success in time 0.453 s
% 3.85/1.51 % Vampire exiting
%------------------------------------------------------------------------------