%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN065+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 : n008.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 12:26:42 PM UTC 2026
% Result : Theorem 0.14s 1.14s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 69 ( 11 unt; 2 def)
% Number of atoms : 163 ( 79 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 148 ( 54 ~; 76 |; 16 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 86 ( 0 sgn 79 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0] :
! [X1] :
( ( ~ r1(X1)
& X1 != X0 )
| ( r1(X1)
& X1 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( ~ r2(X0,X2)
& X2 != X1 )
| ( r2(X0,X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f7,axiom,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ~ r2(X0,X3)
| X3 != X2 )
| ~ r2(X1,X2) )
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).
fof(f11,axiom,
! [X0,X1] :
( ! [X2] :
( ~ r1(X2)
| X2 != X1 )
| ~ r2(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f12,conjecture,
? [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| X0 != X1 )
& ! [X3] :
( ~ r1(X3)
| X0 != X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nononesexist) ).
fof(f13,negated_conjecture,
~ ? [X0] :
( ! [X1] :
( ! [X2] :
( ~ r1(X2)
| ~ r2(X2,X1) )
| X0 != X1 )
& ! [X3] :
( ~ r1(X3)
| X0 != X3 ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( r1(X2)
& r2(X2,X1) )
& X0 = X1 )
| ? [X3] :
( r1(X3)
& X0 = X3 ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
! [X1] :
( ( ~ r1(X1)
& sK0 != X1 )
| ( r1(X1)
& sK0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f1]) ).
fof(f16,plain,
! [X0,X2] :
( ( ~ r2(X0,X2)
& sK1(X0) != X2 )
| ( r2(X0,X2)
& sK1(X0) = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f2]) ).
fof(f24,plain,
! [X0] :
( ( r1(sK21(X0))
& r2(sK21(X0),sK20(X0))
& sK20(X0) = X0 )
| ( r1(sK22(X0))
& sK22(X0) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22]),skolemize(X1,sK20(X0)),skolemize(X2,sK21(X0)),skolemize(X3,sK22(X0))],[f14]) ).
fof(f26,plain,
! [X1] :
( sK0 != X1
| r1(X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X1] :
( ~ r1(X1)
| sK0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X2,X0] :
( sK1(X0) != X2
| r2(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| sK1(X0) = X2 ),
inference(cnf_transformation,[],[f16]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( ~ r2(X0,X3)
| X2 != X3
| ~ r2(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f7]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ r1(X2)
| X1 != X2
| ~ r2(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f64,plain,
! [X0] :
( sK20(X0) = X0
| sK22(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f65,plain,
! [X0] :
( r1(sK22(X0))
| sK20(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f66,plain,
! [X0] :
( r2(sK21(X0),sK20(X0))
| sK22(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f67,plain,
! [X0] :
( r1(sK22(X0))
| r2(sK21(X0),sK20(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f68,plain,
! [X0] :
( r1(sK21(X0))
| sK22(X0) = X0 ),
inference(cnf_transformation,[],[f24]) ).
fof(f69,plain,
! [X0] :
( r1(sK22(X0))
| r1(sK21(X0)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f70,plain,
r1(sK0),
inference(equality_resolution,[],[f26]) ).
fof(f72,plain,
! [X0] : r2(X0,sK1(X0)),
inference(equality_resolution,[],[f30]) ).
fof(f78,plain,
! [X3,X0,X1] :
( ~ r2(X0,X3)
| ~ r2(X1,X3)
| X0 = X1 ),
inference(equality_resolution,[],[f51]) ).
fof(f79,plain,
! [X2,X0] :
( ~ r2(X0,X2)
| ~ r1(X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f80,plain,
! [X0] :
( r2(sK21(X0),X0)
| sK22(X0) = X0
| sK22(X0) = X0 ),
inference(superposition,[],[f66,f64]) ).
fof(f81,plain,
! [X0] :
( r2(sK21(X0),X0)
| sK22(X0) = X0 ),
inference(duplicate_literal_removal,[],[f80]) ).
fof(f86,plain,
! [X0] :
( sK22(X0) = X0
| sK0 = sK21(X0) ),
inference(resolution,[],[f27,f68]) ).
fof(f87,plain,
! [X0] :
( r2(sK21(X0),sK20(X0))
| sK0 = sK22(X0) ),
inference(resolution,[],[f27,f67]) ).
fof(f88,plain,
! [X0] :
( sK20(X0) = X0
| sK0 = sK22(X0) ),
inference(resolution,[],[f27,f65]) ).
fof(f89,plain,
! [X0] :
( r1(sK21(X0))
| sK0 = sK22(X0) ),
inference(resolution,[],[f27,f69]) ).
fof(f90,plain,
! [X0] :
( sK0 = sK21(X0)
| sK0 = sK22(X0) ),
inference(resolution,[],[f89,f27]) ).
fof(f93,plain,
! [X0] :
( r1(X0)
| r1(sK21(X0))
| sK0 = sK21(X0) ),
inference(superposition,[],[f69,f86]) ).
fof(f94,plain,
! [X0] :
( r1(X0)
| sK0 = sK21(X0) ),
inference(forward_subsumption_resolution,[],[f93,f27]) ).
fof(f103,plain,
! [X0] : ~ r1(sK1(X0)),
inference(resolution,[],[f79,f72]) ).
fof(f123,plain,
! [X0] :
( r2(sK21(X0),X0)
| sK0 = sK22(X0)
| sK0 = sK22(X0) ),
inference(superposition,[],[f87,f88]) ).
fof(f125,plain,
! [X0] :
( r2(sK21(X0),X0)
| sK0 = sK22(X0) ),
inference(duplicate_literal_removal,[],[f123]) ).
fof(f141,plain,
! [X0] :
( r2(sK0,X0)
| sK0 = sK22(X0)
| sK0 = sK22(X0) ),
inference(superposition,[],[f125,f90]) ).
fof(f143,plain,
! [X0] :
( r2(sK0,X0)
| sK0 = sK22(X0) ),
inference(duplicate_literal_removal,[],[f141]) ).
fof(f147,plain,
! [X0] :
( sK1(sK21(X0)) = X0
| sK22(X0) = X0 ),
inference(resolution,[],[f31,f81]) ).
fof(f151,plain,
! [X0] :
( sK0 = sK22(X0)
| sK1(sK0) = X0 ),
inference(resolution,[],[f143,f31]) ).
fof(f292,plain,
! [X0,X1] :
( ~ r2(X0,sK1(X1))
| X0 = X1 ),
inference(resolution,[],[f78,f72]) ).
fof(f357,plain,
! [X0] : sK0 = sK21(sK1(X0)),
inference(resolution,[],[f103,f94]) ).
fof(f366,plain,
! [X0] :
( r2(sK0,sK1(X0))
| sK1(X0) = sK22(sK1(X0)) ),
inference(superposition,[],[f81,f357]) ).
fof(f515,plain,
! [X0] :
( r2(sK0,X0)
| sK22(X0) = X0
| sK22(X0) = X0 ),
inference(superposition,[],[f366,f147]) ).
fof(f516,plain,
! [X0] :
( r2(sK0,X0)
| sK22(X0) = X0 ),
inference(duplicate_literal_removal,[],[f515]) ).
fof(f523,plain,
! [X0] :
( sK22(X0) = X0
| sK1(sK0) = X0 ),
inference(resolution,[],[f516,f31]) ).
fof(f551,plain,
! [X0] :
( sK0 = X0
| sK1(sK0) = X0
| sK1(sK0) = X0 ),
inference(superposition,[],[f151,f523]) ).
fof(f553,plain,
! [X0] :
( sK1(sK0) = X0
| sK0 = X0 ),
inference(duplicate_literal_removal,[],[f551]) ).
fof(f569,plain,
! [X0] :
( r2(sK0,X0)
| sK0 = X0 ),
inference(superposition,[],[f72,f553]) ).
fof(f671,definition,
( spl23_8
<=> ! [X0] : sK0 = X0 ),
introduced(definition,[new_symbols(definition,[spl23_8])],[avatar_definition]) ).
fof(f672,plain,
( ! [X0] : sK0 = X0
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f704,definition,
( spl23_10
<=> ! [X0] :
( sK0 = X0
| sK0 = sK1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl23_10])],[avatar_definition]) ).
fof(f705,plain,
( ! [X0] :
( sK0 = sK1(X0)
| sK0 = X0 )
| ~ spl23_10 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f760,plain,
! [X0] :
( sK0 = sK1(X0)
| sK0 = X0 ),
inference(resolution,[],[f569,f292]) ).
fof(f761,plain,
spl23_10,
inference(avatar_split_clause,[],[f760,f704]) ).
fof(f901,plain,
( ! [X0] :
( ~ r1(sK0)
| sK0 = X0 )
| ~ spl23_10 ),
inference(superposition,[],[f103,f705]) ).
fof(f926,plain,
( ! [X0] : sK0 = X0
| ~ spl23_10 ),
inference(forward_subsumption_resolution,[],[f901,f70]) ).
fof(f928,plain,
( spl23_8
| ~ spl23_10 ),
inference(avatar_split_clause,[],[f926,f704,f671]) ).
fof(f963,plain,
( ~ r1(sK0)
| ~ spl23_8 ),
inference(superposition,[],[f103,f672]) ).
fof(f1122,plain,
( $false
| ~ spl23_8 ),
inference(forward_subsumption_resolution,[],[f963,f70]) ).
fof(f1123,plain,
~ spl23_8,
inference(avatar_contradiction_clause,[],[f1122]) ).
cnf(s9,plain,
spl23_10,
inference(sat_conversion,[],[f761]) ).
cnf(s14,plain,
( spl23_8
| ~ spl23_10 ),
inference(sat_conversion,[],[f928]) ).
cnf(s21,plain,
~ spl23_8,
inference(sat_conversion,[],[f1123]) ).
cnf(s25,plain,
~ spl23_10,
inference(rat,[],[s14,s21]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s9,s25]) ).
fof(f1167,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN065+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 21:54:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.14/1.14 % (1640939)Detected formulas, will run a generic FOF schedule.
% 0.14/1.14 % (1640949)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3139929174:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.14/1.14 % (1640950)dis-21_1_sil=8000:lcm=predicate:random_seed=1851888624: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)
% 0.14/1.14 % (1640948)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2699783741:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.14/1.14 % (1640945)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=2578965392:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.14/1.14 % (1640947)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1278059120:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.14/1.14 % (1640944)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=224596999:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.14/1.14 % (1640946)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=4274168162:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.14/1.14 % (1640950)Refutation not found, incomplete strategy
% 0.14/1.14 % (1640950)------------------------------
% 0.14/1.14 % (1640950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (1640950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (1640950)CaDiCaL version: 2.1.3
% 0.14/1.14 % (1640950)Termination reason: Refutation not found, incomplete strategy
% 0.14/1.14 % (1640950)Time elapsed: 0.002 s
% 0.14/1.14 % (1640950)Peak memory usage: 88 MB
% 0.14/1.14 % (1640950)Instructions burned: 2 (million)
% 0.14/1.14 % (1640949)First to succeed.
% 0.14/1.14 % (1640949)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1640939"
% 0.14/1.14 % (1640947)Refutation not found, incomplete strategy
% 0.14/1.14 % (1640947)------------------------------
% 0.14/1.14 % (1640947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (1640947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (1640947)CaDiCaL version: 2.1.3
% 0.14/1.14 % (1640947)Termination reason: Refutation not found, incomplete strategy
% 0.14/1.14 % (1640947)Time elapsed: 0.045 s
% 0.14/1.14 % (1640947)Peak memory usage: 88 MB
% 0.14/1.14 % (1640947)Instructions burned: 86 (million)
% 0.14/1.14 % (1640948)Instruction limit reached!
% 0.14/1.14 % (1640948)------------------------------
% 0.14/1.14 % (1640948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (1640948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (1640948)CaDiCaL version: 2.1.3
% 0.14/1.14 % (1640948)Termination reason: Instruction limit
% 0.14/1.14 % (1640948)Termination phase: Saturation
% 0.14/1.14 % (1640948)Time elapsed: 0.065 s
% 0.14/1.14 % (1640948)Peak memory usage: 88 MB
% 0.14/1.14 % (1640948)Instructions burned: 121 (million)
% 0.14/1.14 % (1640949)Refutation found. Thanks to Tanya!
% 0.14/1.14 % SZS status Theorem for theBenchmark
% 0.14/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/1.14 % (1640949)------------------------------
% 0.14/1.14 % (1640949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.14/1.14 % (1640949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/1.14 % (1640949)CaDiCaL version: 2.1.3
% 0.14/1.14 % (1640949)Termination reason: Refutation
% 0.14/1.14 % (1640949)Time elapsed: 0.013 s
% 0.14/1.14 % (1640949)Peak memory usage: 90 MB
% 0.14/1.14 % (1640949)Instructions burned: 35 (million)
% 0.14/1.14 % (1640949)------------------------------
% 0.14/1.14 % (1640949)------------------------------
% 0.14/1.14 % (1640939)Success in time 0.335 s
% 0.14/1.14 % Vampire exiting
%------------------------------------------------------------------------------