%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET071+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 12:39:56 PM UTC 2026
% Result : Theorem 5.04s 1.88s
% Output : Refutation 5.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 75 ( 36 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 78 ( 27 ~; 26 |; 21 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 30 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f41,axiom,
! [X0] :
( X0 != null_class
=> ? [X1] :
( member(X1,universal_class)
& member(X1,X0)
& disjoint(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
fof(f44,conjecture,
! [X0,X1] :
( ( ~ member(X0,universal_class)
& ~ member(X1,universal_class) )
=> unordered_pair(X0,X1) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( ( ~ member(X0,universal_class)
& ~ member(X1,universal_class) )
=> unordered_pair(X0,X1) = null_class ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
? [X0,X1] :
( unordered_pair(X0,X1) != null_class
& ~ member(X0,universal_class)
& ~ member(X1,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f47,plain,
? [X0,X1] :
( unordered_pair(X0,X1) != null_class
& ~ member(X0,universal_class)
& ~ member(X1,universal_class) ),
inference(flattening,[],[f46]) ).
fof(f50,plain,
! [X0] :
( ? [X1] :
( member(X1,universal_class)
& member(X1,X0)
& disjoint(X1,X0) )
| null_class = X0 ),
inference(ennf_transformation,[],[f41]) ).
fof(f60,plain,
( null_class != unordered_pair(sK0,sK1)
& ~ member(sK0,universal_class)
& ~ member(sK1,universal_class) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f47]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ~ member(X0,universal_class)
| ( X0 != X1
& X0 != X2 ) )
& ( ( member(X0,universal_class)
& ( X0 = X1
| X0 = X2 ) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f61]) ).
fof(f64,plain,
! [X0] :
( ( member(sK3(X0),universal_class)
& member(sK3(X0),X0)
& disjoint(sK3(X0),X0) )
| null_class = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f50]) ).
fof(f102,plain,
~ member(sK1,universal_class),
inference(cnf_transformation,[],[f60]) ).
fof(f103,plain,
~ member(sK0,universal_class),
inference(cnf_transformation,[],[f60]) ).
fof(f104,plain,
null_class != unordered_pair(sK0,sK1),
inference(cnf_transformation,[],[f60]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f115,plain,
! [X0] :
( member(sK3(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f64]) ).
fof(f116,plain,
! [X0] :
( member(sK3(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f64]) ).
fof(f231,plain,
! [X0,X1] :
( sK3(unordered_pair(X0,X1)) = X1
| sK3(unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = null_class ),
inference(resolution,[],[f115,f108]) ).
fof(f235,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| sK3(unordered_pair(X0,X1)) = X1
| unordered_pair(X0,X1) = null_class ),
inference(superposition,[],[f116,f231]) ).
fof(f238,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = null_class
| sK3(unordered_pair(X0,X1)) = X1 ),
inference(duplicate_literal_removal,[],[f235]) ).
fof(f243,plain,
! [X0] :
( sK3(unordered_pair(sK0,X0)) = X0
| null_class = unordered_pair(sK0,X0) ),
inference(resolution,[],[f238,f103]) ).
fof(f246,plain,
! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(sK0,X0)
| null_class = unordered_pair(sK0,X0) ),
inference(superposition,[],[f116,f243]) ).
fof(f247,plain,
! [X0] :
( member(X0,universal_class)
| null_class = unordered_pair(sK0,X0) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f256,plain,
$false,
inference(unit_resulting_resolution,[],[f247,f102,f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET071+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.57 % Computer : n016.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 28 00:34:48 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.60 Running first-order theorem proving
% 0.10/0.60 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
% 5.04/1.88 % (3149865)Detected formulas, will run a generic FOF schedule.
% 5.04/1.88 % (3149871)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=2442675321:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.04/1.88 % (3149872)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=1449921459:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.04/1.88 % (3149873)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1791932149:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.04/1.88 % (3149876)dis-21_1_sil=8000:lcm=predicate:random_seed=1490572395: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)
% 5.04/1.88 % (3149870)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=2672826620:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.04/1.88 % (3149874)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1966093126:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.04/1.88 % (3149873)Refutation not found, incomplete strategy
% 5.04/1.88 % (3149873)------------------------------
% 5.04/1.88 % (3149873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.88 % (3149873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.88 % (3149873)CaDiCaL version: 2.1.3
% 5.04/1.88 % (3149873)Termination reason: Refutation not found, incomplete strategy
% 5.04/1.88 % (3149873)Time elapsed: 0.001 s
% 5.04/1.88 % (3149873)Peak memory usage: 88 MB
% 5.04/1.88 % (3149874)Refutation not found, incomplete strategy
% 5.04/1.88 % (3149874)------------------------------
% 5.04/1.88 % (3149874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.88 % (3149874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.88 % (3149874)CaDiCaL version: 2.1.3
% 5.04/1.88 % (3149874)Termination reason: Refutation not found, incomplete strategy
% 5.04/1.88 % (3149874)Time elapsed: 0.002 s
% 5.04/1.88 % (3149874)Peak memory usage: 87 MB
% 5.04/1.88 % (3149874)Instructions burned: 1 (million)
% 5.04/1.88 % (3149875)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3011813100:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.04/1.88 % (3149876)Instruction limit reached!
% 5.04/1.88 % (3149876)------------------------------
% 5.04/1.88 % (3149876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.88 % (3149876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.88 % (3149876)CaDiCaL version: 2.1.3
% 5.04/1.88 % (3149876)Termination reason: Instruction limit
% 5.04/1.88 % (3149876)Termination phase: Saturation
% 5.04/1.88 % (3149876)Time elapsed: 0.076 s
% 5.04/1.88 % (3149876)Peak memory usage: 89 MB
% 5.04/1.88 % (3149876)Instructions burned: 130 (million)
% 5.04/1.88 % (3149875)Instruction limit reached!
% 5.04/1.88 % (3149875)------------------------------
% 5.04/1.88 % (3149875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.88 % (3149875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.88 % (3149875)CaDiCaL version: 2.1.3
% 5.04/1.88 % (3149875)Termination reason: Instruction limit
% 5.04/1.88 % (3149875)Termination phase: Saturation
% 5.04/1.88 % (3149875)Time elapsed: 0.103 s
% 5.04/1.88 % (3149875)Peak memory usage: 90 MB
% 5.04/1.88 % (3149875)Instructions burned: 139 (million)
% 5.04/1.88 % (3149873)------------------------------
% 5.04/1.88 % (3149873)------------------------------
% 5.04/1.88 % (3149874)------------------------------
% 5.04/1.88 % (3149874)------------------------------
% 5.04/1.88 % (3149884)lrs+10_1_sil=8000:sp=occurrence:random_seed=2440093513:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.04/1.88 % (3149885)lrs+10_1_sil=32000:urr=on:br=off:random_seed=727822995:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.04/1.88 % (3149871)First to succeed.
% 5.04/1.88 % (3149885)Refutation not found, incomplete strategy
% 5.04/1.88 % (3149885)------------------------------
% 5.04/1.88 % (3149885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.88 % (3149885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.88 % (3149885)CaDiCaL version: 2.1.3
% 5.04/1.88 % (3149885)Termination reason: Refutation not found, incomplete strategy
% 5.04/1.88 % (3149885)Time elapsed: 0.003 s
% 5.04/1.88 % (3149885)Peak memory usage: 88 MB
% 5.04/1.88 % (3149885)Instructions burned: 3 (million)
% 5.04/1.88 % (3149871)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3149865"
% 5.04/1.88 % (3149887)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1575862547:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 5.04/1.88 % (3149888)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3412019032:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 5.04/1.88 % (3149884)Instruction limit reached!
% 5.04/1.88 % (3149884)------------------------------
% 5.04/1.88 % (3149884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.88 % (3149884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.88 % (3149884)CaDiCaL version: 2.1.3
% 5.04/1.88 % (3149884)Termination reason: Instruction limit
% 5.04/1.88 % (3149884)Termination phase: Saturation
% 5.04/1.88 % (3149884)Time elapsed: 0.188 s
% 5.04/1.88 % (3149884)Peak memory usage: 92 MB
% 5.04/1.88 % (3149884)Instructions burned: 285 (million)
% 5.04/1.88 % (3149871)Refutation found. Thanks to Tanya!
% 5.04/1.88 % SZS status Theorem for theBenchmark
% 5.04/1.88 % SZS output start Proof for theBenchmark
% See solution above
% 5.04/1.88 % (3149871)------------------------------
% 5.04/1.88 % (3149871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.04/1.88 % (3149871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.04/1.88 % (3149871)CaDiCaL version: 2.1.3
% 5.04/1.88 % (3149871)Termination reason: Refutation
% 5.04/1.88 % (3149871)Time elapsed: 0.346 s
% 5.04/1.88 % (3149871)Peak memory usage: 129 MB
% 5.04/1.88 % (3149871)Instructions burned: 938 (million)
% 5.04/1.88 % (3149871)------------------------------
% 5.04/1.88 % (3149871)------------------------------
% 5.04/1.88 % (3149865)Success in time 0.638 s
% 5.04/1.88 % Vampire exiting
%------------------------------------------------------------------------------