%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET872+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:42:12 PM UTC 2026
% Result : Theorem 3.76s 11.51s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 11 unt; 0 def)
% Number of atoms : 149 ( 72 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 183 ( 68 ~; 73 |; 35 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 88 ( 79 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,conjecture,
! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
? [X0,X1] : ~ subset(singleton(X0),unordered_pair(X0,X1)),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f15,plain,
~ subset(singleton(sK0),unordered_pair(sK0,sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK2(X0,X1,X2) != X0
& sK2(X0,X1,X2) != X1 )
| ~ in(sK2(X0,X1,X2),X2) )
& ( sK2(X0,X1,X2) = X0
| sK2(X0,X1,X2) = X1
| in(sK2(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X3,sK2(X0,X1,X2))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f21,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) )
& ( sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f24]) ).
fof(f26,plain,
~ subset(singleton(sK0),unordered_pair(sK0,sK1)),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f34,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f45,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f28]) ).
fof(f46,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f45]) ).
fof(f50,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f34]) ).
fof(f55,plain,
~ subset(singleton(sK0),unordered_pair(sK1,sK0)),
inference(superposition,[],[f26,f33]) ).
fof(f63,plain,
! [X0,X1] :
( sK4(singleton(X0),X1) = X0
| subset(singleton(X0),X1) ),
inference(resolution,[],[f40,f50]) ).
fof(f109,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1)
| subset(singleton(X0),X1) ),
inference(superposition,[],[f41,f63]) ).
fof(f112,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(duplicate_literal_removal,[],[f109]) ).
fof(f123,plain,
~ in(sK0,unordered_pair(sK1,sK0)),
inference(resolution,[],[f112,f55]) ).
fof(f125,plain,
$false,
inference(forward_subsumption_resolution,[],[f123,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET872+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/10.40 % Computer : n005.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.12/10.40 % DateTime : Mon Sep 28 03:04:28 UTC 2026
% 0.12/10.40 % CPUTime :
% 0.12/10.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/10.44 Running first-order theorem proving
% 0.12/10.44 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
% 3.76/11.51 % (392781)Detected formulas, will run a generic FOF schedule.
% 3.76/11.51 % (392792)dis-21_1_sil=8000:lcm=predicate:random_seed=2639314911: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)
% 3.76/11.51 % (392787)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=2978051100:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.76/11.51 % (392788)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=3248797147:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.76/11.51 % (392786)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=3534123223:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.76/11.51 % (392790)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2053237373:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.76/11.51 % (392790)First to succeed.
% 3.76/11.51 % (392790)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-392781"
% 3.76/11.51 % (392789)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2447882179:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.76/11.51 % (392791)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3324553814:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.76/11.51 % (392789)Refutation not found, incomplete strategy
% 3.76/11.51 % (392789)------------------------------
% 3.76/11.51 % (392789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/11.51 % (392789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/11.51 % (392789)CaDiCaL version: 2.1.3
% 3.76/11.51 % (392789)Termination reason: Refutation not found, incomplete strategy
% 3.76/11.51 % (392789)Time elapsed: 0.001 s
% 3.76/11.51 % (392789)Peak memory usage: 88 MB
% 3.76/11.51 % (392789)Instructions burned: 1 (million)
% 3.76/11.51 % (392791)Also succeeded, but the first one will report.
% 3.76/11.51 % (392792)Instruction limit reached!
% 3.76/11.51 % (392792)------------------------------
% 3.76/11.51 % (392792)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/11.51 % (392792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/11.51 % (392792)CaDiCaL version: 2.1.3
% 3.76/11.51 % (392792)Termination reason: Instruction limit
% 3.76/11.51 % (392792)Termination phase: Saturation
% 3.76/11.51 % (392792)Time elapsed: 0.043 s
% 3.76/11.51 % (392792)Peak memory usage: 88 MB
% 3.76/11.51 % (392792)Instructions burned: 132 (million)
% 3.76/11.51 % (392800)lrs+10_1_sil=8000:sp=occurrence:random_seed=2323258689:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.76/11.51 % (392800)Also succeeded, but the first one will report.
% 3.76/11.51 % (392789)------------------------------
% 3.76/11.51 % (392789)------------------------------
% 3.76/11.51 % (392790)Refutation found. Thanks to Tanya!
% 3.76/11.51 % SZS status Theorem for theBenchmark
% 3.76/11.51 % SZS output start Proof for theBenchmark
% See solution above
% 3.76/11.51 % (392790)------------------------------
% 3.76/11.51 % (392790)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/11.51 % (392790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/11.51 % (392790)CaDiCaL version: 2.1.3
% 3.76/11.51 % (392790)Termination reason: Refutation
% 3.76/11.51 % (392790)Time elapsed: 0.005 s
% 3.76/11.51 % (392790)Peak memory usage: 88 MB
% 3.76/11.51 % (392790)Instructions burned: 4 (million)
% 3.76/11.51 % (392790)------------------------------
% 3.76/11.51 % (392790)------------------------------
% 3.76/11.51 % (392781)Success in time 0.443 s
% 3.76/11.51 % Vampire exiting
%------------------------------------------------------------------------------