%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU148+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 12:47:25 PM UTC 2026
% Result : Theorem 2.32s 0.92s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 10 unt; 1 def)
% Number of atoms : 75 ( 33 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 80 ( 33 ~; 29 |; 12 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 40 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f31,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(f64,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f66,conjecture,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f67,negated_conjecture,
~ ! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f107,plain,
? [X0,X1] :
( X0 != X1
& subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f67]) ).
fof(f114,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,[],[f7]) ).
fof(f115,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,[],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f115]) ).
fof(f143,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f154,plain,
( sK13 != sK14
& subset(singleton(sK13),singleton(sK14)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X0,sK13),skolemize(X1,sK14)],[f107]) ).
fof(f164,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f116]) ).
fof(f211,plain,
! [X0,X1] :
( in(X0,X1)
| ~ subset(singleton(X0),X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f253,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f64]) ).
fof(f255,plain,
subset(singleton(sK13),singleton(sK14)),
inference(cnf_transformation,[],[f154]) ).
fof(f256,plain,
sK13 != sK14,
inference(cnf_transformation,[],[f154]) ).
fof(f267,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f164,f253]) ).
fof(f279,plain,
! [X0,X1] :
( ~ subset(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f211,f253]) ).
fof(f292,plain,
subset(unordered_pair(sK13,sK13),unordered_pair(sK14,sK14)),
inference(definition_unfolding,[],[f255,f253,f253]) ).
fof(f297,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_resolution,[],[f267]) ).
fof(f317,definition,
! [X0,X1] :
( sQ15_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ15_eqProxy])],[equality_proxy_definition]) ).
fof(f324,plain,
! [X3,X0] :
( sQ15_eqProxy(X0,X3)
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_proxy_replacement,[],[f297,f317]) ).
fof(f366,plain,
~ sQ15_eqProxy(sK13,sK14),
inference(equality_proxy_replacement,[],[f256,f317]) ).
fof(f371,plain,
! [X0,X1] :
( sQ15_eqProxy(X1,X0)
| ~ sQ15_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f317]) ).
fof(f378,plain,
~ sQ15_eqProxy(sK14,sK13),
inference(resolution,[],[f371,f366]) ).
fof(f406,plain,
in(sK13,unordered_pair(sK14,sK14)),
inference(resolution,[],[f279,f292]) ).
fof(f414,plain,
~ in(sK13,unordered_pair(sK14,sK14)),
inference(resolution,[],[f324,f378]) ).
fof(f415,plain,
$false,
inference(resolution,[],[f414,f406]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU148+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 03:44:49 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 2.32/0.92 % (2996072)Detected formulas, will run a generic FOF schedule.
% 2.32/0.92 % (2996083)dis-21_1_sil=8000:lcm=predicate:random_seed=3250392796: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)
% 2.32/0.92 % (2996078)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=2060134150:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.32/0.92 % (2996077)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=2107988991:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.32/0.92 % (2996081)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2896058919:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.32/0.92 % (2996079)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=2210113048:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.32/0.92 % (2996082)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1558316238:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.32/0.92 % (2996080)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=862098664:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.32/0.92 % (2996083)First to succeed.
% 2.32/0.92 % (2996083)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2996072"
% 2.32/0.92 % (2996080)Also succeeded, but the first one will report.
% 2.32/0.92 % (2996081)Also succeeded, but the first one will report.
% 2.32/0.92 % (2996082)Also succeeded, but the first one will report.
% 2.32/0.92 % (2996083)Refutation found. Thanks to Tanya!
% 2.32/0.92 % SZS status Theorem for theBenchmark
% 2.32/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/0.92 % (2996083)------------------------------
% 2.32/0.92 % (2996083)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.92 % (2996083)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.92 % (2996083)CaDiCaL version: 2.1.3
% 2.32/0.92 % (2996083)Termination reason: Refutation
% 2.32/0.92 % (2996083)Time elapsed: 0.003 s
% 2.32/0.92 % (2996083)Peak memory usage: 88 MB
% 2.32/0.92 % (2996083)Instructions burned: 6 (million)
% 2.32/0.92 % (2996083)------------------------------
% 2.32/0.92 % (2996083)------------------------------
% 2.32/0.92 % (2996072)Success in time 0.298 s
% 2.32/0.92 % Vampire exiting
%------------------------------------------------------------------------------