%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU151+2 : TPTP v9.3.1. Released v3.3.0.
% 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 12:47:26 PM UTC 2026
% Result : Theorem 2.82s 1.38s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 7 unt; 0 def)
% Number of atoms : 93 ( 69 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 119 ( 47 ~; 42 |; 28 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 44 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,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(f39,conjecture,
! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f40,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f85,plain,
? [X0,X1,X2,X3] :
( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(ennf_transformation,[],[f40]) ).
fof(f117,plain,
( unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3)
& sK0 != sK2
& sK0 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f85]) ).
fof(f139,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,[],[f10]) ).
fof(f140,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,[],[f139]) ).
fof(f141,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,[],[f140]) ).
fof(f142,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK11(X0,X1,X2) != X0
& sK11(X0,X1,X2) != X1 )
| ~ in(sK11(X0,X1,X2),X2) )
& ( sK11(X0,X1,X2) = X0
| sK11(X0,X1,X2) = X1
| in(sK11(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,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f141]) ).
fof(f164,plain,
sK0 != sK3,
inference(cnf_transformation,[],[f117]) ).
fof(f165,plain,
sK0 != sK2,
inference(cnf_transformation,[],[f117]) ).
fof(f166,plain,
unordered_pair(sK0,sK1) = unordered_pair(sK2,sK3),
inference(cnf_transformation,[],[f117]) ).
fof(f223,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f142]) ).
fof(f225,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f142]) ).
fof(f301,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f225]) ).
fof(f302,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f301]) ).
fof(f305,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f223]) ).
fof(f318,plain,
in(sK0,unordered_pair(sK2,sK3)),
inference(superposition,[],[f302,f166]) ).
fof(f1027,plain,
( sK0 = sK3
| sK0 = sK2 ),
inference(resolution,[],[f305,f318]) ).
fof(f1046,plain,
sK0 = sK2,
inference(forward_subsumption_resolution,[],[f1027,f164]) ).
fof(f1047,plain,
$false,
inference(forward_subsumption_resolution,[],[f1046,f165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n005.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 28 03:45:47 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 2.82/1.38 % (416215)Detected formulas, will run a generic FOF schedule.
% 2.82/1.38 % (416224)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1641522270:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.82/1.38 % (416224)First to succeed.
% 2.82/1.38 % (416224)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-416215"
% 2.82/1.38 % (416223)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3670474829:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.82/1.38 % (416220)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=4083896981:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.82/1.38 % (416222)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=4254705302:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.82/1.38 % (416226)dis-21_1_sil=8000:lcm=predicate:random_seed=2622266980: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)
% 2.82/1.38 % (416221)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=3461607510:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.82/1.38 % (416223)Also succeeded, but the first one will report.
% 2.82/1.38 % (416225)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2372845127:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.82/1.38 % (416225)Also succeeded, but the first one will report.
% 2.82/1.38 % (416226)Instruction limit reached!
% 2.82/1.38 % (416226)------------------------------
% 2.82/1.38 % (416226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.38 % (416226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.38 % (416226)CaDiCaL version: 2.1.3
% 2.82/1.38 % (416226)Termination reason: Instruction limit
% 2.82/1.38 % (416226)Termination phase: Saturation
% 2.82/1.38 % (416226)Time elapsed: 0.086 s
% 2.82/1.38 % (416226)Peak memory usage: 89 MB
% 2.82/1.38 % (416226)Instructions burned: 130 (million)
% 2.82/1.38 % (416224)Refutation found. Thanks to Tanya!
% 2.82/1.38 % SZS status Theorem for theBenchmark
% 2.82/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.38 % (416224)------------------------------
% 2.82/1.38 % (416224)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.38 % (416224)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.38 % (416224)CaDiCaL version: 2.1.3
% 2.82/1.38 % (416224)Termination reason: Refutation
% 2.82/1.38 % (416224)Time elapsed: 0.011 s
% 2.82/1.38 % (416224)Peak memory usage: 88 MB
% 2.82/1.38 % (416224)Instructions burned: 26 (million)
% 2.82/1.38 % (416224)------------------------------
% 2.82/1.38 % (416224)------------------------------
% 2.82/1.38 % (416215)Success in time 0.319 s
% 2.82/1.38 % Vampire exiting
%------------------------------------------------------------------------------