%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 12:52:07 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 113 ( 83 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 131 ( 52 ~; 49 |; 28 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 62 ( 55 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f6,conjecture,
! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2,X3] :
( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,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,[],[f3]) ).
fof(f11,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,[],[f10]) ).
fof(f12,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,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK0(X0,X1,X2) != X0
& sK0(X0,X1,X2) != X1 )
| ~ in(sK0(X0,X1,X2),X2) )
& ( sK0(X0,X1,X2) = X0
| sK0(X0,X1,X2) = X1
| in(sK0(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,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f12]) ).
fof(f16,plain,
( unordered_pair(sK3,sK4) = unordered_pair(sK5,sK6)
& sK3 != sK5
& sK3 != sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f9]) ).
fof(f19,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f27,plain,
sK3 != sK6,
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
sK3 != sK5,
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
unordered_pair(sK3,sK4) = unordered_pair(sK5,sK6),
inference(cnf_transformation,[],[f16]) ).
fof(f30,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f21]) ).
fof(f31,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f30]) ).
fof(f32,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f20]) ).
fof(f33,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f19]) ).
fof(f41,plain,
in(sK5,unordered_pair(sK3,sK4)),
inference(superposition,[],[f31,f29]) ).
fof(f45,plain,
in(sK6,unordered_pair(sK3,sK4)),
inference(superposition,[],[f33,f29]) ).
fof(f64,plain,
( sK4 = sK5
| sK3 = sK5 ),
inference(resolution,[],[f34,f41]) ).
fof(f65,plain,
( sK4 = sK6
| sK3 = sK6 ),
inference(resolution,[],[f34,f45]) ).
fof(f69,plain,
sK4 = sK6,
inference(forward_subsumption_resolution,[],[f65,f27]) ).
fof(f70,plain,
sK4 = sK5,
inference(forward_subsumption_resolution,[],[f64,f28]) ).
fof(f86,plain,
sK5 = sK6,
inference(superposition,[],[f70,f69]) ).
fof(f93,plain,
unordered_pair(sK3,sK4) = unordered_pair(sK5,sK5),
inference(superposition,[],[f29,f86]) ).
fof(f98,plain,
unordered_pair(sK3,sK6) = unordered_pair(sK5,sK5),
inference(forward_demodulation,[],[f93,f69]) ).
fof(f99,plain,
unordered_pair(sK3,sK5) = unordered_pair(sK5,sK5),
inference(forward_demodulation,[],[f98,f86]) ).
fof(f104,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK3,sK5))
| sK5 = X0
| sK5 = X0 ),
inference(superposition,[],[f34,f99]) ).
fof(f107,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK3,sK5))
| sK5 = X0 ),
inference(duplicate_literal_removal,[],[f104]) ).
fof(f114,plain,
sK3 = sK5,
inference(resolution,[],[f107,f31]) ).
fof(f116,plain,
$false,
inference(forward_subsumption_resolution,[],[f114,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:48:37 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.40 Running first-order model finding
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.44 % (4129086)Will run a generic schedule for satisfiability detection.
% 0.12/0.44 % (4129093)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3988311689:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.44 % (4129093) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4129086-4129093"...
% 0.12/0.44 % (4129093)...printing done.
% 0.12/0.44 % (4129092)% WARNING: option uhcvi not known.
% 0.12/0.44 % (4129093)Refutation found. Thanks to Tanya!
% 0.12/0.44 % SZS status Theorem for theBenchmark
% 0.12/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.44 % (4129093)------------------------------
% 0.12/0.44 % (4129093)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.44 % (4129093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.44 % (4129093)CaDiCaL version: 2.1.3
% 0.12/0.44 % (4129093)Termination reason: Refutation
% 0.12/0.44 % (4129093)Time elapsed: 0.002 s
% 0.12/0.44 % (4129093)Peak memory usage: 12 MB
% 0.12/0.44 % (4129093)Instructions burned: 4 (million)
% 0.12/0.44 % (4129086)Success in time 0.036 s
% 0.12/0.44 % Vampire exiting
%------------------------------------------------------------------------------