%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU142+1 : 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 : n026.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 12:47:23 PM UTC 2026
% Result : Theorem 2.65s 6.37s
% Output : Refutation 2.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 12 unt; 0 def)
% Number of atoms : 161 ( 112 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 189 ( 69 ~; 87 |; 29 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 96 ( 90 !; 6 ?)
% 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(f8,conjecture,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f9,negated_conjecture,
~ ! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
? [X0] : singleton(X0) != unordered_pair(X0,X0),
inference(ennf_transformation,[],[f9]) ).
fof(f13,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(f14,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,[],[f13]) ).
fof(f15,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))],[f14]) ).
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)
| ( ( ( sK1(X0,X1,X2) != X0
& sK1(X0,X1,X2) != X1 )
| ~ in(sK1(X0,X1,X2),X2) )
& ( sK1(X0,X1,X2) = X0
| sK1(X0,X1,X2) = X1
| in(sK1(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,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f18]) ).
fof(f22,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f12]) ).
fof(f24,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f27,plain,
! [X0,X1] :
( sK0(X0,X1) = X0
| singleton(X0) = X1
| in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| sK0(X0,X1) != X0
| singleton(X0) = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f19]) ).
fof(f37,plain,
singleton(sK3) != unordered_pair(sK3,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f31]) ).
fof(f42,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f41]) ).
fof(f43,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f30]) ).
fof(f44,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f43]) ).
fof(f45,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f29]) ).
fof(f69,plain,
! [X0,X1] :
( ~ in(X0,X1)
| X0 != X0
| singleton(X0) = X1
| singleton(X0) = X1
| in(sK0(X0,X1),X1) ),
inference(superposition,[],[f28,f27]) ).
fof(f70,plain,
! [X0,X1] :
( ~ in(X0,X1)
| X0 != X0
| singleton(X0) = X1
| in(sK0(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ~ in(X0,X1)
| singleton(X0) = X1
| in(sK0(X0,X1),X1) ),
inference(trivial_inequality_removal,[],[f70]) ).
fof(f73,plain,
! [X0,X1] :
( in(sK0(X0,unordered_pair(X0,X1)),unordered_pair(X0,X1))
| unordered_pair(X0,X1) = singleton(X0) ),
inference(resolution,[],[f71,f42]) ).
fof(f74,plain,
! [X0,X1] :
( in(sK0(X0,unordered_pair(X1,X0)),unordered_pair(X1,X0))
| unordered_pair(X1,X0) = singleton(X0) ),
inference(resolution,[],[f71,f44]) ).
fof(f76,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = singleton(X0)
| sK0(X0,unordered_pair(X0,X1)) != X0
| unordered_pair(X0,X1) = singleton(X0) ),
inference(resolution,[],[f73,f28]) ).
fof(f84,plain,
! [X0,X1] :
( sK0(X0,unordered_pair(X0,X1)) != X0
| unordered_pair(X0,X1) = singleton(X0) ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f91,plain,
! [X0,X1] :
( sK0(X1,unordered_pair(X0,X1)) != X1
| unordered_pair(X0,X1) = singleton(X1) ),
inference(superposition,[],[f84,f24]) ).
fof(f122,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = singleton(X1)
| sK0(X1,unordered_pair(X0,X1)) = X1
| sK0(X1,unordered_pair(X0,X1)) = X0 ),
inference(resolution,[],[f74,f45]) ).
fof(f131,plain,
! [X0,X1] :
( sK0(X1,unordered_pair(X0,X1)) = X0
| unordered_pair(X0,X1) = singleton(X1) ),
inference(forward_subsumption_resolution,[],[f122,f91]) ).
fof(f145,plain,
! [X0] :
( X0 != X0
| singleton(X0) = unordered_pair(X0,X0)
| singleton(X0) = unordered_pair(X0,X0) ),
inference(superposition,[],[f84,f131]) ).
fof(f156,plain,
! [X0] :
( X0 != X0
| singleton(X0) = unordered_pair(X0,X0) ),
inference(duplicate_literal_removal,[],[f145]) ).
fof(f157,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(trivial_inequality_removal,[],[f156]) ).
fof(f166,plain,
singleton(sK3) != singleton(sK3),
inference(superposition,[],[f37,f157]) ).
fof(f175,plain,
$false,
inference(trivial_inequality_removal,[],[f166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU142+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.40 % Computer : n026.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Mon Sep 28 03:45:18 UTC 2026
% 0.13/5.41 % CPUTime :
% 0.13/5.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/5.44 Running first-order theorem proving
% 0.13/5.44 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
% 2.65/6.37 % (3439723)Detected formulas, will run a generic FOF schedule.
% 2.65/6.37 % (3439733)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3446858008:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.65/6.37 % (3439733)First to succeed.
% 2.65/6.37 % (3439733)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3439723"
% 2.65/6.37 % (3439730)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=2222004410:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.65/6.37 % (3439729)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=3928064660:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.65/6.37 % (3439728)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=1965490169:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.65/6.37 % (3439731)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3062985273:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.65/6.37 % (3439732)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=794243988:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.65/6.37 % (3439731)Refutation not found, incomplete strategy
% 2.65/6.37 % (3439731)------------------------------
% 2.65/6.37 % (3439731)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/6.37 % (3439731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/6.37 % (3439731)CaDiCaL version: 2.1.3
% 2.65/6.37 % (3439731)Termination reason: Refutation not found, incomplete strategy
% 2.65/6.37 % (3439731)Time elapsed: 0.002 s
% 2.65/6.37 % (3439731)Peak memory usage: 88 MB
% 2.65/6.37 % (3439732)Also succeeded, but the first one will report.
% 2.65/6.37 % (3439734)dis-21_1_sil=8000:lcm=predicate:random_seed=2667362864: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)
% 2.65/6.37 % (3439734)Instruction limit reached!
% 2.65/6.37 % (3439734)------------------------------
% 2.65/6.37 % (3439734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/6.37 % (3439734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/6.37 % (3439734)CaDiCaL version: 2.1.3
% 2.65/6.37 % (3439734)Termination reason: Instruction limit
% 2.65/6.37 % (3439734)Termination phase: Saturation
% 2.65/6.37 % (3439734)Time elapsed: 0.072 s
% 2.65/6.37 % (3439734)Peak memory usage: 89 MB
% 2.65/6.37 % (3439734)Instructions burned: 130 (million)
% 2.65/6.37 % (3439733)Refutation found. Thanks to Tanya!
% 2.65/6.37 % SZS status Theorem for theBenchmark
% 2.65/6.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.65/6.37 % (3439733)------------------------------
% 2.65/6.37 % (3439733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.65/6.37 % (3439733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/6.37 % (3439733)CaDiCaL version: 2.1.3
% 2.65/6.37 % (3439733)Termination reason: Refutation
% 2.65/6.37 % (3439733)Time elapsed: 0.004 s
% 2.65/6.37 % (3439733)Peak memory usage: 89 MB
% 2.65/6.37 % (3439733)Instructions burned: 8 (million)
% 2.65/6.37 % (3439733)------------------------------
% 2.65/6.37 % (3439733)------------------------------
% 2.65/6.37 % (3439723)Success in time 0.29 s
% 2.65/6.37 % Vampire exiting
%------------------------------------------------------------------------------