%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU151+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 : n016.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 3.35s 1.40s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 119 ( 86 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 140 ( 55 ~; 55 |; 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 : 65 ( 58 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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,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(f6,negated_conjecture,
~ ! [X0,X1,X2,X3] :
~ ( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f8,plain,
? [X0,X1,X2,X3] :
( unordered_pair(X0,X1) = unordered_pair(X2,X3)
& X0 != X2
& X0 != X3 ),
inference(ennf_transformation,[],[f6]) ).
fof(f9,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(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(flattening,[],[f9]) ).
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) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f10]) ).
fof(f12,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))],[f11]) ).
fof(f13,plain,
( unordered_pair(sK1,sK2) = unordered_pair(sK3,sK4)
& sK1 != sK3
& sK1 != sK4 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f8]) ).
fof(f16,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f12]) ).
fof(f22,plain,
sK1 != sK4,
inference(cnf_transformation,[],[f13]) ).
fof(f23,plain,
sK1 != sK3,
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
unordered_pair(sK1,sK2) = unordered_pair(sK3,sK4),
inference(cnf_transformation,[],[f13]) ).
fof(f25,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f18]) ).
fof(f26,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f25]) ).
fof(f27,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f17]) ).
fof(f28,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f27]) ).
fof(f29,plain,
! [X0,X1,X4] :
( ~ in(X4,unordered_pair(X0,X1))
| X1 = X4
| X0 = X4 ),
inference(equality_resolution,[],[f16]) ).
fof(f30,plain,
in(sK3,unordered_pair(sK1,sK2)),
inference(superposition,[],[f26,f24]) ).
fof(f31,plain,
in(sK4,unordered_pair(sK1,sK2)),
inference(superposition,[],[f28,f24]) ).
fof(f43,plain,
( sK2 = sK3
| sK1 = sK3 ),
inference(resolution,[],[f29,f30]) ).
fof(f44,plain,
( sK2 = sK4
| sK1 = sK4 ),
inference(resolution,[],[f29,f31]) ).
fof(f45,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK1,sK2))
| sK4 = X0
| sK3 = X0 ),
inference(superposition,[],[f29,f24]) ).
fof(f48,plain,
sK2 = sK4,
inference(forward_subsumption_resolution,[],[f44,f22]) ).
fof(f49,plain,
sK2 = sK3,
inference(forward_subsumption_resolution,[],[f43,f23]) ).
fof(f52,plain,
sK3 = sK4,
inference(superposition,[],[f49,f48]) ).
fof(f67,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK1,sK4))
| sK4 = X0
| sK3 = X0 ),
inference(forward_demodulation,[],[f45,f48]) ).
fof(f68,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK1,sK3))
| sK4 = X0
| sK3 = X0 ),
inference(forward_demodulation,[],[f67,f52]) ).
fof(f69,plain,
! [X0] :
( sK3 = X0
| ~ in(X0,unordered_pair(sK1,sK3))
| sK3 = X0 ),
inference(forward_demodulation,[],[f68,f52]) ).
fof(f70,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK1,sK3))
| sK3 = X0 ),
inference(duplicate_literal_removal,[],[f69]) ).
fof(f73,plain,
sK1 = sK3,
inference(resolution,[],[f70,f26]) ).
fof(f75,plain,
$false,
inference(forward_subsumption_resolution,[],[f73,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU151+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:50:48 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 3.35/1.40 % (3239933)Detected formulas, will run a generic FOF schedule.
% 3.35/1.40 % (3239940)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=2114875177:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.35/1.40 % (3239941)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3760797134:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.35/1.40 % (3239939)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=386759362:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.35/1.40 % (3239944)dis-21_1_sil=8000:lcm=predicate:random_seed=243382940: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)
% 3.35/1.40 % (3239938)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=2034482304:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.35/1.40 % (3239942)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2631855967:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.35/1.40 % (3239943)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1110496157:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.35/1.40 % (3239941)Refutation not found, incomplete strategy
% 3.35/1.40 % (3239941)------------------------------
% 3.35/1.40 % (3239941)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.40 % (3239941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.40 % (3239942)Refutation not found, incomplete strategy
% 3.35/1.40 % (3239942)------------------------------
% 3.35/1.40 % (3239942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.40 % (3239941)CaDiCaL version: 2.1.3
% 3.35/1.40 % (3239941)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.40 % (3239941)Time elapsed: 0.001 s
% 3.35/1.40 % (3239942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.40 % (3239941)Peak memory usage: 88 MB
% 3.35/1.40 % (3239942)CaDiCaL version: 2.1.3
% 3.35/1.40 % (3239942)Termination reason: Refutation not found, incomplete strategy
% 3.35/1.40 % (3239942)Time elapsed: 0.001 s
% 3.35/1.40 % (3239942)Peak memory usage: 88 MB
% 3.35/1.40 % (3239943)First to succeed.
% 3.35/1.40 % (3239943)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3239933"
% 3.35/1.40 % (3239944)Instruction limit reached!
% 3.35/1.40 % (3239944)------------------------------
% 3.35/1.40 % (3239944)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.35/1.40 % (3239944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.35/1.40 % (3239944)CaDiCaL version: 2.1.3
% 3.35/1.40 % (3239944)Termination reason: Instruction limit
% 3.35/1.40 % (3239944)Termination phase: Saturation
% 3.35/1.40 % (3239944)Time elapsed: 0.075 s
% 3.35/1.40 % (3239944)Peak memory usage: 89 MB
% 3.35/1.40 % (3239944)Instructions burned: 129 (million)
% 3.35/1.40 % (3239952)lrs+10_1_sil=8000:sp=occurrence:random_seed=1662365312:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.35/1.40 % (3239952)Also succeeded, but the first one will report.
% 3.35/1.40 % (3239941)------------------------------
% 3.35/1.40 % (3239941)------------------------------
% 3.35/1.40 % (3239942)------------------------------
% 3.35/1.40 % (3239942)------------------------------
% 3.35/1.40 % (3239943)Refutation found. Thanks to Tanya!
% 3.35/1.40 % SZS status Theorem for theBenchmark
% 3.35/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.40 % (3239943)------------------------------
% 0.17/1.40 % (3239943)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.40 % (3239943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.40 % (3239943)CaDiCaL version: 2.1.3
% 0.17/1.40 % (3239943)Termination reason: Refutation
% 0.17/1.40 % (3239943)Time elapsed: 0.004 s
% 0.17/1.40 % (3239943)Peak memory usage: 89 MB
% 0.17/1.40 % (3239943)Instructions burned: 3 (million)
% 0.17/1.40 % (3239943)------------------------------
% 0.17/1.40 % (3239943)------------------------------
% 0.17/1.40 % (3239933)Success in time 0.404 s
% 0.17/1.40 % Vampire exiting
%------------------------------------------------------------------------------