%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU150+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 : n006.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 3.46s 1.46s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 5 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 27 ( 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f5,conjecture,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,plain,
? [X0,X1,X2] :
( X1 != X2
& singleton(X0) = unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f4]) ).
fof(f9,plain,
( sK1 != sK2
& singleton(sK0) = unordered_pair(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f7]) ).
fof(f10,plain,
singleton(sK0) = unordered_pair(sK1,sK2),
inference(cnf_transformation,[],[f9]) ).
fof(f11,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f13,plain,
! [X2,X0,X1] :
( singleton(X0) != unordered_pair(X1,X2)
| X0 = X1 ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X0] :
( singleton(X0) != singleton(sK0)
| sK1 = X0 ),
inference(superposition,[],[f13,f10]) ).
fof(f15,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) != singleton(X2)
| X1 = X2 ),
inference(superposition,[],[f13,f12]) ).
fof(f17,plain,
sK0 = sK1,
inference(equality_resolution,[],[f14]) ).
fof(f19,plain,
! [X0] :
( singleton(X0) != singleton(sK0)
| sK2 = X0 ),
inference(superposition,[],[f15,f10]) ).
fof(f24,plain,
sK0 = sK2,
inference(equality_resolution,[],[f19]) ).
fof(f27,plain,
sK0 != sK1,
inference(superposition,[],[f11,f24]) ).
fof(f28,plain,
$false,
inference(forward_subsumption_resolution,[],[f27,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU150+1 : 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 : n006.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 03:45:25 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
% 3.46/1.45 % (3556623)Detected formulas, will run a generic FOF schedule.
% 3.46/1.45 % (3556628)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=1687914277:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.46/1.45 % (3556634)dis-21_1_sil=8000:lcm=predicate:random_seed=2926915200: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)
% 3.46/1.45 % (3556634)Refutation not found, incomplete strategy
% 3.46/1.45 % (3556634)------------------------------
% 3.46/1.45 % (3556634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.45 % (3556634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.45 % (3556634)CaDiCaL version: 2.1.3
% 3.46/1.45 % (3556634)Termination reason: Refutation not found, incomplete strategy
% 3.46/1.45 % (3556634)Time elapsed: 0.001 s
% 3.46/1.45 % (3556634)Peak memory usage: 88 MB
% 3.46/1.45 % (3556630)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=4086039626:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.46/1.45 % (3556632)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2701967342:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.46/1.45 % (3556629)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=1558950173:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.46/1.45 % (3556631)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1520228923:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.46/1.45 % (3556631)Also succeeded, but the first one will report.
% 3.46/1.45 % (3556632)First to succeed.
% 3.46/1.45 % (3556632)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3556623"
% 3.46/1.45 % (3556633)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3987756973:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.46/1.45 % (3556633)Also succeeded, but the first one will report.
% 3.46/1.46 % (3556634)------------------------------
% 3.46/1.46 % (3556634)------------------------------
% 3.46/1.46 % (3556632)Refutation found. Thanks to Tanya!
% 3.46/1.46 % SZS status Theorem for theBenchmark
% 3.46/1.46 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.46 % (3556632)------------------------------
% 3.46/1.46 % (3556632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.46 % (3556632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.46 % (3556632)CaDiCaL version: 2.1.3
% 3.46/1.46 % (3556632)Termination reason: Refutation
% 3.46/1.46 % (3556632)Time elapsed: 0.002 s
% 3.46/1.46 % (3556632)Peak memory usage: 88 MB
% 3.46/1.46 % (3556632)Instructions burned: 1 (million)
% 3.46/1.46 % (3556632)------------------------------
% 3.46/1.46 % (3556632)------------------------------
% 3.46/1.46 % (3556623)Success in time 0.406 s
% 3.46/1.46 % Vampire exiting
%------------------------------------------------------------------------------