%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 12:52:17 PM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 16 unt; 0 def)
% Number of atoms : 77 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 33 ~; 22 |; 8 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 60 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f4,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f11,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f23,conjecture,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f28,plain,
! [X0] :
( relation(X0)
=> ! [X1] :
~ ( in(X1,X0)
& ! [X2,X3] : X1 != ordered_pair(X2,X3) ) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ? [X2,X3] : ordered_pair(X2,X3) = X1 )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f33,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f36,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(flattening,[],[f35]) ).
fof(f37,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ~ in(X1,X0)
| ordered_pair(sK0(X1),sK1(X1)) = X1 )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X1)),skolemize(X3,sK1(X1))],[f31]) ).
fof(f41,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f11]) ).
fof(f46,plain,
( empty_set != sK7
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f36]) ).
fof(f49,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ordered_pair(sK0(X1),sK1(X1)) = X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f51,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f52,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f41]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f67,plain,
relation(sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f68,plain,
! [X2,X1] : ~ in(ordered_pair(X1,X2),sK7),
inference(cnf_transformation,[],[f46]) ).
fof(f69,plain,
empty_set != sK7,
inference(cnf_transformation,[],[f46]) ).
fof(f70,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f37]) ).
fof(f73,plain,
! [X0,X1] :
( ~ relation(X0)
| unordered_pair(unordered_pair(sK0(X1),sK1(X1)),singleton(sK0(X1))) = X1
| ~ in(X1,X0) ),
inference(definition_unfolding,[],[f50,f51]) ).
fof(f75,plain,
! [X2,X1] : ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),sK7),
inference(definition_unfolding,[],[f68,f51]) ).
fof(f96,plain,
! [X0,X1] : ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK7),
inference(superposition,[],[f75,f49]) ).
fof(f110,plain,
! [X0] :
( empty(X0)
| in(sK2(X0),X0) ),
inference(resolution,[],[f66,f52]) ).
fof(f119,plain,
! [X0] :
( unordered_pair(unordered_pair(sK0(X0),sK1(X0)),singleton(sK0(X0))) = X0
| ~ in(X0,sK7) ),
inference(resolution,[],[f73,f67]) ).
fof(f120,plain,
! [X0] :
( ~ in(X0,sK7)
| unordered_pair(singleton(sK0(X0)),unordered_pair(sK0(X0),sK1(X0))) = X0 ),
inference(forward_demodulation,[],[f119,f49]) ).
fof(f128,plain,
! [X0] :
( in(sK2(X0),X0)
| empty_set = X0 ),
inference(resolution,[],[f110,f70]) ).
fof(f150,plain,
( empty_set = sK7
| sK2(sK7) = unordered_pair(singleton(sK0(sK2(sK7))),unordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7)))) ),
inference(resolution,[],[f128,f120]) ).
fof(f151,plain,
sK2(sK7) = unordered_pair(singleton(sK0(sK2(sK7))),unordered_pair(sK0(sK2(sK7)),sK1(sK2(sK7)))),
inference(forward_subsumption_resolution,[],[f150,f69]) ).
fof(f152,plain,
~ in(sK2(sK7),sK7),
inference(superposition,[],[f96,f151]) ).
fof(f173,plain,
empty_set = sK7,
inference(resolution,[],[f152,f128]) ).
fof(f174,plain,
$false,
inference(forward_subsumption_resolution,[],[f173,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.31 % Computer : n012.cluster.edu
% 0.03/0.31 % Model : x86_64 x86_64
% 0.03/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.31 % Memory : 8046.5625MB
% 0.03/0.31 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Mon Sep 28 03:57:04 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.33 Running first-order model finding
% 0.08/0.33 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
% 0.08/0.36 % (3001490)Will run a generic schedule for satisfiability detection.
% 0.08/0.36 % (3001496)% WARNING: option uhcvi not known.
% 0.08/0.36 % (3001497)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1843809183:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.36 % (3001495)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1210604888_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.36 % (3001500)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1536280356:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.36 % (3001498)dis+10_1_sil=32000:sp=arity:random_seed=2427564120:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.36 % (3001496)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2290532410:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.36 % (3001499)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=816338249:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.36 % (3001501)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2783539896:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.36 % TRYING [1]
% 0.08/0.36 % TRYING [2]
% 0.08/0.36 % TRYING [3]
% 0.08/0.36 % (3001500) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3001490-3001500"...
% 0.08/0.36 % (3001499) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3001490-3001499"...
% 0.08/0.36 % (3001498) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3001490-3001498"...
% 0.08/0.36 % (3001496) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3001490-3001496"...
% 0.08/0.36 % (3001501) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3001490-3001501"...
% 0.08/0.36 % (3001500)...printing done.
% 0.08/0.36 % (3001499)...printing done.
% 0.08/0.36 % (3001498)...printing done.
% 0.08/0.36 % (3001496)...printing done.
% 0.08/0.36 % (3001501)...printing done.
% 0.08/0.36 % (3001500)Refutation found. Thanks to Tanya!
% 0.08/0.36 % SZS status Theorem for theBenchmark
% 0.08/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.36 % (3001500)------------------------------
% 0.08/0.36 % (3001500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.36 % (3001500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.36 % (3001500)CaDiCaL version: 2.1.3
% 0.08/0.36 % (3001500)Termination reason: Refutation
% 0.08/0.36 % (3001500)Time elapsed: 0.002 s
% 0.08/0.36 % (3001500)Peak memory usage: 12 MB
% 0.08/0.36 % (3001500)Instructions burned: 4 (million)
% 0.08/0.36 % (3001490)Success in time 0.026 s
% 0.08/0.36 % Vampire exiting
%------------------------------------------------------------------------------