%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU186+2 : 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 : 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 12:52:18 PM UTC 2026
% Result : Theorem 1.10s 0.58s
% Output : Refutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 23 unt; 0 def)
% Number of atoms : 93 ( 33 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 90 ( 41 ~; 32 |; 5 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 61 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f11,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f25,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(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f64,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f69,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f147,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(f148,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f147]) ).
fof(f153,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_inverse(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f209,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f276,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(ennf_transformation,[],[f148]) ).
fof(f277,plain,
? [X0] :
( empty_set != X0
& ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
& relation(X0) ),
inference(flattening,[],[f276]) ).
fof(f296,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f318,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f11]) ).
fof(f378,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f25]) ).
fof(f382,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK29(X0,X1),sK28(X0,X1)),X0)
| in(ordered_pair(sK28(X0,X1),sK29(X0,X1)),X1)
| relation_inverse(X0) = X1 ),
inference(cnf_transformation,[],[f188]) ).
fof(f415,plain,
relation(empty_set),
inference(cnf_transformation,[],[f64]) ).
fof(f421,plain,
! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 ),
inference(cnf_transformation,[],[f209]) ).
fof(f532,plain,
relation(sK47),
inference(cnf_transformation,[],[f277]) ).
fof(f533,plain,
! [X2,X1] : ~ in(ordered_pair(X1,X2),sK47),
inference(cnf_transformation,[],[f277]) ).
fof(f534,plain,
empty_set != sK47,
inference(cnf_transformation,[],[f277]) ).
fof(f540,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f153]) ).
fof(f557,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f378,f540]) ).
fof(f584,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK28(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK28(X0,X1),sK29(X0,X1)),unordered_pair(sK28(X0,X1),sK28(X0,X1))),X1)
| relation_inverse(X0) = X1 ),
inference(definition_unfolding,[],[f382,f557,f557]) ).
fof(f634,plain,
! [X2,X1] : ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK47),
inference(definition_unfolding,[],[f533,f557]) ).
fof(f652,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f318]) ).
fof(f709,plain,
! [X1] : in(X1,empty_set),
inference(consistent_polarity_flipping,[],[f652]) ).
fof(f770,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK28(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK29(X0,X1)),unordered_pair(sK28(X0,X1),sK28(X0,X1))),X1)
| relation_inverse(X0) = X1 ),
inference(consistent_polarity_flipping,[],[f584]) ).
fof(f894,plain,
! [X2,X1] : in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),sK47),
inference(consistent_polarity_flipping,[],[f634]) ).
fof(f965,plain,
! [X0,X1] : in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),sK47),
inference(superposition,[],[f894,f296]) ).
fof(f966,plain,
! [X0,X1] : in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X1)),sK47),
inference(superposition,[],[f894,f296]) ).
fof(f988,plain,
empty_set = relation_inverse(relation_inverse(empty_set)),
inference(resolution,[],[f421,f415]) ).
fof(f4248,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK29(X0,X1)),unordered_pair(sK28(X0,X1),sK28(X0,X1))),X1)
| relation_inverse(X0) = X1 ),
inference(forward_demodulation,[],[f770,f296]) ).
fof(f4249,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK28(X0,X1)),unordered_pair(sK28(X0,X1),sK29(X0,X1))),X1)
| relation_inverse(X0) = X1 ),
inference(forward_demodulation,[],[f4248,f296]) ).
fof(f4297,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(sK28(X0,sK47),sK29(X0,sK47)),unordered_pair(sK29(X0,sK47),sK29(X0,sK47))),X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK28(X0,sK47),sK28(X0,sK47)),unordered_pair(sK28(X0,sK47),sK29(X0,sK47))),sK47)
| relation_inverse(X0) = sK47 ),
inference(resolution,[],[f4249,f532]) ).
fof(f4298,plain,
! [X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(sK28(X0,sK47),sK29(X0,sK47)),unordered_pair(sK29(X0,sK47),sK29(X0,sK47))),X0)
| relation_inverse(X0) = sK47 ),
inference(forward_subsumption_resolution,[],[f4297,f966]) ).
fof(f4648,plain,
( ~ in(unordered_pair(unordered_pair(sK28(empty_set,sK47),sK29(empty_set,sK47)),unordered_pair(sK29(empty_set,sK47),sK29(empty_set,sK47))),empty_set)
| sK47 = relation_inverse(empty_set) ),
inference(resolution,[],[f4298,f415]) ).
fof(f4665,plain,
( ~ in(unordered_pair(unordered_pair(sK28(sK47,sK47),sK29(sK47,sK47)),unordered_pair(sK29(sK47,sK47),sK29(sK47,sK47))),sK47)
| sK47 = relation_inverse(sK47) ),
inference(resolution,[],[f4298,f532]) ).
fof(f4666,plain,
sK47 = relation_inverse(sK47),
inference(forward_subsumption_resolution,[],[f4665,f965]) ).
fof(f4712,plain,
sK47 = relation_inverse(empty_set),
inference(forward_subsumption_resolution,[],[f4648,f709]) ).
fof(f4884,plain,
empty_set = relation_inverse(sK47),
inference(forward_demodulation,[],[f988,f4712]) ).
fof(f4892,plain,
empty_set = sK47,
inference(superposition,[],[f4666,f4884]) ).
fof(f4895,plain,
$false,
inference(forward_subsumption_resolution,[],[f4892,f534]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU186+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 04:00:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 Running first-order model finding
% 0.13/0.40 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
% 1.10/0.58 % (4133599)Will run a generic schedule for satisfiability detection.
% 1.10/0.58 % (4133608)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3769815107:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.10/0.58 % (4133605)% WARNING: option uhcvi not known.
% 1.10/0.58 % (4133604)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3330168046_2999 on theBenchmark for (2999ds/0Mi)
% 1.10/0.58 % (4133606)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=970043713:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.10/0.58 % (4133607)dis+10_1_sil=32000:sp=arity:random_seed=3520510747:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.10/0.58 % (4133610)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2964727111:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.10/0.58 % (4133609)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=252203480:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.10/0.58 % (4133605)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3611339979:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.10/0.58 % TRYING [1]
% 1.10/0.58 % TRYING [2]
% 1.10/0.58 % (4133608)Instruction limit reached!
% 1.10/0.58 % (4133608)------------------------------
% 1.10/0.58 % (4133608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.58 % (4133608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.58 % (4133608)CaDiCaL version: 2.1.3
% 1.10/0.58 % (4133608)Termination reason: Instruction limit
% 1.10/0.58 % (4133608)Termination phase: Saturation
% 1.10/0.58 % (4133608)Time elapsed: 0.042 s
% 1.10/0.58 % (4133608)Peak memory usage: 13 MB
% 1.10/0.58 % (4133608)Instructions burned: 116 (million)
% 1.10/0.58 % TRYING [3]
% 1.10/0.58 % (4133618)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1353245961:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.10/0.58 % TRYING [1]
% 1.10/0.58 % TRYING [2]
% 1.10/0.58 % TRYING [3]
% 1.10/0.58 % (4133609)Instruction limit reached!
% 1.10/0.58 % (4133609)------------------------------
% 1.10/0.58 % (4133609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.58 % (4133609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.58 % (4133609)CaDiCaL version: 2.1.3
% 1.10/0.58 % (4133609)Termination reason: Instruction limit
% 1.10/0.58 % (4133609)Termination phase: Saturation
% 1.10/0.58 % (4133609)Time elapsed: 0.066 s
% 1.10/0.58 % (4133609)Peak memory usage: 13 MB
% 1.10/0.58 % (4133609)Instructions burned: 131 (million)
% 1.10/0.58 % (4133607)Instruction limit reached!
% 1.10/0.58 % (4133607)------------------------------
% 1.10/0.58 % (4133607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.58 % (4133607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.58 % (4133607)CaDiCaL version: 2.1.3
% 1.10/0.58 % (4133607)Termination reason: Instruction limit
% 1.10/0.58 % (4133607)Termination phase: Saturation
% 1.10/0.58 % (4133607)Time elapsed: 0.071 s
% 1.10/0.58 % (4133607)Peak memory usage: 13 MB
% 1.10/0.58 % (4133607)Instructions burned: 104 (million)
% 1.10/0.58 % (4133620)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1394859842:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.10/0.58 % (4133621)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=647682889:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.10/0.58 % TRYING [4]
% 1.10/0.58 % (4133610)Instruction limit reached!
% 1.10/0.58 % (4133610)------------------------------
% 1.10/0.58 % (4133610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.58 % (4133610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.58 % (4133610)CaDiCaL version: 2.1.3
% 1.10/0.58 % (4133610)Termination reason: Instruction limit
% 1.10/0.58 % (4133610)Termination phase: Saturation
% 1.10/0.58 % (4133610)Time elapsed: 0.100 s
% 1.10/0.58 % (4133610)Peak memory usage: 13 MB
% 1.10/0.58 % (4133610)Instructions burned: 159 (million)
% 1.10/0.58 % TRYING [4]
% 1.10/0.58 % (4133624)ott-21_1_sil=16000:fs=off:random_seed=1807948865:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.10/0.58 % (4133605) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4133599-4133605"...
% 1.10/0.58 % (4133605)...printing done.
% 1.10/0.58 % (4133605)Refutation found. Thanks to Tanya!
% 1.10/0.58 % SZS status Theorem for theBenchmark
% 1.10/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.10/0.58 % (4133605)------------------------------
% 1.10/0.58 % (4133605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.10/0.58 % (4133605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.58 % (4133605)CaDiCaL version: 2.1.3
% 1.10/0.58 % (4133605)Termination reason: Refutation
% 1.10/0.58 % (4133605)Time elapsed: 0.133 s
% 1.10/0.58 % (4133605)Peak memory usage: 14 MB
% 1.10/0.58 % (4133605)Instructions burned: 206 (million)
% 1.10/0.58 % (4133599)Success in time 0.173 s
% 1.10/0.58 % Vampire exiting
%------------------------------------------------------------------------------