%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 0.09s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 20 unt; 2 def)
% Number of atoms : 207 ( 44 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 230 ( 96 ~; 96 |; 23 &)
% ( 10 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 2 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 108 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f3,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] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f14,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f22,axiom,
? [X0] :
( empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f27,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f29,conjecture,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f30,negated_conjecture,
~ ( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f32,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f35,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f44,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f43]) ).
fof(f46,plain,
( empty_set != relation_dom(empty_set)
| empty_set != relation_rng(empty_set) ),
inference(ennf_transformation,[],[f30]) ).
fof(f47,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f36]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f37]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X2,sK3(X0,X1)),skolemize(X4,sK4(X0,X1)),skolemize(X7,sK5(X0,X5))],[f54]) ).
fof(f56,plain,
! [X0] : element(sK6(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X0))],[f14]) ).
fof(f57,plain,
( empty(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X0,sK7)],[f22]) ).
fof(f64,plain,
! [X0] :
( ~ empty(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f66,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f70,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f74,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f75,plain,
! [X0] : element(sK6(X0),X0),
inference(cnf_transformation,[],[f56]) ).
fof(f76,plain,
empty(empty_set),
inference(cnf_transformation,[],[f15]) ).
fof(f85,plain,
empty(sK7),
inference(cnf_transformation,[],[f57]) ).
fof(f91,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f94,plain,
( empty_set != relation_dom(empty_set)
| empty_set != relation_rng(empty_set) ),
inference(cnf_transformation,[],[f46]) ).
fof(f95,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f96,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f101,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f66,f74]) ).
fof(f105,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f70,f74]) ).
fof(f108,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK2(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f101]) ).
fof(f110,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK5(X0,X5),X5),singleton(sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f105]) ).
fof(f112,definition,
( spl12_1
<=> empty_set = relation_rng(empty_set) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f114,plain,
( empty_set != relation_rng(empty_set)
| spl12_1 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f116,definition,
( spl12_2
<=> empty_set = relation_dom(empty_set) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f119,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f94,f116,f112]) ).
fof(f124,plain,
empty_set = sK7,
inference(resolution,[],[f95,f85]) ).
fof(f137,plain,
! [X0] :
( in(sK6(X0),X0)
| empty(X0) ),
inference(resolution,[],[f91,f75]) ).
fof(f168,plain,
! [X0,X5] :
( in(unordered_pair(singleton(X5),unordered_pair(X5,sK2(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f108,f65]) ).
fof(f173,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ empty(X1) ),
inference(resolution,[],[f168,f96]) ).
fof(f178,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(X1))
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[],[f173,f64]) ).
fof(f183,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(resolution,[],[f178,f137]) ).
fof(f185,plain,
! [X0,X5] :
( in(unordered_pair(singleton(sK5(X0,X5)),unordered_pair(sK5(X0,X5),X5)),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f110,f65]) ).
fof(f186,plain,
! [X0,X5] :
( in(unordered_pair(singleton(sK5(X0,X5)),unordered_pair(X5,sK5(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(forward_demodulation,[],[f185,f65]) ).
fof(f189,plain,
! [X0] :
( ~ empty(X0)
| relation_dom(X0) = empty_set ),
inference(resolution,[],[f183,f95]) ).
fof(f193,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ empty(X1) ),
inference(resolution,[],[f186,f96]) ).
fof(f195,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ empty(X1) ),
inference(forward_subsumption_resolution,[],[f193,f64]) ).
fof(f201,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(resolution,[],[f195,f137]) ).
fof(f208,plain,
! [X0] :
( ~ empty(X0)
| relation_rng(X0) = empty_set ),
inference(resolution,[],[f201,f95]) ).
fof(f217,plain,
empty_set = relation_dom(empty_set),
inference(resolution,[],[f189,f76]) ).
fof(f222,plain,
spl12_2,
inference(avatar_split_clause,[],[f217,f116]) ).
fof(f230,plain,
empty_set = relation_rng(sK7),
inference(resolution,[],[f208,f85]) ).
fof(f233,plain,
empty_set = relation_rng(empty_set),
inference(forward_demodulation,[],[f230,f124]) ).
fof(f238,plain,
( $false
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f233,f114]) ).
fof(f239,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f238]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f119]) ).
cnf(s2,plain,
spl12_2,
inference(sat_conversion,[],[f222]) ).
cnf(s7,plain,
spl12_1,
inference(sat_conversion,[],[f239]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s2,s7]) ).
fof(f240,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU187+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:57:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.46 % (2647319)Will run a generic schedule for satisfiability detection.
% 0.09/0.46 % (2647326)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1845048548:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.46 % (2647325)% WARNING: option uhcvi not known.
% 0.09/0.46 % (2647324)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=138334944_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.46 % (2647328)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1318847336:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.46 % (2647325)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=986380326:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.46 % (2647327)dis+10_1_sil=32000:sp=arity:random_seed=922389776:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.46 % (2647330)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=688422169:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.46 % (2647329)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2254672207:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.46 % TRYING [1]
% 0.09/0.46 % TRYING [2]
% 0.09/0.46 % TRYING [3]
% 0.09/0.46 % (2647328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2647319-2647328"...
% 0.09/0.46 % (2647327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2647319-2647327"...
% 0.09/0.46 % (2647325) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2647319-2647325"...
% 0.09/0.46 % (2647329) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2647319-2647329"...
% 0.09/0.46 % (2647328)...printing done.
% 0.09/0.46 % (2647327)...printing done.
% 0.09/0.46 % (2647329)...printing done.
% 0.09/0.46 % (2647325)...printing done.
% 0.09/0.46 % (2647327)Refutation found. Thanks to Tanya!
% 0.09/0.46 % SZS status Theorem for theBenchmark
% 0.09/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (2647327)------------------------------
% 0.15/0.46 % (2647327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (2647327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (2647327)CaDiCaL version: 2.1.3
% 0.15/0.46 % (2647327)Termination reason: Refutation
% 0.15/0.46 % (2647327)Time elapsed: 0.007 s
% 0.15/0.46 % (2647327)Peak memory usage: 12 MB
% 0.15/0.46 % (2647327)Instructions burned: 8 (million)
% 0.15/0.46 % (2647319)Success in time 0.046 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------