%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU177+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 : 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 12:52:15 PM UTC 2026
% Result : Theorem 0.18s 0.51s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 15 unt; 2 def)
% Number of atoms : 159 ( 25 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 184 ( 71 ~; 71 |; 26 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 78 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f21,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f23,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(f94,conjecture,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f95,negated_conjecture,
~ ! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_dom(X2))
& in(X1,relation_rng(X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f131,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f160,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f161,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f202,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(ennf_transformation,[],[f95]) ).
fof(f203,plain,
? [X0,X1,X2] :
( ( ~ in(X0,relation_dom(X2))
| ~ in(X1,relation_rng(X2)) )
& in(ordered_pair(X0,X1),X2)
& relation(X2) ),
inference(flattening,[],[f202]) ).
fof(f277,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,[],[f160]) ).
fof(f278,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,[],[f277]) ).
fof(f279,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK15(X0,X1),X3),X0)
| ~ in(sK15(X0,X1),X1) )
& ( in(ordered_pair(sK15(X0,X1),sK16(X0,X1)),X0)
| in(sK15(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK17(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X2,sK15(X0,X1)),skolemize(X4,sK16(X0,X1)),skolemize(X7,sK17(X0,X5))],[f278]) ).
fof(f287,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,[],[f161]) ).
fof(f288,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,[],[f287]) ).
fof(f289,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK22(X0,X1)),X0)
| ~ in(sK22(X0,X1),X1) )
& ( in(ordered_pair(sK23(X0,X1),sK22(X0,X1)),X0)
| in(sK22(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK24(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23,sK24]),skolemize(X2,sK22(X0,X1)),skolemize(X4,sK23(X0,X1)),skolemize(X7,sK24(X0,X5))],[f288]) ).
fof(f311,plain,
( ( ~ in(sK34,relation_dom(sK36))
| ~ in(sK35,relation_rng(sK36)) )
& in(ordered_pair(sK34,sK35),sK36)
& relation(sK36) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34,sK35,sK36]),skolemize(X0,sK34),skolemize(X1,sK35),skolemize(X2,sK36)],[f203]) ).
fof(f387,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f404,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f408,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f485,plain,
relation(sK36),
inference(cnf_transformation,[],[f311]) ).
fof(f486,plain,
in(ordered_pair(sK34,sK35),sK36),
inference(cnf_transformation,[],[f311]) ).
fof(f487,plain,
( ~ in(sK34,relation_dom(sK36))
| ~ in(sK35,relation_rng(sK36)) ),
inference(cnf_transformation,[],[f311]) ).
fof(f537,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f131]) ).
fof(f554,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f408,f537]) ).
fof(f572,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f387,f554]) ).
fof(f576,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f404,f554]) ).
fof(f602,plain,
in(unordered_pair(unordered_pair(sK34,sK35),unordered_pair(sK34,sK34)),sK36),
inference(definition_unfolding,[],[f486,f554]) ).
fof(f652,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f572]) ).
fof(f660,plain,
! [X0,X6,X5] :
( ~ in(unordered_pair(unordered_pair(X6,X5),unordered_pair(X6,X6)),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f576]) ).
fof(f669,definition,
( spl42_1
<=> in(sK35,relation_rng(sK36)) ),
introduced(definition,[new_symbols(definition,[spl42_1])],[avatar_definition]) ).
fof(f671,plain,
( ~ in(sK35,relation_rng(sK36))
| spl42_1 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f673,definition,
( spl42_2
<=> in(sK34,relation_dom(sK36)) ),
introduced(definition,[new_symbols(definition,[spl42_2])],[avatar_definition]) ).
fof(f676,plain,
( ~ spl42_1
| ~ spl42_2 ),
inference(avatar_split_clause,[],[f487,f673,f669]) ).
fof(f2584,plain,
( in(sK34,relation_dom(sK36))
| ~ relation(sK36) ),
inference(resolution,[],[f652,f602]) ).
fof(f2606,plain,
in(sK34,relation_dom(sK36)),
inference(forward_subsumption_resolution,[],[f2584,f485]) ).
fof(f2607,plain,
spl42_2,
inference(avatar_split_clause,[],[f2606,f673]) ).
fof(f2614,plain,
( in(sK35,relation_rng(sK36))
| ~ relation(sK36) ),
inference(resolution,[],[f660,f602]) ).
fof(f2636,plain,
( ~ relation(sK36)
| spl42_1 ),
inference(forward_subsumption_resolution,[],[f2614,f671]) ).
fof(f2637,plain,
( $false
| spl42_1 ),
inference(forward_subsumption_resolution,[],[f2636,f485]) ).
fof(f2638,plain,
spl42_1,
inference(avatar_contradiction_clause,[],[f2637]) ).
cnf(s1,plain,
( ~ spl42_1
| ~ spl42_2 ),
inference(sat_conversion,[],[f676]) ).
cnf(s6,plain,
spl42_2,
inference(sat_conversion,[],[f2607]) ).
cnf(s7,plain,
spl42_1,
inference(sat_conversion,[],[f2638]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s6,s7]) ).
fof(f2639,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU177+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n009.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:54:15 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 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
% 0.18/0.51 % (2645593)Will run a generic schedule for satisfiability detection.
% 0.18/0.51 % (2645602)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2931108584:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.51 % (2645599)% WARNING: option uhcvi not known.
% 0.18/0.51 % (2645598)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3179497081_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.51 % (2645599)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1426356075:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.51 % (2645603)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=524875973:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.51 % (2645600)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4246835766:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.51 % (2645601)dis+10_1_sil=32000:sp=arity:random_seed=1975886765:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.51 % (2645604)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4052381015:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.51 % TRYING [1]
% 0.18/0.51 % TRYING [2]
% 0.18/0.51 % TRYING [3]
% 0.18/0.51 % (2645602)Instruction limit reached!
% 0.18/0.51 % (2645602)------------------------------
% 0.18/0.51 % (2645602)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.51 % (2645602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.51 % (2645602)CaDiCaL version: 2.1.3
% 0.18/0.51 % (2645602)Termination reason: Instruction limit
% 0.18/0.51 % (2645602)Termination phase: Saturation
% 0.18/0.51 % (2645602)Time elapsed: 0.044 s
% 0.18/0.51 % (2645602)Peak memory usage: 13 MB
% 0.18/0.51 % (2645602)Instructions burned: 116 (million)
% 0.18/0.51 % (2645612)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=755729634:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.51 % (2645601) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2645593-2645601"...
% 0.18/0.51 % TRYING [1]
% 0.18/0.51 % TRYING [2]
% 0.18/0.51 % (2645601)...printing done.
% 0.18/0.51 % (2645601)Refutation found. Thanks to Tanya!
% 0.18/0.51 % SZS status Theorem for theBenchmark
% 0.18/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52 % (2645601)------------------------------
% 0.18/0.52 % (2645601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.52 % (2645601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.52 % (2645601)CaDiCaL version: 2.1.3
% 0.18/0.52 % (2645601)Termination reason: Refutation
% 0.18/0.52 % (2645601)Time elapsed: 0.057 s
% 0.18/0.52 % (2645601)Peak memory usage: 13 MB
% 0.18/0.52 % (2645601)Instructions burned: 83 (million)
% 0.18/0.52 % (2645593)Success in time 0.094 s
% 0.18/0.52 % Vampire exiting
%------------------------------------------------------------------------------