%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU193+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 : 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 12:52:19 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 11 unt; 2 def)
% Number of atoms : 129 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 62 ~; 58 |; 3 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 75 ( 0 sgn 73 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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,X2] :
( relation(X2)
=> ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_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(f12,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f35,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f36,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f41,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_dom_restriction(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(X3,X1)
& in(ordered_pair(X3,X4),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f43,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f53,plain,
? [X0,X1] :
( ~ subset(relation_dom_restriction(X1,X0),X1)
& relation(X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f57,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f61,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X2)
| in(ordered_pair(X3,X4),X0)
| ~ in(ordered_pair(X3,X4),X2)
| relation_dom_restriction(X0,X1) != X2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f65,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f67,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f68,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f96,plain,
relation(sK12),
inference(cnf_transformation,[],[f53]) ).
fof(f97,plain,
~ subset(relation_dom_restriction(sK12,sK11),sK12),
inference(cnf_transformation,[],[f53]) ).
fof(f101,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X2)
| relation_dom_restriction(X0,X1) != X2 ),
inference(definition_unfolding,[],[f61,f67,f67]) ).
fof(f105,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f66,f67]) ).
fof(f106,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK2(X0,X1),sK3(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f65,f67]) ).
fof(f111,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(relation_dom_restriction(X0,X1))
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_dom_restriction(X0,X1)) ),
inference(equality_resolution,[],[f101]) ).
fof(f112,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_dom_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f111,f68]) ).
fof(f115,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),X0)
| ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_dom_restriction(X0,X1)) ),
inference(forward_demodulation,[],[f112,f57]) ).
fof(f118,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),X0)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_dom_restriction(X0,X1)) ),
inference(forward_demodulation,[],[f115,f57]) ).
fof(f218,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),relation_dom_restriction(sK12,X2))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK12) ),
inference(resolution,[],[f118,f96]) ).
fof(f229,plain,
( ~ relation(sK12)
| ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12)),singleton(sK2(relation_dom_restriction(sK12,sK11),sK12))),sK12)
| ~ relation(relation_dom_restriction(sK12,sK11)) ),
inference(resolution,[],[f105,f97]) ).
fof(f232,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12)),singleton(sK2(relation_dom_restriction(sK12,sK11),sK12))),sK12)
| ~ relation(relation_dom_restriction(sK12,sK11)) ),
inference(forward_subsumption_resolution,[],[f229,f96]) ).
fof(f233,plain,
( ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK12,sK11),sK12)),unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12))),sK12)
| ~ relation(relation_dom_restriction(sK12,sK11)) ),
inference(forward_demodulation,[],[f232,f57]) ).
fof(f235,definition,
( spl13_1
<=> relation(relation_dom_restriction(sK12,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f236,plain,
( relation(relation_dom_restriction(sK12,sK11))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f237,plain,
( ~ relation(relation_dom_restriction(sK12,sK11))
| spl13_1 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f239,definition,
( spl13_2
<=> in(unordered_pair(singleton(sK2(relation_dom_restriction(sK12,sK11),sK12)),unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12))),sK12) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f241,plain,
( ~ in(unordered_pair(singleton(sK2(relation_dom_restriction(sK12,sK11),sK12)),unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12))),sK12)
| spl13_2 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f242,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f233,f239,f235]) ).
fof(f243,plain,
( ~ relation(sK12)
| spl13_1 ),
inference(resolution,[],[f237,f68]) ).
fof(f244,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f243,f96]) ).
fof(f245,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f246,plain,
( ~ relation(sK12)
| in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12)),singleton(sK2(relation_dom_restriction(sK12,sK11),sK12))),relation_dom_restriction(sK12,sK11))
| ~ relation(relation_dom_restriction(sK12,sK11)) ),
inference(resolution,[],[f106,f97]) ).
fof(f249,plain,
( in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12)),singleton(sK2(relation_dom_restriction(sK12,sK11),sK12))),relation_dom_restriction(sK12,sK11))
| ~ relation(relation_dom_restriction(sK12,sK11)) ),
inference(forward_subsumption_resolution,[],[f246,f96]) ).
fof(f250,plain,
( in(unordered_pair(unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12)),singleton(sK2(relation_dom_restriction(sK12,sK11),sK12))),relation_dom_restriction(sK12,sK11))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f249,f236]) ).
fof(f251,plain,
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK12,sK11),sK12)),unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12))),relation_dom_restriction(sK12,sK11))
| ~ spl13_1 ),
inference(forward_demodulation,[],[f250,f57]) ).
fof(f468,plain,
( in(unordered_pair(singleton(sK2(relation_dom_restriction(sK12,sK11),sK12)),unordered_pair(sK2(relation_dom_restriction(sK12,sK11),sK12),sK3(relation_dom_restriction(sK12,sK11),sK12))),sK12)
| ~ spl13_1 ),
inference(resolution,[],[f251,f218]) ).
fof(f473,plain,
( $false
| ~ spl13_1
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f468,f241]) ).
fof(f474,plain,
( ~ spl13_1
| spl13_2 ),
inference(avatar_contradiction_clause,[],[f473]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f242]) ).
cnf(s2,plain,
spl13_1,
inference(sat_conversion,[],[f245]) ).
cnf(s3,plain,
( ~ spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f474]) ).
cnf(s4,plain,
spl13_2,
inference(rat,[],[s3,s2]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s2]) ).
fof(f475,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU193+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:58:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.39 Running first-order model finding
% 0.10/0.39 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
% 0.10/0.44 % (3562813)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (3562822)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=332667094:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.44 % (3562822) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3562813-3562822"...
% 0.10/0.44 % (3562819)% WARNING: option uhcvi not known.
% 0.10/0.44 % (3562818)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1169482082_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.44 % (3562822)...printing done.
% 0.10/0.44 % (3562824)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=125377063:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.44 % (3562820)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1547486218:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (3562821)dis+10_1_sil=32000:sp=arity:random_seed=298103815:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.44 % (3562823)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1074976953:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (3562822)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (3562822)------------------------------
% 0.10/0.44 % (3562822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (3562822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (3562822)CaDiCaL version: 2.1.3
% 0.10/0.44 % (3562822)Termination reason: Refutation
% 0.10/0.44 % (3562822)Time elapsed: 0.006 s
% 0.10/0.44 % (3562822)Peak memory usage: 12 MB
% 0.10/0.44 % (3562822)Instructions burned: 18 (million)
% 0.10/0.44 % (3562813)Success in time 0.039 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------