%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:51:49 PM UTC 2026
% Result : Theorem 0.17s 0.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 8 unt; 0 def)
% Number of atoms : 168 ( 52 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 223 ( 93 ~; 86 |; 32 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 72 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0) )
=> ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X1,X3) = apply(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).
fof(f37,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,set_intersection2(relation_dom(X2),X0))
=> apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f51,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f56,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_dom_restriction(X0,X1))
& function(relation_dom_restriction(X0,X1)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f56]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ( X1 = relation_dom_restriction(X2,X0)
<=> ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f38]) ).
fof(f73,plain,
? [X0,X1,X2] :
( apply(relation_dom_restriction(X2,X0),X1) != apply(X2,X1)
& in(X1,set_intersection2(relation_dom(X2),X0))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f72]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f70]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X3] :
( apply(X1,X3) = apply(X2,X3)
| ~ in(X3,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ? [X3] :
( apply(X1,X3) != apply(X2,X3)
& in(X3,relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f88]) ).
fof(f90,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X1 = relation_dom_restriction(X2,X0)
| relation_dom(X1) != set_intersection2(relation_dom(X2),X0)
| ( apply(X1,sK11(X1,X2)) != apply(X2,sK11(X1,X2))
& in(sK11(X1,X2),relation_dom(X1)) ) )
& ( ( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
& ! [X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1)) ) )
| relation_dom_restriction(X2,X0) != X1 ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X1,X2))],[f89]) ).
fof(f91,plain,
( apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13)
& in(sK13,set_intersection2(relation_dom(sK14),sK12))
& relation(sK14)
& function(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f73]) ).
fof(f98,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f108,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f142,plain,
! [X2,X0,X1,X4] :
( apply(X1,X4) = apply(X2,X4)
| ~ in(X4,relation_dom(X1))
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f143,plain,
! [X2,X0,X1] :
( relation_dom(X1) = set_intersection2(relation_dom(X2),X0)
| relation_dom_restriction(X2,X0) != X1
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f147,plain,
function(sK14),
inference(cnf_transformation,[],[f91]) ).
fof(f148,plain,
relation(sK14),
inference(cnf_transformation,[],[f91]) ).
fof(f149,plain,
in(sK13,set_intersection2(relation_dom(sK14),sK12)),
inference(cnf_transformation,[],[f91]) ).
fof(f150,plain,
apply(relation_dom_restriction(sK14,sK12),sK13) != apply(sK14,sK13),
inference(cnf_transformation,[],[f91]) ).
fof(f153,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f143]) ).
fof(f154,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(relation_dom_restriction(X2,X0))
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(equality_resolution,[],[f142]) ).
fof(f247,plain,
! [X2,X0] :
( set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f153,f98]) ).
fof(f248,plain,
! [X2,X0] :
( ~ relation(X2)
| set_intersection2(relation_dom(X2),X0) = relation_dom(relation_dom_restriction(X2,X0))
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f247,f108]) ).
fof(f261,plain,
! [X0] :
( set_intersection2(relation_dom(sK14),X0) = relation_dom(relation_dom_restriction(sK14,X0))
| ~ function(sK14) ),
inference(resolution,[],[f248,f148]) ).
fof(f262,plain,
! [X0] : set_intersection2(relation_dom(sK14),X0) = relation_dom(relation_dom_restriction(sK14,X0)),
inference(forward_subsumption_resolution,[],[f261,f147]) ).
fof(f297,plain,
in(sK13,relation_dom(relation_dom_restriction(sK14,sK12))),
inference(superposition,[],[f149,f262]) ).
fof(f319,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| ~ relation(X2)
| ~ function(X2)
| ~ function(relation_dom_restriction(X2,X0)) ),
inference(forward_subsumption_resolution,[],[f154,f98]) ).
fof(f320,plain,
! [X2,X0,X4] :
( ~ in(X4,relation_dom(relation_dom_restriction(X2,X0)))
| apply(X2,X4) = apply(relation_dom_restriction(X2,X0),X4)
| ~ relation(X2)
| ~ function(X2) ),
inference(forward_subsumption_resolution,[],[f319,f108]) ).
fof(f404,plain,
( apply(relation_dom_restriction(sK14,sK12),sK13) = apply(sK14,sK13)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(resolution,[],[f297,f320]) ).
fof(f408,plain,
( ~ relation(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f404,f150]) ).
fof(f409,plain,
~ function(sK14),
inference(forward_subsumption_resolution,[],[f408,f148]) ).
fof(f410,plain,
$false,
inference(forward_subsumption_resolution,[],[f409,f147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU037+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 % Computer : n014.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Mon Sep 28 03:24:30 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.46 Running first-order model finding
% 0.11/0.46 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
% 0.17/0.51 % (1407298)Will run a generic schedule for satisfiability detection.
% 0.17/0.51 % (1407308)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1428323283:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.51 % (1407304)% WARNING: option uhcvi not known.
% 0.17/0.51 % (1407303)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2406831138_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.51 % (1407304)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=926726627:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.51 % (1407305)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1153017602:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.51 % (1407306)dis+10_1_sil=32000:sp=arity:random_seed=373679824:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.51 % (1407309)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1415041821:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.51 % (1407307)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2274390557:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.51 % TRYING [1]
% 0.17/0.51 % TRYING [2]
% 0.17/0.51 % TRYING [3]
% 0.17/0.51 % (1407306) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1407298-1407306"...
% 0.17/0.51 % TRYING [4]
% 0.17/0.51 % (1407304) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1407298-1407304"...
% 0.17/0.51 % (1407306)...printing done.
% 0.17/0.51 % (1407306)Refutation found. Thanks to Tanya!
% 0.17/0.51 % SZS status Theorem for theBenchmark
% 0.17/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.51 % (1407306)------------------------------
% 0.17/0.51 % (1407306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.51 % (1407306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.51 % (1407306)CaDiCaL version: 2.1.3
% 0.17/0.51 % (1407306)Termination reason: Refutation
% 0.17/0.51 % (1407306)Time elapsed: 0.008 s
% 0.17/0.51 % (1407306)Peak memory usage: 11 MB
% 0.17/0.51 % (1407306)Instructions burned: 11 (million)
% 0.17/0.51 % (1407298)Success in time 0.042 s
% 0.17/0.51 % Vampire exiting
%------------------------------------------------------------------------------