%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU210+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 12:47:45 PM UTC 2026
% Result : Theorem 2.91s 1.26s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 12 unt; 0 def)
% Number of atoms : 214 ( 26 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 263 ( 109 ~; 96 |; 43 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 135 ( 116 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
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(f15,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f21,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f31,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t166_relat_1) ).
fof(f32,conjecture,
! [X0,X1] :
( relation(X1)
=> ~ ( X0 != empty_set
& subset(X0,relation_rng(X1))
& relation_inverse_image(X1,X0) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t174_relat_1) ).
fof(f33,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ~ ( X0 != empty_set
& subset(X0,relation_rng(X1))
& relation_inverse_image(X1,X0) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f35,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f39,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f40,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f43,plain,
? [X0,X1] :
( X0 != empty_set
& subset(X0,relation_rng(X1))
& relation_inverse_image(X1,X0) = empty_set
& relation(X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f44,plain,
? [X0,X1] :
( X0 != empty_set
& subset(X0,relation_rng(X1))
& relation_inverse_image(X1,X0) = empty_set
& relation(X1) ),
inference(flattening,[],[f43]) ).
fof(f50,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f51,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( in(X0,relation_inverse_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f31]) ).
fof(f57,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f58,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f57]) ).
fof(f60,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f62,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(f63,plain,
( empty_set != sK0
& subset(sK0,relation_rng(sK1))
& empty_set = relation_inverse_image(sK1,sK0)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f44]) ).
fof(f67,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f68,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f68]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) ) )
& ( ? [X3] :
( in(X3,relation_rng(X2))
& in(ordered_pair(X0,X3),X2)
& in(X3,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f52]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) ) )
& ( ? [X4] :
( in(X4,relation_rng(X2))
& in(ordered_pair(X0,X4),X2)
& in(X4,X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_inverse_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1) ) )
& ( ( in(sK5(X0,X1,X2),relation_rng(X2))
& in(ordered_pair(X0,sK5(X0,X1,X2)),X2)
& in(sK5(X0,X1,X2),X1) )
| ~ in(X0,relation_inverse_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2))],[f71]) ).
fof(f77,plain,
! [X0] : element(sK10(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X1,sK10(X0))],[f15]) ).
fof(f78,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,[],[f62]) ).
fof(f79,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,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK11(X0,X1)),X0)
| ~ in(sK11(X0,X1),X1) )
& ( in(ordered_pair(sK12(X0,X1),sK11(X0,X1)),X0)
| in(sK11(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK13(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X2,sK11(X0,X1)),skolemize(X4,sK12(X0,X1)),skolemize(X7,sK13(X0,X5))],[f79]) ).
fof(f81,plain,
relation(sK1),
inference(cnf_transformation,[],[f63]) ).
fof(f82,plain,
empty_set = relation_inverse_image(sK1,sK0),
inference(cnf_transformation,[],[f63]) ).
fof(f83,plain,
subset(sK0,relation_rng(sK1)),
inference(cnf_transformation,[],[f63]) ).
fof(f84,plain,
empty_set != sK0,
inference(cnf_transformation,[],[f63]) ).
fof(f97,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f100,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f102,plain,
empty(empty_set),
inference(cnf_transformation,[],[f21]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(X3,relation_rng(X2))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f117,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f119,plain,
! [X0] : element(sK10(X0),X0),
inference(cnf_transformation,[],[f77]) ).
fof(f120,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f123,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK13(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X6,X5),X0)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f127,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X6,X5),X0)
| in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f124]) ).
fof(f128,plain,
! [X0,X5] :
( in(ordered_pair(sK13(X0,X5),X5),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f123]) ).
fof(f132,plain,
! [X0] :
( sK0 != X0
| ~ empty(X0) ),
inference(superposition,[],[f84,f100]) ).
fof(f133,plain,
~ empty(sK0),
inference(equality_resolution,[],[f132]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( in(X0,relation_inverse_image(X2,X1))
| ~ in(ordered_pair(X0,X3),X2)
| ~ in(X3,X1)
| ~ relation(X2) ),
inference(forward_subsumption_resolution,[],[f107,f127]) ).
fof(f246,plain,
! [X0,X1] :
( in(X0,empty_set)
| ~ in(ordered_pair(X0,X1),sK1)
| ~ in(X1,sK0)
| ~ relation(sK1) ),
inference(superposition,[],[f227,f82]) ).
fof(f247,plain,
! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK1)
| in(X0,empty_set)
| ~ in(X1,sK0) ),
inference(forward_subsumption_resolution,[],[f246,f81]) ).
fof(f248,plain,
! [X0] :
( in(sK13(sK1,X0),empty_set)
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ relation(sK1) ),
inference(resolution,[],[f247,f128]) ).
fof(f253,plain,
! [X0] :
( in(sK13(sK1,X0),empty_set)
| ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1)) ),
inference(forward_subsumption_resolution,[],[f248,f81]) ).
fof(f265,plain,
! [X0] :
( ~ in(X0,sK0)
| ~ in(X0,relation_rng(sK1))
| ~ empty(empty_set) ),
inference(resolution,[],[f253,f120]) ).
fof(f268,plain,
! [X0] :
( ~ in(X0,relation_rng(sK1))
| ~ in(X0,sK0) ),
inference(forward_subsumption_resolution,[],[f265,f102]) ).
fof(f269,plain,
! [X0,X1] :
( ~ subset(X1,relation_rng(sK1))
| ~ in(X0,X1)
| ~ in(X0,sK0) ),
inference(resolution,[],[f268,f97]) ).
fof(f299,plain,
! [X0] :
( ~ in(X0,sK0)
| ~ in(X0,sK0) ),
inference(resolution,[],[f269,f83]) ).
fof(f303,plain,
! [X0] : ~ in(X0,sK0),
inference(duplicate_literal_removal,[],[f299]) ).
fof(f305,plain,
! [X0] :
( empty(sK0)
| ~ element(X0,sK0) ),
inference(resolution,[],[f303,f117]) ).
fof(f311,plain,
! [X0] : ~ element(X0,sK0),
inference(forward_subsumption_resolution,[],[f305,f133]) ).
fof(f330,plain,
$false,
inference(resolution,[],[f311,f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU210+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:04:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.91/1.26 % (3648911)Detected formulas, will run a generic FOF schedule.
% 2.91/1.26 % (3648922)dis-21_1_sil=8000:lcm=predicate:random_seed=929739238:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.91/1.26 % (3648921)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2624069278:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.91/1.26 % (3648920)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1999096197:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.91/1.26 % (3648919)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1045344240:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.91/1.26 % (3648916)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=845925565:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.91/1.26 % (3648917)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3406455338:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.91/1.26 % (3648918)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2397340018:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.91/1.26 % (3648922)Instruction limit reached!
% 2.91/1.26 % (3648922)------------------------------
% 2.91/1.26 % (3648922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.26 % (3648922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.26 % (3648922)CaDiCaL version: 2.1.3
% 2.91/1.26 % (3648922)Termination reason: Instruction limit
% 2.91/1.26 % (3648922)Termination phase: Saturation
% 2.91/1.26 % (3648922)Time elapsed: 0.041 s
% 2.91/1.26 % (3648922)Peak memory usage: 89 MB
% 2.91/1.26 % (3648922)Instructions burned: 132 (million)
% 2.91/1.26 % (3648919)Refutation not found, incomplete strategy
% 2.91/1.26 % (3648919)------------------------------
% 2.91/1.26 % (3648919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.91/1.26 % (3648919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.91/1.26 % (3648919)CaDiCaL version: 2.1.3
% 2.91/1.26 % (3648919)Termination reason: Refutation not found, incomplete strategy
% 2.91/1.26 % (3648919)Time elapsed: 0.002 s
% 2.91/1.26 % (3648919)Peak memory usage: 88 MB
% 2.91/1.26 % (3648919)Instructions burned: 1 (million)
% 2.91/1.26 % (3648920)First to succeed.
% 2.91/1.26 % (3648920)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3648911"
% 2.91/1.26 % (3648921)Also succeeded, but the first one will report.
% 2.91/1.26 % (3648930)lrs+10_1_sil=8000:sp=occurrence:random_seed=4263868464:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.91/1.26 % (3648930)Also succeeded, but the first one will report.
% 2.91/1.26 % (3648919)------------------------------
% 2.91/1.26 % (3648919)------------------------------
% 2.91/1.26 % (3648920)Refutation found. Thanks to Tanya!
% 2.91/1.26 % SZS status Theorem for theBenchmark
% 2.91/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.45 % (3648920)------------------------------
% 3.53/1.45 % (3648920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.45 % (3648920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.45 % (3648920)CaDiCaL version: 2.1.3
% 3.53/1.45 % (3648920)Termination reason: Refutation
% 3.53/1.45 % (3648920)Time elapsed: 0.008 s
% 3.53/1.45 % (3648920)Peak memory usage: 88 MB
% 3.53/1.45 % (3648920)Instructions burned: 11 (million)
% 3.53/1.45 % (3648920)------------------------------
% 3.53/1.45 % (3648920)------------------------------
% 3.53/1.45 % (3648911)Success in time 0.415 s
% 3.53/1.45 % Vampire exiting
%------------------------------------------------------------------------------