%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 12:47:14 PM UTC 2026
% Result : Theorem 2.45s 1.09s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 85 ( 4 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 103 ( 43 ~; 34 |; 19 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 25 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& finite(X1) )
=> finite(relation_image(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_finset_1) ).
fof(f50,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( subset(X0,relation_rng(X1))
=> relation_image(X1,relation_inverse_image(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t147_funct_1) ).
fof(f53,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( subset(X0,relation_rng(X1))
& finite(relation_inverse_image(X1,X0)) )
=> finite(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finset_1) ).
fof(f54,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( subset(X0,relation_rng(X1))
& finite(relation_inverse_image(X1,X0)) )
=> finite(X0) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f100,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f101,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(flattening,[],[f100]) ).
fof(f107,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f108,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f107]) ).
fof(f112,plain,
? [X0,X1] :
( ~ finite(X0)
& subset(X0,relation_rng(X1))
& finite(relation_inverse_image(X1,X0))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f113,plain,
? [X0,X1] :
( ~ finite(X0)
& subset(X0,relation_rng(X1))
& finite(relation_inverse_image(X1,X0))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f112]) ).
fof(f148,plain,
( ~ finite(sK26)
& subset(sK26,relation_rng(sK27))
& finite(relation_inverse_image(sK27,sK26))
& relation(sK27)
& function(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26,sK27]),skolemize(X0,sK26),skolemize(X1,sK27)],[f113]) ).
fof(f175,plain,
! [X0,X1] :
( finite(relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ finite(X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f262,plain,
! [X0,X1] :
( relation_image(X1,relation_inverse_image(X1,X0)) = X0
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f265,plain,
function(sK27),
inference(cnf_transformation,[],[f148]) ).
fof(f266,plain,
relation(sK27),
inference(cnf_transformation,[],[f148]) ).
fof(f267,plain,
finite(relation_inverse_image(sK27,sK26)),
inference(cnf_transformation,[],[f148]) ).
fof(f268,plain,
subset(sK26,relation_rng(sK27)),
inference(cnf_transformation,[],[f148]) ).
fof(f269,plain,
~ finite(sK26),
inference(cnf_transformation,[],[f148]) ).
fof(f287,plain,
! [X0,X1] :
( finite(X0)
| ~ relation(X1)
| ~ function(X1)
| ~ finite(relation_inverse_image(X1,X0))
| ~ subset(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(superposition,[],[f175,f262]) ).
fof(f288,plain,
! [X0,X1] :
( finite(X0)
| ~ relation(X1)
| ~ function(X1)
| ~ finite(relation_inverse_image(X1,X0))
| ~ subset(X0,relation_rng(X1)) ),
inference(duplicate_literal_removal,[],[f287]) ).
fof(f357,plain,
! [X0] :
( ~ subset(sK26,relation_rng(X0))
| ~ function(X0)
| ~ finite(relation_inverse_image(X0,sK26))
| ~ relation(X0) ),
inference(resolution,[],[f288,f269]) ).
fof(f359,plain,
( ~ function(sK27)
| ~ finite(relation_inverse_image(sK27,sK26))
| ~ relation(sK27) ),
inference(resolution,[],[f357,f268]) ).
fof(f361,plain,
( ~ finite(relation_inverse_image(sK27,sK26))
| ~ relation(sK27) ),
inference(forward_subsumption_resolution,[],[f359,f265]) ).
fof(f362,plain,
~ relation(sK27),
inference(forward_subsumption_resolution,[],[f361,f267]) ).
fof(f363,plain,
$false,
inference(forward_subsumption_resolution,[],[f362,f266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU096+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.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 03:34:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.45/1.09 % (1158717)Detected formulas, will run a generic FOF schedule.
% 2.45/1.09 % (1158727)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2899113969:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.45/1.09 % (1158727)First to succeed.
% 2.45/1.09 % (1158727)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1158717"
% 2.45/1.09 % (1158722)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=2249987277:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.45/1.09 % (1158726)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3584953296:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.45/1.09 % (1158725)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=773409860:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.45/1.09 % (1158728)dis-21_1_sil=8000:lcm=predicate:random_seed=3269523496: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)
% 2.45/1.09 % (1158724)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=3330095944:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.45/1.09 % (1158723)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=1156461817:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.45/1.09 % (1158725)Refutation not found, incomplete strategy
% 2.45/1.09 % (1158725)------------------------------
% 2.45/1.09 % (1158725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.09 % (1158725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.09 % (1158725)CaDiCaL version: 2.1.3
% 2.45/1.09 % (1158725)Termination reason: Refutation not found, incomplete strategy
% 2.45/1.09 % (1158725)Time elapsed: 0.002 s
% 2.45/1.09 % (1158725)Peak memory usage: 88 MB
% 2.45/1.09 % (1158725)Instructions burned: 1 (million)
% 2.45/1.09 % (1158726)Also succeeded, but the first one will report.
% 2.45/1.09 % (1158728)Instruction limit reached!
% 2.45/1.09 % (1158728)------------------------------
% 2.45/1.09 % (1158728)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.09 % (1158728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.09 % (1158728)CaDiCaL version: 2.1.3
% 2.45/1.09 % (1158728)Termination reason: Instruction limit
% 2.45/1.09 % (1158728)Termination phase: Saturation
% 2.45/1.09 % (1158728)Time elapsed: 0.078 s
% 2.45/1.09 % (1158728)Peak memory usage: 91 MB
% 2.45/1.09 % (1158728)Instructions burned: 130 (million)
% 2.45/1.09 % (1158727)Refutation found. Thanks to Tanya!
% 2.45/1.09 % SZS status Theorem for theBenchmark
% 2.45/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 2.45/1.09 % (1158727)------------------------------
% 2.45/1.09 % (1158727)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.45/1.09 % (1158727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.45/1.09 % (1158727)CaDiCaL version: 2.1.3
% 2.45/1.09 % (1158727)Termination reason: Refutation
% 2.45/1.09 % (1158727)Time elapsed: 0.004 s
% 2.45/1.09 % (1158727)Peak memory usage: 89 MB
% 2.45/1.09 % (1158727)Instructions burned: 8 (million)
% 2.45/1.09 % (1158727)------------------------------
% 2.45/1.09 % (1158727)------------------------------
% 2.45/1.09 % (1158717)Success in time 0.293 s
% 2.45/1.09 % Vampire exiting
%------------------------------------------------------------------------------