%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU047+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:47:08 PM UTC 2026
% Result : Theorem 2.69s 1.35s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 9 unt; 3 def)
% Number of atoms : 108 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 106 ( 43 ~; 38 |; 13 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 38 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f31,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X0,X1)
=> ( relation_rng_restriction(X1,relation_rng_restriction(X0,X2)) = relation_rng_restriction(X0,X2)
& relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) = relation_rng_restriction(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t97_funct_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( subset(X0,X1)
=> ( relation_rng_restriction(X1,relation_rng_restriction(X0,X2)) = relation_rng_restriction(X0,X2)
& relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) = relation_rng_restriction(X0,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> relation_rng_restriction(X1,relation_rng_restriction(X0,X2)) = relation_rng_restriction(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t129_relat_1) ).
fof(f34,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( subset(X0,X1)
=> relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) = relation_rng_restriction(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t130_relat_1) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f58,plain,
? [X0,X1,X2] :
( ( relation_rng_restriction(X0,X2) != relation_rng_restriction(X1,relation_rng_restriction(X0,X2))
| relation_rng_restriction(X0,X2) != relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) )
& subset(X0,X1)
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f59,plain,
? [X0,X1,X2] :
( ( relation_rng_restriction(X0,X2) != relation_rng_restriction(X1,relation_rng_restriction(X0,X2))
| relation_rng_restriction(X0,X2) != relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) )
& subset(X0,X1)
& relation(X2)
& function(X2) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( relation_rng_restriction(X1,relation_rng_restriction(X0,X2)) = relation_rng_restriction(X0,X2)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f33]) ).
fof(f61,plain,
! [X0,X1,X2] :
( relation_rng_restriction(X1,relation_rng_restriction(X0,X2)) = relation_rng_restriction(X0,X2)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) = relation_rng_restriction(X0,X2)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f63,plain,
! [X0,X1,X2] :
( relation_rng_restriction(X0,relation_rng_restriction(X1,X2)) = relation_rng_restriction(X0,X2)
| ~ subset(X0,X1)
| ~ relation(X2) ),
inference(flattening,[],[f62]) ).
fof(f76,plain,
( ( relation_rng_restriction(sK11,sK13) != relation_rng_restriction(sK12,relation_rng_restriction(sK11,sK13))
| relation_rng_restriction(sK11,sK13) != relation_rng_restriction(sK11,relation_rng_restriction(sK12,sK13)) )
& subset(sK11,sK12)
& relation(sK13)
& function(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f59]) ).
fof(f97,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
relation(sK13),
inference(cnf_transformation,[],[f76]) ).
fof(f122,plain,
subset(sK11,sK12),
inference(cnf_transformation,[],[f76]) ).
fof(f123,plain,
( relation_rng_restriction(sK11,sK13) != relation_rng_restriction(sK12,relation_rng_restriction(sK11,sK13))
| relation_rng_restriction(sK11,sK13) != relation_rng_restriction(sK11,relation_rng_restriction(sK12,sK13)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_rng_restriction(X0,X2) = relation_rng_restriction(X1,relation_rng_restriction(X0,X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f61]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| relation_rng_restriction(X0,X2) = relation_rng_restriction(X0,relation_rng_restriction(X1,X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f127,definition,
( spl14_1
<=> relation_rng_restriction(sK11,sK13) = relation_rng_restriction(sK11,relation_rng_restriction(sK12,sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f128,plain,
( relation_rng_restriction(sK11,sK13) = relation_rng_restriction(sK11,relation_rng_restriction(sK12,sK13))
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f129,plain,
( relation_rng_restriction(sK11,sK13) != relation_rng_restriction(sK11,relation_rng_restriction(sK12,sK13))
| spl14_1 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f131,definition,
( spl14_2
<=> relation_rng_restriction(sK11,sK13) = relation_rng_restriction(sK12,relation_rng_restriction(sK11,sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f134,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f123,f131,f127]) ).
fof(f156,plain,
! [X0] :
( relation_rng_restriction(sK11,X0) = relation_rng_restriction(sK12,relation_rng_restriction(sK11,X0))
| ~ relation(X0) ),
inference(resolution,[],[f124,f122]) ).
fof(f160,plain,
! [X0] :
( relation_rng_restriction(sK11,X0) = relation_rng_restriction(sK11,relation_rng_restriction(sK12,X0))
| ~ relation(X0) ),
inference(resolution,[],[f125,f122]) ).
fof(f162,plain,
( relation_rng_restriction(sK11,sK13) != relation_rng_restriction(sK11,sK13)
| ~ relation(sK13)
| spl14_1 ),
inference(superposition,[],[f129,f160]) ).
fof(f166,plain,
( ~ relation(sK13)
| spl14_1 ),
inference(trivial_inequality_removal,[],[f162]) ).
fof(f168,plain,
( $false
| spl14_1 ),
inference(forward_subsumption_resolution,[],[f166,f121]) ).
fof(f169,plain,
spl14_1,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f170,plain,
( relation_rng_restriction(sK11,sK13) = relation_rng_restriction(sK12,relation_rng_restriction(sK11,sK13))
| ~ relation(relation_rng_restriction(sK12,sK13))
| ~ spl14_1 ),
inference(superposition,[],[f156,f128]) ).
fof(f174,definition,
( spl14_3
<=> relation(relation_rng_restriction(sK12,sK13)) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f176,plain,
( ~ relation(relation_rng_restriction(sK12,sK13))
| spl14_3 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f191,plain,
( ~ spl14_3
| spl14_2
| ~ spl14_1 ),
inference(avatar_split_clause,[],[f170,f127,f131,f174]) ).
fof(f192,plain,
( ~ relation(sK13)
| spl14_3 ),
inference(resolution,[],[f176,f97]) ).
fof(f194,plain,
( $false
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f192,f121]) ).
fof(f195,plain,
spl14_3,
inference(avatar_contradiction_clause,[],[f194]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2 ),
inference(sat_conversion,[],[f134]) ).
cnf(s2,plain,
spl14_1,
inference(sat_conversion,[],[f169]) ).
cnf(s5,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_3 ),
inference(sat_conversion,[],[f191]) ).
cnf(s6,plain,
spl14_3,
inference(sat_conversion,[],[f195]) ).
cnf(s7,plain,
( ~ spl14_1
| spl14_2 ),
inference(rat,[],[s5,s6]) ).
cnf(s10,plain,
spl14_2,
inference(rat,[],[s7,s2]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s10,s2]) ).
fof(f196,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU047+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/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
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:29:20 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.69/1.35 % (1154488)Detected formulas, will run a generic FOF schedule.
% 2.69/1.35 % (1154498)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2067353195:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.35 % (1154498)First to succeed.
% 2.69/1.35 % (1154498)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1154488"
% 2.69/1.35 % (1154496)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3317904779:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.35 % (1154494)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=1021070980:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.35 % (1154495)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=4009180319:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.35 % (1154499)dis-21_1_sil=8000:lcm=predicate:random_seed=1839788243: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)
% 2.69/1.35 % (1154493)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=3050453335:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.35 % (1154497)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2931600500:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.35 % (1154496)Also succeeded, but the first one will report.
% 2.69/1.35 % (1154497)Also succeeded, but the first one will report.
% 2.69/1.35 % (1154499)Also succeeded, but the first one will report.
% 2.69/1.35 % (1154498)Refutation found. Thanks to Tanya!
% 2.69/1.35 % SZS status Theorem for theBenchmark
% 2.69/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.35 % (1154498)------------------------------
% 2.69/1.35 % (1154498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.35 % (1154498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.35 % (1154498)CaDiCaL version: 2.1.3
% 2.69/1.35 % (1154498)Termination reason: Refutation
% 2.69/1.35 % (1154498)Time elapsed: 0.003 s
% 2.69/1.35 % (1154498)Peak memory usage: 90 MB
% 2.69/1.35 % (1154498)Instructions burned: 5 (million)
% 2.69/1.35 % (1154498)------------------------------
% 2.69/1.35 % (1154498)------------------------------
% 2.69/1.35 % (1154488)Success in time 0.298 s
% 2.69/1.35 % Vampire exiting
%------------------------------------------------------------------------------