%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU444+3 : TPTP v9.3.1. Released v3.4.0.
% 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 12:49:07 PM UTC 2026
% Result : Theorem 8.43s 3.44s
% Output : Refutation 8.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 8 unt; 2 def)
% Number of atoms : 53 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 19 ~; 15 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 21 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19122,axiom,
! [X0,X1,X2] :
( m2_relset_1(X2,X1,X0)
=> ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k2_funct_5(X2) = k10_relset_1(X1,X0,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_relset_2) ).
fof(f19127,conjecture,
! [X0,X1,X2] :
( m2_relset_1(X2,X1,X0)
=> ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k10_relset_1(X1,X0,X2,X1)) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k2_funct_5(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relset_2) ).
fof(f19128,negated_conjecture,
~ ! [X0,X1,X2] :
( m2_relset_1(X2,X1,X0)
=> ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k10_relset_1(X1,X0,X2,X1)) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k2_funct_5(X2)) ) ),
inference(negated_conjecture,[status(cth)],[f19127]) ).
fof(f19145,plain,
? [X0,X1,X2] :
( ( k1_funct_5(X2) != k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
| k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k10_relset_1(X1,X0,X2,X1)) != k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),k2_funct_5(X2)) )
& m2_relset_1(X2,X1,X0) ),
inference(ennf_transformation,[],[f19128]) ).
fof(f19149,plain,
! [X0,X1,X2] :
( ( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
& k2_funct_5(X2) = k10_relset_1(X1,X0,X2,X1) )
| ~ m2_relset_1(X2,X1,X0) ),
inference(ennf_transformation,[],[f19122]) ).
fof(f19177,plain,
( ( k1_funct_5(sK2) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0)
| k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1)) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)) )
& m2_relset_1(sK2,sK1,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19145]) ).
fof(f19194,plain,
m2_relset_1(sK2,sK1,sK0),
inference(cnf_transformation,[],[f19177]) ).
fof(f19195,plain,
( k1_funct_5(sK2) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0)
| k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1)) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)) ),
inference(cnf_transformation,[],[f19177]) ).
fof(f19203,plain,
! [X2,X0,X1] :
( k10_relset_1(X1,X0,X2,X1) = k2_funct_5(X2)
| ~ m2_relset_1(X2,X1,X0) ),
inference(cnf_transformation,[],[f19149]) ).
fof(f19204,plain,
! [X2,X0,X1] :
( ~ m2_relset_1(X2,X1,X0)
| k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0) ),
inference(cnf_transformation,[],[f19149]) ).
fof(f19285,definition,
( spl13_1
<=> k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1)) = k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f19287,plain,
( k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1)) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2))
| spl13_1 ),
inference(avatar_component_clause,[],[f19285]) ).
fof(f19289,definition,
( spl13_2
<=> k1_funct_5(sK2) = k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f19291,plain,
( k1_funct_5(sK2) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0)
| spl13_2 ),
inference(avatar_component_clause,[],[f19289]) ).
fof(f19292,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f19195,f19289,f19285]) ).
fof(f19854,plain,
( k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)) != k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2))
| ~ m2_relset_1(sK2,sK1,sK0)
| spl13_1 ),
inference(superposition,[],[f19287,f19203]) ).
fof(f19855,plain,
( ~ m2_relset_1(sK2,sK1,sK0)
| spl13_1 ),
inference(trivial_inequality_removal,[],[f19854]) ).
fof(f19856,plain,
( $false
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f19855,f19194]) ).
fof(f19857,plain,
spl13_1,
inference(avatar_contradiction_clause,[],[f19856]) ).
fof(f19947,plain,
k1_funct_5(sK2) = k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0),
inference(resolution,[],[f19204,f19194]) ).
fof(f19949,plain,
( $false
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f19947,f19291]) ).
fof(f19950,plain,
spl13_2,
inference(avatar_contradiction_clause,[],[f19949]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f19292]) ).
cnf(s18,plain,
spl13_1,
inference(sat_conversion,[],[f19857]) ).
cnf(s22,plain,
spl13_2,
inference(sat_conversion,[],[f19950]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s1,s22,s18]) ).
fof(f19951,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU444+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n003.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 28 05:34:14 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 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
% 8.43/3.44 % (1255229)Detected formulas, will run a generic FOF schedule.
% 8.43/3.44 % (1255242)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2703259794:i=109:sd=1:ins=1:gsp=on:ss=axioms_2987 on theBenchmark for (2987ds/109Mi)
% 8.43/3.44 % (1255244)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1644529018:s2a=on:i=139:gtg=position_2987 on theBenchmark for (2987ds/139Mi)
% 8.43/3.44 % (1255241)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=3328161266:i=141695:sd=1:nm=32:gsp=on:ss=included_2987 on theBenchmark for (2987ds/141695Mi)
% 8.43/3.44 % (1255239)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=2529177201:i=141193_2987 on theBenchmark for (2987ds/141193Mi)
% 8.43/3.44 % (1255240)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=3569543292:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2987 on theBenchmark for (2987ds/134677Mi)
% 8.43/3.44 % (1255245)dis-21_1_sil=8000:lcm=predicate:random_seed=1723798472:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2987 on theBenchmark for (2987ds/129Mi)
% 8.43/3.44 % (1255242)Instruction limit reached!
% 8.43/3.44 % (1255242)------------------------------
% 8.43/3.44 % (1255242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/3.44 % (1255242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/3.44 % (1255242)CaDiCaL version: 2.1.3
% 8.43/3.44 % (1255242)Termination reason: Instruction limit
% 8.43/3.44 % (1255242)Termination phase: SInE selection
% 8.43/3.44 % (1255242)Time elapsed: 0.070 s
% 8.43/3.44 % (1255242)Peak memory usage: 112 MB
% 8.43/3.44 % (1255242)Instructions burned: 109 (million)
% 8.43/3.44 % (1255243)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2340142517:i=119:av=off:ss=axioms_2987 on theBenchmark for (2987ds/119Mi)
% 8.43/3.44 % (1255244)Instruction limit reached!
% 8.43/3.44 % (1255244)------------------------------
% 8.43/3.44 % (1255244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/3.44 % (1255244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/3.44 % (1255244)CaDiCaL version: 2.1.3
% 8.43/3.44 % (1255244)Termination reason: Instruction limit
% 8.43/3.44 % (1255244)Termination phase: Property scanning
% 8.43/3.44 % (1255244)Time elapsed: 0.114 s
% 8.43/3.44 % (1255244)Peak memory usage: 112 MB
% 8.43/3.44 % (1255244)Instructions burned: 140 (million)
% 8.43/3.44 % (1255245)Instruction limit reached!
% 8.43/3.44 % (1255245)------------------------------
% 8.43/3.44 % (1255245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/3.44 % (1255245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/3.44 % (1255245)CaDiCaL version: 2.1.3
% 8.43/3.44 % (1255245)Termination reason: Instruction limit
% 8.43/3.44 % (1255245)Termination phase: SInE selection
% 8.43/3.44 % (1255245)Time elapsed: 0.094 s
% 8.43/3.44 % (1255245)Peak memory usage: 113 MB
% 8.43/3.44 % (1255245)Instructions burned: 129 (million)
% 8.43/3.44 % (1255243)Instruction limit reached!
% 8.43/3.44 % (1255243)------------------------------
% 8.43/3.44 % (1255243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/3.44 % (1255243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/3.44 % (1255243)CaDiCaL version: 2.1.3
% 8.43/3.44 % (1255243)Termination reason: Instruction limit
% 8.43/3.44 % (1255243)Termination phase: Preprocessing 1
% 8.43/3.44 % (1255243)Time elapsed: 0.150 s
% 8.43/3.44 % (1255243)Peak memory usage: 113 MB
% 8.43/3.44 % (1255243)Instructions burned: 119 (million)
% 8.43/3.44 % (1255252)lrs+10_1_sil=8000:sp=occurrence:random_seed=1083090073:i=285:sd=3:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/285Mi)
% 8.43/3.44 % (1255255)lrs+1011_1_sil=32000:sp=occurrence:random_seed=287350325:i=325:sd=1:ss=axioms:sgt=32_2984 on theBenchmark for (2984ds/325Mi)
% 8.43/3.44 % (1255254)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3453208527:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2984 on theBenchmark for (2984ds/157Mi)
% 8.43/3.44 % (1255255)First to succeed.
% 8.43/3.44 % (1255255)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1255229"
% 8.43/3.44 % (1255254)Instruction limit reached!
% 8.43/3.44 % (1255254)------------------------------
% 8.43/3.44 % (1255254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/3.44 % (1255254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/3.44 % (1255254)CaDiCaL version: 2.1.3
% 8.43/3.44 % (1255254)Termination reason: Instruction limit
% 8.43/3.44 % (1255254)Termination phase: Property scanning
% 8.43/3.44 % (1255254)Time elapsed: 0.131 s
% 8.43/3.44 % (1255254)Peak memory usage: 112 MB
% 8.43/3.44 % (1255254)Instructions burned: 157 (million)
% 8.43/3.44 % (1255256)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3909072105:s2a=on:i=248:s2at=1.23:gtg=position_2983 on theBenchmark for (2983ds/248Mi)
% 8.43/3.44 % (1255252)Instruction limit reached!
% 8.43/3.44 % (1255252)------------------------------
% 8.43/3.44 % (1255252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/3.44 % (1255252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/3.44 % (1255252)CaDiCaL version: 2.1.3
% 8.43/3.44 % (1255252)Termination reason: Instruction limit
% 8.43/3.44 % (1255252)Termination phase: Saturation
% 8.43/3.44 % (1255252)Time elapsed: 0.315 s
% 8.43/3.44 % (1255252)Peak memory usage: 120 MB
% 8.43/3.44 % (1255252)Instructions burned: 285 (million)
% 8.43/3.44 % (1255255)Refutation found. Thanks to Tanya!
% 8.43/3.44 % SZS status Theorem for theBenchmark
% 8.43/3.44 % SZS output start Proof for theBenchmark
% See solution above
% 8.43/3.44 % (1255255)------------------------------
% 8.43/3.44 % (1255255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.43/3.44 % (1255255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.43/3.44 % (1255255)CaDiCaL version: 2.1.3
% 8.43/3.44 % (1255255)Termination reason: Refutation
% 8.43/3.44 % (1255255)Time elapsed: 0.105 s
% 8.43/3.44 % (1255255)Peak memory usage: 119 MB
% 8.43/3.44 % (1255255)Instructions burned: 146 (million)
% 8.43/3.44 % (1255255)------------------------------
% 8.43/3.44 % (1255255)------------------------------
% 8.43/3.44 % (1255229)Success in time 2.142 s
% 8.43/3.44 % Vampire exiting
%------------------------------------------------------------------------------