%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU444+2 : 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 : n016.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 3.99s 1.67s
% Output : Refutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 9 unt; 4 def)
% Number of atoms : 60 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 28 ~; 18 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 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(f4523,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(f4528,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(f4529,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)],[f4528]) ).
fof(f4542,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,[],[f4529]) ).
fof(f4557,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,[],[f4523]) ).
fof(f4565,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)],[f4542]) ).
fof(f4575,plain,
m2_relset_1(sK2,sK1,sK0),
inference(cnf_transformation,[],[f4565]) ).
fof(f4576,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,[],[f4565]) ).
fof(f4588,plain,
! [X2,X0,X1] :
( k10_relset_1(X1,X0,X2,X1) = k2_funct_5(X2)
| ~ m2_relset_1(X2,X1,X0) ),
inference(cnf_transformation,[],[f4557]) ).
fof(f4589,plain,
! [X2,X0,X1] :
( k1_funct_5(X2) = k10_relset_1(X0,X1,k6_relset_1(X1,X0,X2),X0)
| ~ m2_relset_1(X2,X1,X0) ),
inference(cnf_transformation,[],[f4557]) ).
fof(f4634,definition,
~ sP12(k1_funct_5(sK2)),
introduced(definition,[new_symbols(definition,[sP12])],[inequality_splitting_name_introduction]) ).
fof(f4635,definition,
~ sP13(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k10_relset_1(sK1,sK0,sK2,sK1))),
introduced(definition,[new_symbols(definition,[sP13])],[inequality_splitting_name_introduction]) ).
fof(f4636,plain,
( sP12(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0))
| sP13(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2))) ),
inference(inequality_splitting,[],[f4576,f4635,f4634]) ).
fof(f4662,definition,
( spl24_1
<=> sP13(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2))) ),
introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition]) ).
fof(f4664,plain,
( sP13(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)))
| ~ spl24_1 ),
inference(avatar_component_clause,[],[f4662]) ).
fof(f4666,definition,
( spl24_2
<=> sP12(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0)) ),
introduced(definition,[new_symbols(definition,[spl24_2])],[avatar_definition]) ).
fof(f4668,plain,
( sP12(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),sK0))
| ~ spl24_2 ),
inference(avatar_component_clause,[],[f4666]) ).
fof(f4669,plain,
( spl24_1
| spl24_2 ),
inference(avatar_split_clause,[],[f4636,f4666,f4662]) ).
fof(f4684,plain,
( sP12(k1_funct_5(sK2))
| ~ m2_relset_1(sK2,sK1,sK0)
| ~ spl24_2 ),
inference(superposition,[],[f4668,f4589]) ).
fof(f4695,plain,
( ~ m2_relset_1(sK2,sK1,sK0)
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f4684,f4634]) ).
fof(f4696,plain,
( $false
| ~ spl24_2 ),
inference(forward_subsumption_resolution,[],[f4695,f4575]) ).
fof(f4697,plain,
~ spl24_2,
inference(avatar_contradiction_clause,[],[f4696]) ).
fof(f4722,plain,
( ~ sP13(k10_relset_1(sK0,sK1,k6_relset_1(sK1,sK0,sK2),k2_funct_5(sK2)))
| ~ m2_relset_1(sK2,sK1,sK0) ),
inference(superposition,[],[f4635,f4588]) ).
fof(f4723,plain,
( ~ m2_relset_1(sK2,sK1,sK0)
| ~ spl24_1 ),
inference(forward_subsumption_resolution,[],[f4722,f4664]) ).
fof(f4724,plain,
( $false
| ~ spl24_1 ),
inference(forward_subsumption_resolution,[],[f4723,f4575]) ).
fof(f4725,plain,
~ spl24_1,
inference(avatar_contradiction_clause,[],[f4724]) ).
cnf(s1,plain,
( spl24_1
| spl24_2 ),
inference(sat_conversion,[],[f4669]) ).
cnf(s4,plain,
~ spl24_2,
inference(sat_conversion,[],[f4697]) ).
cnf(s8,plain,
~ spl24_1,
inference(sat_conversion,[],[f4725]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s4,s8]) ).
fof(f4726,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU444+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 05:37:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.99/1.67 % (3308256)Detected formulas, will run a generic FOF schedule.
% 3.99/1.67 % (3308262)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=3646021361:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.99/1.67 % (3308267)dis-21_1_sil=8000:lcm=predicate:random_seed=2429100979:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 3.99/1.67 % (3308264)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=513745648:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.99/1.67 % (3308263)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=2692928636:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.99/1.67 % (3308266)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2187311308:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.99/1.67 % (3308265)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3482384827:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.99/1.67 % (3308261)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=2891960048:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.99/1.67 % (3308264)First to succeed.
% 3.99/1.67 % (3308264)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3308256"
% 3.99/1.67 % (3308265)Instruction limit reached!
% 3.99/1.67 % (3308265)------------------------------
% 3.99/1.67 % (3308265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.67 % (3308265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.67 % (3308265)CaDiCaL version: 2.1.3
% 3.99/1.67 % (3308265)Termination reason: Instruction limit
% 3.99/1.67 % (3308265)Termination phase: Saturation
% 3.99/1.67 % (3308265)Time elapsed: 0.075 s
% 3.99/1.67 % (3308265)Peak memory usage: 94 MB
% 3.99/1.67 % (3308265)Instructions burned: 119 (million)
% 3.99/1.67 % (3308266)Instruction limit reached!
% 3.99/1.67 % (3308266)------------------------------
% 3.99/1.67 % (3308266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.67 % (3308266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.67 % (3308266)CaDiCaL version: 2.1.3
% 3.99/1.67 % (3308266)Termination reason: Instruction limit
% 3.99/1.67 % (3308266)Termination phase: Preprocessing 3
% 3.99/1.67 % (3308266)Time elapsed: 0.090 s
% 3.99/1.67 % (3308266)Peak memory usage: 94 MB
% 3.99/1.67 % (3308266)Instructions burned: 140 (million)
% 3.99/1.67 % (3308267)Instruction limit reached!
% 3.99/1.67 % (3308267)------------------------------
% 3.99/1.67 % (3308267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.67 % (3308267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.67 % (3308267)CaDiCaL version: 2.1.3
% 3.99/1.67 % (3308267)Termination reason: Instruction limit
% 3.99/1.67 % (3308267)Termination phase: Preprocessing 3
% 3.99/1.67 % (3308267)Time elapsed: 0.115 s
% 3.99/1.67 % (3308267)Peak memory usage: 94 MB
% 3.99/1.67 % (3308267)Instructions burned: 129 (million)
% 3.99/1.67 % (3308275)lrs+10_1_sil=8000:sp=occurrence:random_seed=41117700:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 3.99/1.67 % (3308276)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2948001042:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 3.99/1.67 % (3308277)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3586397478:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 3.99/1.67 % (3308264)Refutation found. Thanks to Tanya!
% 3.99/1.67 % SZS status Theorem for theBenchmark
% 3.99/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 3.99/1.67 % (3308264)------------------------------
% 3.99/1.67 % (3308264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.99/1.67 % (3308264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.99/1.67 % (3308264)CaDiCaL version: 2.1.3
% 3.99/1.67 % (3308264)Termination reason: Refutation
% 3.99/1.67 % (3308264)Time elapsed: 0.022 s
% 3.99/1.67 % (3308264)Peak memory usage: 94 MB
% 3.99/1.67 % (3308264)Instructions burned: 26 (million)
% 3.99/1.67 % (3308264)------------------------------
% 3.99/1.67 % (3308264)------------------------------
% 3.99/1.67 % (3308256)Success in time 0.628 s
% 3.99/1.67 % Vampire exiting
%------------------------------------------------------------------------------