%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET825-2 : 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 : n010.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 12:42:01 PM UTC 2026
% Result : Unsatisfiable 3.55s 7.43s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 8 unt; 2 def)
% Number of atoms : 52 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 48 ( 23 ~; 23 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 7 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdI_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f3,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f4,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f5,negated_conjecture,
! [X0] :
( c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6,negated_conjecture,
! [X0] :
( ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolution,[],[f2,f5]) ).
fof(f9,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(forward_subsumption_resolution,[],[f8,f1]) ).
fof(f11,definition,
( spl0_1
<=> c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f13,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f11]) ).
fof(f15,definition,
( spl0_2
<=> v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f17,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f18,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f9,f15,f11]) ).
fof(f19,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_2 ),
inference(superposition,[],[f6,f17]) ).
fof(f21,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f19,f1]) ).
fof(f22,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f21,f1]) ).
fof(f23,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f22,f15,f11]) ).
fof(f24,plain,
( v_n = v_m
| ~ spl0_1 ),
inference(resolution,[],[f13,f2]) ).
fof(f26,plain,
( ~ v_Q(v_n)
| ~ spl0_1 ),
inference(superposition,[],[f4,f24]) ).
fof(f27,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f26,f3]) ).
fof(f28,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f27]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f18]) ).
cnf(s2,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
~ spl0_2,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
fof(f29,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : SET825-2 : TPTP v9.3.1. Released v3.2.0.
% 0.03/0.26 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/6.23 % Computer : n010.cluster.edu
% 0.10/6.23 % Model : x86_64 x86_64
% 0.10/6.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.23 % Memory : 8046.5625MB
% 0.10/6.23 % OS : Linux 6.8.0-71-generic
% 0.10/6.23 % CPULimit : 300
% 0.10/6.23 % WCLimit : 300
% 0.10/6.23 % DateTime : Mon Sep 28 02:56:03 UTC 2026
% 0.10/6.23 % CPUTime :
% 0.10/6.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/6.27 Running first-order theorem proving
% 0.10/6.27 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
% 3.55/7.43 % (1515490)Input is clausal, will run a generic CNF schedule.
% 3.55/7.43 % (1515495)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=921410400:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.55/7.43 % (1515497)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2482720731:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.55/7.43 % (1515498)lrs+10_1_sil=8000:sp=occurrence:random_seed=3170138480:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.55/7.43 % (1515499)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3998452244:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.55/7.43 % (1515496)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3099307531:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.55/7.43 % (1515501)dis-21_1_sil=8000:lcm=predicate:random_seed=2992957483:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.55/7.43 % (1515499)Refutation not found, incomplete strategy
% 3.55/7.43 % (1515499)------------------------------
% 3.55/7.43 % (1515499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/7.43 % (1515499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/7.43 % (1515499)CaDiCaL version: 2.1.3
% 3.55/7.43 % (1515499)Termination reason: Refutation not found, incomplete strategy
% 3.55/7.43 % (1515499)Time elapsed: 0.001 s
% 3.55/7.43 % (1515499)Peak memory usage: 87 MB
% 3.55/7.43 % (1515501)Refutation not found, incomplete strategy
% 3.55/7.43 % (1515501)------------------------------
% 3.55/7.43 % (1515501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/7.43 % (1515501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/7.43 % (1515501)CaDiCaL version: 2.1.3
% 3.55/7.43 % (1515501)Termination reason: Refutation not found, incomplete strategy
% 3.55/7.43 % (1515501)Time elapsed: 0.001 s
% 3.55/7.43 % (1515501)Peak memory usage: 87 MB
% 3.55/7.43 % (1515498)First to succeed.
% 3.55/7.43 % (1515498)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1515490"
% 3.55/7.43 % (1515500)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1339713969:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.55/7.43 % (1515500)Also succeeded, but the first one will report.
% 3.55/7.43 % (1515501)------------------------------
% 3.55/7.43 % (1515501)------------------------------
% 3.55/7.43 % (1515499)------------------------------
% 3.55/7.43 % (1515499)------------------------------
% 3.55/7.43 % (1515498)Refutation found. Thanks to Tanya!
% 3.55/7.43 % SZS status Unsatisfiable for theBenchmark
% 3.55/7.43 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/7.43 % (1515498)------------------------------
% 3.55/7.43 % (1515498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/7.43 % (1515498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/7.43 % (1515498)CaDiCaL version: 2.1.3
% 3.55/7.43 % (1515498)Termination reason: Refutation
% 3.55/7.43 % (1515498)Time elapsed: 0.003 s
% 3.55/7.43 % (1515498)Peak memory usage: 89 MB
% 3.55/7.43 % (1515498)Instructions burned: 1 (million)
% 3.55/7.43 % (1515498)------------------------------
% 3.55/7.43 % (1515498)------------------------------
% 3.55/7.43 % (1515490)Success in time 0.49 s
% 3.55/7.43 % Vampire exiting
%------------------------------------------------------------------------------