%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:44:42 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : Refutation 0.13s
% 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(f173,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Relation_OIdI_0) ).
fof(f178,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/Axioms/MSC001-2.ax',cls_Relation_Opair__in__Id__conv__iff1_0) ).
fof(f1434,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1435,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1436,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(f1437,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(f2267,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,[],[f178,f1436]) ).
fof(f2268,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,[],[f2267,f173]) ).
fof(f2270,definition,
( spl0_5
<=> 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_5])],[avatar_definition]) ).
fof(f2272,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f2270]) ).
fof(f2274,definition,
( spl0_6
<=> v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f2276,plain,
( v_x(c_Relation_OId) = v_xa(c_Relation_OId)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f2274]) ).
fof(f2277,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f2268,f2274,f2270]) ).
fof(f2278,plain,
( v_n = v_m
| ~ spl0_5 ),
inference(resolution,[],[f2272,f178]) ).
fof(f2280,plain,
( ~ v_Q(v_n)
| ~ spl0_5 ),
inference(superposition,[],[f1435,f2278]) ).
fof(f2281,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f2280,f1434]) ).
fof(f2282,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f2281]) ).
fof(f2286,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_6 ),
inference(superposition,[],[f1437,f2276]) ).
fof(f2288,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_6 ),
inference(forward_subsumption_resolution,[],[f2286,f173]) ).
fof(f2289,plain,
( c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f2288,f173]) ).
fof(f2290,plain,
( spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f2289,f2274,f2270]) ).
cnf(s4,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f2277]) ).
cnf(s5,plain,
~ spl0_5,
inference(sat_conversion,[],[f2282]) ).
cnf(s6,plain,
( spl0_5
| ~ spl0_6 ),
inference(sat_conversion,[],[f2290]) ).
cnf(s7,plain,
~ spl0_6,
inference(rat,[],[s6,s5]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s4,s7,s5]) ).
fof(f2291,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n014.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 28 02:55:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 Running first-order model finding
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.46 % (1395249)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (1395255)% WARNING: option uhcvi not known.
% 0.13/0.46 % (1395255)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4127887849:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.46 % (1395254)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1929231943_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.46 % (1395257)dis+10_1_sil=32000:sp=arity:random_seed=688670997:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.46 % (1395256)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1459419150:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.46 % (1395258)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4191965350:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.46 % (1395259)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1915957317:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.46 % (1395260)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2348693456:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % (1395255) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1395249-1395255"...
% 0.13/0.46 % (1395255)...printing done.
% 0.13/0.46 % (1395255)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (1395255)------------------------------
% 0.13/0.46 % (1395255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (1395255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (1395255)CaDiCaL version: 2.1.3
% 0.13/0.46 % (1395255)Termination reason: Refutation
% 0.13/0.46 % (1395255)Time elapsed: 0.015 s
% 0.13/0.46 % (1395255)Peak memory usage: 14 MB
% 0.13/0.46 % (1395255)Instructions burned: 35 (million)
% 0.13/0.46 % (1395249)Success in time 0.057 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------