%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 12:42:25 PM UTC 2026
% Result : Theorem 3.57s 1.50s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 8 unt; 3 def)
% Number of atoms : 139 ( 36 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 157 ( 64 ~; 52 |; 28 &)
% ( 8 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 70 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
=> X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
fof(f10,plain,
~ ! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X5] :
~ ( in(X5,X1)
& ! [X6,X7] : ordered_pair(X6,X7) != X5 )
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<=> in(ordered_pair(X8,X9),X1) ) )
=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f12,plain,
? [X0,X1] :
( X0 != X1
& ! [X2] :
( ~ in(X2,X0)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X5] :
( ~ in(X5,X1)
| ? [X6,X7] : ordered_pair(X6,X7) = X5 )
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<=> in(ordered_pair(X8,X9),X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
? [X0,X1] :
( X0 != X1
& ! [X2] :
( ~ in(X2,X0)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X5] :
( ~ in(X5,X1)
| ? [X6,X7] : ordered_pair(X6,X7) = X5 )
& ! [X8,X9] :
( in(ordered_pair(X8,X9),X0)
<=> in(ordered_pair(X8,X9),X1) ) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
? [X0,X1] :
( X0 != X1
& ! [X2] :
( ~ in(X2,X0)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X5] :
( ~ in(X5,X1)
| ? [X6,X7] : ordered_pair(X6,X7) = X5 )
& ! [X8,X9] :
( ( in(ordered_pair(X8,X9),X0)
| ~ in(ordered_pair(X8,X9),X1) )
& ( in(ordered_pair(X8,X9),X1)
| ~ in(ordered_pair(X8,X9),X0) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f17,plain,
( sK0 != sK1
& ! [X2] :
( ~ in(X2,sK0)
| ordered_pair(sK2(X2),sK3(X2)) = X2 )
& ! [X5] :
( ~ in(X5,sK1)
| ordered_pair(sK4(X5),sK5(X5)) = X5 )
& ! [X8,X9] :
( ( in(ordered_pair(X8,X9),sK0)
| ~ in(ordered_pair(X8,X9),sK1) )
& ( in(ordered_pair(X8,X9),sK1)
| ~ in(ordered_pair(X8,X9),sK0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2)),skolemize(X4,sK3(X2)),skolemize(X6,sK4(X5)),skolemize(X7,sK5(X5))],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f19,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK6(X0,X1),X1)
| ~ in(sK6(X0,X1),X0) )
& ( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f18]) ).
fof(f20,plain,
! [X8,X9] :
( ~ in(ordered_pair(X8,X9),sK0)
| in(ordered_pair(X8,X9),sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f21,plain,
! [X8,X9] :
( ~ in(ordered_pair(X8,X9),sK1)
| in(ordered_pair(X8,X9),sK0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f22,plain,
! [X5] :
( ordered_pair(sK4(X5),sK5(X5)) = X5
| ~ in(X5,sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f23,plain,
! [X2] :
( ordered_pair(sK2(X2),sK3(X2)) = X2
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| X0 = X1
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| X0 = X1
| ~ in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f28,definition,
~ sP7(sK0),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f29,plain,
sP7(sK1),
inference(inequality_splitting,[],[f24,f28]) ).
fof(f30,plain,
! [X0] :
( ~ in(X0,sK1)
| in(X0,sK0)
| ~ in(X0,sK1) ),
inference(superposition,[],[f21,f22]) ).
fof(f32,plain,
! [X0] :
( ~ in(X0,sK1)
| in(X0,sK0) ),
inference(duplicate_literal_removal,[],[f30]) ).
fof(f34,plain,
! [X0] :
( ~ in(X0,sK0)
| in(X0,sK1)
| ~ in(X0,sK0) ),
inference(superposition,[],[f20,f23]) ).
fof(f35,plain,
! [X0] :
( ~ in(X0,sK0)
| in(X0,sK1) ),
inference(duplicate_literal_removal,[],[f34]) ).
fof(f36,plain,
! [X0] :
( in(sK6(X0,sK1),sK0)
| sK1 = X0
| in(sK6(X0,sK1),X0) ),
inference(resolution,[],[f32,f25]) ).
fof(f40,plain,
( in(sK6(sK0,sK1),sK0)
| sK0 = sK1 ),
inference(factoring,[],[f36]) ).
fof(f42,definition,
( spl8_1
<=> sK0 = sK1 ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f43,plain,
( sK0 != sK1
| spl8_1 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f44,plain,
( sK0 = sK1
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f46,definition,
( spl8_2
<=> in(sK6(sK0,sK1),sK0) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f48,plain,
( in(sK6(sK0,sK1),sK0)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f49,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f40,f46,f42]) ).
fof(f62,plain,
( sP7(sK0)
| ~ spl8_1 ),
inference(superposition,[],[f29,f44]) ).
fof(f63,plain,
( $false
| ~ spl8_1 ),
inference(forward_subsumption_resolution,[],[f62,f28]) ).
fof(f64,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f63]) ).
fof(f65,plain,
( in(sK6(sK0,sK1),sK1)
| ~ spl8_2 ),
inference(resolution,[],[f48,f35]) ).
fof(f70,plain,
( sK0 = sK1
| ~ in(sK6(sK0,sK1),sK0)
| ~ spl8_2 ),
inference(resolution,[],[f65,f26]) ).
fof(f72,plain,
( ~ in(sK6(sK0,sK1),sK0)
| spl8_1
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f70,f43]) ).
fof(f73,plain,
( $false
| spl8_1
| ~ spl8_2 ),
inference(forward_subsumption_resolution,[],[f72,f48]) ).
fof(f74,plain,
( spl8_1
| ~ spl8_2 ),
inference(avatar_contradiction_clause,[],[f73]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
~ spl8_1,
inference(sat_conversion,[],[f64]) ).
cnf(s4,plain,
( spl8_1
| ~ spl8_2 ),
inference(sat_conversion,[],[f74]) ).
cnf(s5,plain,
~ spl8_2,
inference(rat,[],[s4,s3]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s5,s3]) ).
fof(f75,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n011.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 03:16:15 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 3.57/1.50 % (2983564)Detected formulas, will run a generic FOF schedule.
% 3.57/1.50 % (2983671)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=182217847:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.57/1.50 % (2983669)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=1341848845:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.57/1.50 % (2983672)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2363059535:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.57/1.50 % (2983670)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=1091052567:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.57/1.50 % (2983672)First to succeed.
% 3.57/1.50 % (2983672)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2983564"
% 3.57/1.50 % (2983673)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2486067495:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.57/1.50 % (2983673)Also succeeded, but the first one will report.
% 3.57/1.50 % (2983675)dis-21_1_sil=8000:lcm=predicate:random_seed=4077506654: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)
% 3.57/1.50 % (2983675)Refutation not found, incomplete strategy
% 3.57/1.50 % (2983675)------------------------------
% 3.57/1.50 % (2983675)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.50 % (2983675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.50 % (2983675)CaDiCaL version: 2.1.3
% 3.57/1.50 % (2983675)Termination reason: Refutation not found, incomplete strategy
% 3.57/1.50 % (2983675)Time elapsed: 0.002 s
% 3.57/1.50 % (2983675)Peak memory usage: 88 MB
% 3.57/1.50 % (2983675)Instructions burned: 1 (million)
% 3.57/1.50 % (2983674)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2719345462:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.57/1.50 % (2983674)Also succeeded, but the first one will report.
% 3.57/1.50 % (2983672)Refutation found. Thanks to Tanya!
% 3.57/1.50 % SZS status Theorem for theBenchmark
% 3.57/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.50 % (2983672)------------------------------
% 3.70/1.50 % (2983672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.50 % (2983672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.50 % (2983672)CaDiCaL version: 2.1.3
% 3.70/1.50 % (2983672)Termination reason: Refutation
% 3.70/1.50 % (2983672)Time elapsed: 0.004 s
% 3.70/1.50 % (2983672)Peak memory usage: 89 MB
% 3.70/1.50 % (2983672)Instructions burned: 3 (million)
% 3.70/1.50 % (2983672)------------------------------
% 3.70/1.50 % (2983672)------------------------------
% 3.70/1.50 % (2983564)Success in time 0.422 s
% 3.70/1.50 % Vampire exiting
%------------------------------------------------------------------------------