%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET016-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:39:34 PM UTC 2026
% Result : Unsatisfiable 2.70s 1.28s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 39 ( 16 unt; 2 def)
% Number of atoms : 68 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 55 ( 26 ~; 27 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] :
( ~ member(X0,non_ordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair1) ).
fof(f6,axiom,
! [X2,X0,X1] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair2) ).
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair4) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f162,axiom,
little_set(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',little_set_a) ).
fof(f163,axiom,
little_set(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',little_set_b) ).
fof(f164,axiom,
ordered_pair(a,c) = ordered_pair(b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f165,negated_conjecture,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_first_components_equal) ).
fof(f166,plain,
! [X2,X1] :
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(equality_resolution,[],[f6]) ).
fof(f180,plain,
! [X0] : little_set(singleton_set(X0)),
inference(superposition,[],[f8,f9]) ).
fof(f182,plain,
! [X0] :
( member(X0,singleton_set(X0))
| ~ little_set(X0) ),
inference(superposition,[],[f166,f9]) ).
fof(f205,plain,
! [X0,X1] :
( member(singleton_set(X0),ordered_pair(X0,X1))
| ~ little_set(singleton_set(X0)) ),
inference(superposition,[],[f166,f10]) ).
fof(f207,plain,
! [X0,X1] : member(singleton_set(X0),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[],[f205,f180]) ).
fof(f221,plain,
! [X0,X1] :
( ~ member(X1,singleton_set(X0))
| X0 = X1
| X0 = X1 ),
inference(superposition,[],[f5,f9]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ~ member(X2,ordered_pair(X0,X1))
| singleton_set(X0) = X2
| non_ordered_pair(X0,X1) = X2 ),
inference(superposition,[],[f5,f10]) ).
fof(f223,plain,
! [X0,X1] :
( ~ member(X1,singleton_set(X0))
| X0 = X1 ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f261,plain,
member(singleton_set(b),ordered_pair(a,c)),
inference(superposition,[],[f207,f164]) ).
fof(f784,plain,
( singleton_set(b) = singleton_set(a)
| singleton_set(b) = non_ordered_pair(a,c) ),
inference(resolution,[],[f222,f261]) ).
fof(f794,definition,
( spl0_28
<=> singleton_set(b) = non_ordered_pair(a,c) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f796,plain,
( singleton_set(b) = non_ordered_pair(a,c)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f798,definition,
( spl0_29
<=> singleton_set(b) = singleton_set(a) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f800,plain,
( singleton_set(b) = singleton_set(a)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f798]) ).
fof(f801,plain,
( spl0_28
| spl0_29 ),
inference(avatar_split_clause,[],[f784,f798,f794]) ).
fof(f835,plain,
( member(a,singleton_set(b))
| ~ little_set(a)
| ~ spl0_28 ),
inference(superposition,[],[f166,f796]) ).
fof(f837,plain,
( member(a,singleton_set(b))
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f835,f162]) ).
fof(f921,plain,
( a = b
| ~ spl0_28 ),
inference(resolution,[],[f837,f223]) ).
fof(f922,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f921,f165]) ).
fof(f923,plain,
~ spl0_28,
inference(avatar_contradiction_clause,[],[f922]) ).
fof(f964,plain,
( member(b,singleton_set(a))
| ~ little_set(b)
| ~ spl0_29 ),
inference(superposition,[],[f182,f800]) ).
fof(f978,plain,
( member(b,singleton_set(a))
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f964,f163]) ).
fof(f985,plain,
( a = b
| ~ spl0_29 ),
inference(resolution,[],[f978,f223]) ).
fof(f986,plain,
( $false
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f985,f165]) ).
fof(f987,plain,
~ spl0_29,
inference(avatar_contradiction_clause,[],[f986]) ).
cnf(s28,plain,
( spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f801]) ).
cnf(s37,plain,
~ spl0_28,
inference(sat_conversion,[],[f923]) ).
cnf(s41,plain,
~ spl0_29,
inference(sat_conversion,[],[f987]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s28,s41,s37]) ).
fof(f988,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 00:11:16 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.70/1.28 % (2152491)Input is clausal, will run a generic CNF schedule.
% 2.70/1.28 % (2152543)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3274947372:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.70/1.28 % (2152543)First to succeed.
% 2.70/1.28 % (2152543)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2152491"
% 2.70/1.28 % (2152539)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4149257273:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.70/1.28 % (2152544)dis-21_1_sil=8000:lcm=predicate:random_seed=2911381478: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)
% 2.70/1.28 % (2152540)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3527290581:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.70/1.28 % (2152541)lrs+10_1_sil=8000:sp=occurrence:random_seed=1675011513:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.70/1.28 % (2152538)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=4210416004:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.70/1.28 % (2152542)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1709491201:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.70/1.28 % (2152541)Refutation not found, incomplete strategy
% 2.70/1.28 % (2152541)------------------------------
% 2.70/1.28 % (2152541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2152541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2152541)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2152541)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.28 % (2152541)Time elapsed: 0.001 s
% 2.70/1.28 % (2152541)Peak memory usage: 87 MB
% 2.70/1.28 % (2152542)Refutation not found, incomplete strategy
% 2.70/1.28 % (2152542)------------------------------
% 2.70/1.28 % (2152542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2152542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2152542)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2152542)Termination reason: Refutation not found, incomplete strategy
% 2.70/1.28 % (2152542)Time elapsed: 0.002 s
% 2.70/1.28 % (2152542)Peak memory usage: 88 MB
% 2.70/1.28 % (2152542)Instructions burned: 1 (million)
% 2.70/1.28 % (2152544)Instruction limit reached!
% 2.70/1.28 % (2152544)------------------------------
% 2.70/1.28 % (2152544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2152544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2152544)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2152544)Termination reason: Instruction limit
% 2.70/1.28 % (2152544)Termination phase: Saturation
% 2.70/1.28 % (2152544)Time elapsed: 0.062 s
% 2.70/1.28 % (2152544)Peak memory usage: 88 MB
% 2.70/1.28 % (2152544)Instructions burned: 118 (million)
% 2.70/1.28 % (2152543)Refutation found. Thanks to Tanya!
% 2.70/1.28 % SZS status Unsatisfiable for theBenchmark
% 2.70/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.28 % (2152543)------------------------------
% 2.70/1.28 % (2152543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.28 % (2152543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.28 % (2152543)CaDiCaL version: 2.1.3
% 2.70/1.28 % (2152543)Termination reason: Refutation
% 2.70/1.28 % (2152543)Time elapsed: 0.017 s
% 2.70/1.28 % (2152543)Peak memory usage: 90 MB
% 2.70/1.28 % (2152543)Instructions burned: 38 (million)
% 2.70/1.28 % (2152543)------------------------------
% 2.70/1.28 % (2152543)------------------------------
% 2.70/1.28 % (2152491)Success in time 0.322 s
% 2.70/1.28 % Vampire exiting
%------------------------------------------------------------------------------