%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:39:35 PM UTC 2026
% Result : Unsatisfiable 2.76s 1.15s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 20 unt; 7 def)
% Number of atoms : 156 ( 48 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 142 ( 64 ~; 71 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : member(X0,singleton_set(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ member(X0,singleton_set(X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_2) ).
fof(f3,axiom,
! [X0,X1] : member(X0,unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_1) ).
fof(f4,axiom,
! [X0,X1] : member(X0,unordered_pair(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_2) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_3) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f7,axiom,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f8,negated_conjecture,
r1 != r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
fof(f11,plain,
! [X0,X1] : member(singleton_set(X0),ordered_pair(X0,X1)),
inference(superposition,[],[f3,f6]) ).
fof(f12,plain,
! [X0,X1] : member(unordered_pair(X0,X1),ordered_pair(X0,X1)),
inference(superposition,[],[f4,f6]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ member(X2,ordered_pair(X0,X1))
| singleton_set(X0) = X2
| unordered_pair(X0,X1) = X2 ),
inference(superposition,[],[f5,f6]) ).
fof(f25,plain,
! [X0] :
( ~ member(X0,ordered_pair(m1,r1))
| singleton_set(m2) = X0
| unordered_pair(m2,r2) = X0 ),
inference(superposition,[],[f15,f7]) ).
fof(f27,definition,
( spl0_1
<=> singleton_set(m2) = unordered_pair(m1,r1) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f29,plain,
( singleton_set(m2) = unordered_pair(m1,r1)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f31,definition,
( spl0_2
<=> singleton_set(m2) = singleton_set(m1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f32,plain,
( singleton_set(m2) != singleton_set(m1)
| spl0_2 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f33,plain,
( singleton_set(m2) = singleton_set(m1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f40,plain,
( member(m2,singleton_set(m1))
| ~ spl0_2 ),
inference(superposition,[],[f1,f33]) ).
fof(f44,plain,
member(unordered_pair(m2,r2),ordered_pair(m1,r1)),
inference(superposition,[],[f12,f7]) ).
fof(f45,plain,
( m1 = m2
| ~ spl0_2 ),
inference(resolution,[],[f40,f2]) ).
fof(f76,definition,
( spl0_3
<=> unordered_pair(m1,r1) = unordered_pair(m1,r2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f78,plain,
( unordered_pair(m1,r1) = unordered_pair(m1,r2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f80,definition,
( spl0_4
<=> singleton_set(m1) = unordered_pair(m1,r2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f82,plain,
( singleton_set(m1) = unordered_pair(m1,r2)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f80]) ).
fof(f89,definition,
( spl0_5
<=> singleton_set(m1) = unordered_pair(m1,r1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f91,plain,
( singleton_set(m1) = unordered_pair(m1,r1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f97,plain,
( member(r2,unordered_pair(m1,r1))
| ~ spl0_3 ),
inference(superposition,[],[f4,f78]) ).
fof(f111,plain,
( m1 = r2
| r1 = r2
| ~ spl0_3 ),
inference(resolution,[],[f97,f5]) ).
fof(f112,plain,
( m1 = r2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f111,f8]) ).
fof(f120,plain,
( unordered_pair(r2,r1) = unordered_pair(r2,r2)
| ~ spl0_3 ),
inference(superposition,[],[f78,f112]) ).
fof(f129,definition,
( spl0_6
<=> unordered_pair(r2,r1) = unordered_pair(r2,r2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f131,plain,
( unordered_pair(r2,r1) = unordered_pair(r2,r2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f129]) ).
fof(f146,plain,
( singleton_set(m2) = singleton_set(m1)
| unordered_pair(m2,r2) = singleton_set(m1) ),
inference(resolution,[],[f25,f11]) ).
fof(f148,plain,
( singleton_set(m2) = unordered_pair(m1,r1)
| unordered_pair(m2,r2) = unordered_pair(m1,r1) ),
inference(resolution,[],[f25,f12]) ).
fof(f150,definition,
( spl0_8
<=> unordered_pair(m2,r2) = unordered_pair(m1,r1) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f152,plain,
( unordered_pair(m2,r2) = unordered_pair(m1,r1)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f153,plain,
( spl0_8
| spl0_1 ),
inference(avatar_split_clause,[],[f148,f27,f150]) ).
fof(f154,plain,
( unordered_pair(m2,r2) = singleton_set(m1)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f146,f32]) ).
fof(f155,plain,
( member(m2,singleton_set(m1))
| spl0_2 ),
inference(superposition,[],[f3,f154]) ).
fof(f167,plain,
( m1 = m2
| spl0_2 ),
inference(resolution,[],[f155,f2]) ).
fof(f172,plain,
( singleton_set(m1) != singleton_set(m1)
| spl0_2 ),
inference(superposition,[],[f32,f167]) ).
fof(f175,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f172]) ).
fof(f176,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f175]) ).
fof(f185,plain,
( member(r1,singleton_set(m1))
| ~ spl0_5 ),
inference(superposition,[],[f4,f91]) ).
fof(f196,plain,
( member(unordered_pair(m1,r2),ordered_pair(m1,r1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f44,f45]) ).
fof(f197,plain,
( m1 = r1
| ~ spl0_5 ),
inference(resolution,[],[f185,f2]) ).
fof(f199,plain,
( singleton_set(m1) = unordered_pair(m1,r2)
| unordered_pair(m1,r1) = unordered_pair(m1,r2)
| ~ spl0_2 ),
inference(resolution,[],[f196,f15]) ).
fof(f244,plain,
( singleton_set(r1) = unordered_pair(r1,r2)
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f82,f197]) ).
fof(f247,plain,
( member(r2,singleton_set(r1))
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f4,f244]) ).
fof(f257,plain,
( r1 = r2
| ~ spl0_4
| ~ spl0_5 ),
inference(resolution,[],[f247,f2]) ).
fof(f258,plain,
( $false
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f257,f8]) ).
fof(f259,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f260,plain,
( spl0_6
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f120,f76,f129]) ).
fof(f262,plain,
( spl0_3
| spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f199,f31,f80,f76]) ).
fof(f264,plain,
( singleton_set(m1) = unordered_pair(m1,r1)
| ~ spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f29,f45]) ).
fof(f266,plain,
( spl0_5
| ~ spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f264,f31,f27,f89]) ).
fof(f268,plain,
( unordered_pair(m1,r1) = unordered_pair(m1,r2)
| ~ spl0_2
| ~ spl0_8 ),
inference(forward_demodulation,[],[f152,f45]) ).
fof(f270,plain,
( spl0_3
| ~ spl0_2
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f268,f150,f31,f76]) ).
fof(f394,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(r2,r1))
| r2 = X0
| r2 = X0 )
| ~ spl0_6 ),
inference(superposition,[],[f5,f131]) ).
fof(f400,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(r2,r1))
| r2 = X0 )
| ~ spl0_6 ),
inference(duplicate_literal_removal,[],[f394]) ).
fof(f421,plain,
( r1 = r2
| ~ spl0_6 ),
inference(resolution,[],[f400,f4]) ).
fof(f422,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f421,f8]) ).
fof(f423,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f422]) ).
cnf(s5,plain,
( spl0_1
| spl0_8 ),
inference(sat_conversion,[],[f153]) ).
cnf(s6,plain,
spl0_2,
inference(sat_conversion,[],[f176]) ).
cnf(s12,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f259]) ).
cnf(s13,plain,
( ~ spl0_3
| spl0_6 ),
inference(sat_conversion,[],[f260]) ).
cnf(s14,plain,
( ~ spl0_2
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f262]) ).
cnf(s15,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f266]) ).
cnf(s17,plain,
( ~ spl0_2
| spl0_3
| ~ spl0_8 ),
inference(sat_conversion,[],[f270]) ).
cnf(s24,plain,
~ spl0_6,
inference(sat_conversion,[],[f423]) ).
cnf(s26,plain,
~ spl0_3,
inference(rat,[],[s13,s24]) ).
cnf(s27,plain,
~ spl0_8,
inference(rat,[],[s17,s26,s6]) ).
cnf(s28,plain,
spl0_4,
inference(rat,[],[s14,s26,s6]) ).
cnf(s29,plain,
~ spl0_5,
inference(rat,[],[s12,s28]) ).
cnf(s30,plain,
~ spl0_1,
inference(rat,[],[s15,s6,s29]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s5,s27,s30]) ).
fof(f424,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:08:31 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 2.76/1.15 % (314957)Input is clausal, will run a generic CNF schedule.
% 2.76/1.15 % (314967)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2512739171:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.76/1.15 % (314964)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=584895826:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.76/1.15 % (314965)lrs+10_1_sil=8000:sp=occurrence:random_seed=3104120758:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.76/1.15 % (314966)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2890429954:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.76/1.15 % (314963)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=409435226:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.76/1.15 % (314968)dis-21_1_sil=8000:lcm=predicate:random_seed=2560606250: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)
% 2.76/1.15 % (314962)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=3370533103:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.76/1.15 % (314968)Refutation not found, incomplete strategy
% 2.76/1.15 % (314968)------------------------------
% 2.76/1.15 % (314968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.15 % (314968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.15 % (314968)CaDiCaL version: 2.1.3
% 2.76/1.15 % (314968)Termination reason: Refutation not found, incomplete strategy
% 2.76/1.15 % (314968)Time elapsed: 0.001 s
% 2.76/1.15 % (314968)Peak memory usage: 88 MB
% 2.76/1.15 % (314967)First to succeed.
% 2.76/1.15 % (314966)Also succeeded, but the first one will report.
% 2.76/1.15 % (314965)Also succeeded, but the first one will report.
% 2.76/1.15 % (314967)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-314957"
% 2.76/1.15 % (314967)Refutation found. Thanks to Tanya!
% 2.76/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.76/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/1.15 % (314967)------------------------------
% 2.76/1.15 % (314967)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.76/1.15 % (314967)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.76/1.15 % (314967)CaDiCaL version: 2.1.3
% 2.76/1.15 % (314967)Termination reason: Refutation
% 2.76/1.15 % (314967)Time elapsed: 0.007 s
% 2.76/1.15 % (314967)Peak memory usage: 89 MB
% 2.76/1.15 % (314967)Instructions burned: 15 (million)
% 2.76/1.15 % (314967)------------------------------
% 2.76/1.15 % (314967)------------------------------
% 2.76/1.15 % (314957)Success in time 0.33 s
% 2.76/1.15 % Vampire exiting
%------------------------------------------------------------------------------