%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET018-3 : 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 : n019.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 4.39s 1.60s
% Output : Refutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 67 ( 18 unt; 3 def)
% Number of atoms : 155 ( 63 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 164 ( 76 ~; 85 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X2,X0,X1] :
( ~ member(X0,non_ordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair1) ).
fof(f7,axiom,
! [X2,X0,X1] :
( member(X0,non_ordered_pair(X1,X2))
| ~ little_set(X0)
| X0 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair3) ).
fof(f8,axiom,
! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_ordered_pair4) ).
fof(f9,axiom,
! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f162,axiom,
! [X2,X3,X0,X1] :
( ~ little_set(X0)
| ~ little_set(X1)
| ordered_pair(X0,X2) != ordered_pair(X1,X3)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_components_are_equal) ).
fof(f163,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X1,X3) != ordered_pair(X0,X2)
| ~ little_set(X1)
| ~ little_set(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f162]) ).
fof(f164,axiom,
! [X2,X0,X1] :
( non_ordered_pair(X2,X0) != non_ordered_pair(X2,X1)
| ~ little_set(X1)
| ~ little_set(X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
fof(f165,axiom,
little_set(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_little_set) ).
fof(f166,axiom,
little_set(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_little_set) ).
fof(f167,axiom,
little_set(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_little_set) ).
fof(f168,axiom,
little_set(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_little_set) ).
fof(f169,axiom,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pair) ).
fof(f170,negated_conjecture,
b != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_second_components_equal) ).
fof(f172,plain,
! [X2,X1] :
( member(X2,non_ordered_pair(X1,X2))
| ~ little_set(X2) ),
inference(equality_resolution,[],[f7]) ).
fof(f196,plain,
! [X0,X1] :
( member(non_ordered_pair(X0,X1),ordered_pair(X0,X1))
| ~ little_set(non_ordered_pair(X0,X1)) ),
inference(superposition,[],[f172,f10]) ).
fof(f200,plain,
! [X0,X1] : member(non_ordered_pair(X0,X1),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[],[f196,f8]) ).
fof(f216,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(f275,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(a,b)
| ~ little_set(X0)
| ~ little_set(c)
| c = X0 ),
inference(superposition,[],[f163,f169]) ).
fof(f278,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(a,b)
| ~ little_set(X0)
| c = X0 ),
inference(forward_subsumption_resolution,[],[f275,f167]) ).
fof(f282,plain,
! [X0,X1] :
( non_ordered_pair(X0,X1) != singleton_set(X0)
| ~ little_set(X1)
| ~ little_set(X0)
| X0 = X1 ),
inference(superposition,[],[f164,f9]) ).
fof(f330,plain,
member(non_ordered_pair(c,d),ordered_pair(a,b)),
inference(superposition,[],[f200,f169]) ).
fof(f753,plain,
( ~ little_set(a)
| a = c ),
inference(equality_resolution,[],[f278]) ).
fof(f754,plain,
a = c,
inference(forward_subsumption_resolution,[],[f753,f165]) ).
fof(f901,plain,
( non_ordered_pair(c,d) = singleton_set(a)
| non_ordered_pair(c,d) = non_ordered_pair(a,b) ),
inference(resolution,[],[f216,f330]) ).
fof(f915,plain,
! [X0] :
( ~ member(X0,ordered_pair(a,b))
| singleton_set(c) = X0
| non_ordered_pair(c,d) = X0 ),
inference(superposition,[],[f216,f169]) ).
fof(f916,plain,
! [X0] :
( singleton_set(a) = X0
| ~ member(X0,ordered_pair(a,b))
| non_ordered_pair(c,d) = X0 ),
inference(forward_demodulation,[],[f915,f754]) ).
fof(f919,definition,
( spl0_25
<=> non_ordered_pair(a,d) = non_ordered_pair(a,b) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f921,plain,
( non_ordered_pair(a,d) = non_ordered_pair(a,b)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f919]) ).
fof(f923,definition,
( spl0_26
<=> singleton_set(a) = non_ordered_pair(a,d) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f925,plain,
( singleton_set(a) = non_ordered_pair(a,d)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f927,plain,
( singleton_set(a) = non_ordered_pair(a,d)
| non_ordered_pair(c,d) = non_ordered_pair(a,b) ),
inference(forward_demodulation,[],[f901,f754]) ).
fof(f928,plain,
! [X0] :
( non_ordered_pair(a,d) = X0
| singleton_set(a) = X0
| ~ member(X0,ordered_pair(a,b)) ),
inference(forward_demodulation,[],[f916,f754]) ).
fof(f929,plain,
( non_ordered_pair(a,d) = non_ordered_pair(a,b)
| singleton_set(a) = non_ordered_pair(a,d) ),
inference(forward_demodulation,[],[f927,f754]) ).
fof(f930,plain,
( spl0_26
| spl0_25 ),
inference(avatar_split_clause,[],[f929,f919,f923]) ).
fof(f1548,plain,
( member(d,non_ordered_pair(a,b))
| ~ little_set(d)
| ~ spl0_25 ),
inference(superposition,[],[f172,f921]) ).
fof(f1577,plain,
( member(d,non_ordered_pair(a,b))
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1548,f168]) ).
fof(f1583,definition,
( spl0_58
<=> a = d ),
introduced(definition,[new_symbols(definition,[spl0_58])],[avatar_definition]) ).
fof(f1585,plain,
( a = d
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1583]) ).
fof(f1614,plain,
( singleton_set(a) != singleton_set(a)
| ~ little_set(d)
| ~ little_set(a)
| a = d
| ~ spl0_26 ),
inference(superposition,[],[f282,f925]) ).
fof(f1615,plain,
( ~ little_set(d)
| ~ little_set(a)
| a = d
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f1614]) ).
fof(f1616,plain,
( ~ little_set(a)
| a = d
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1615,f168]) ).
fof(f1621,plain,
( a = d
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f1616,f165]) ).
fof(f1623,plain,
( spl0_58
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f1621,f923,f1583]) ).
fof(f1656,plain,
( a = d
| b = d
| ~ spl0_25 ),
inference(resolution,[],[f1577,f5]) ).
fof(f1657,plain,
( a = d
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f1656,f170]) ).
fof(f1658,plain,
( spl0_58
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f1657,f919,f1583]) ).
fof(f3312,plain,
( ! [X0] :
( non_ordered_pair(d,d) = X0
| singleton_set(a) = X0
| ~ member(X0,ordered_pair(a,b)) )
| ~ spl0_58 ),
inference(forward_demodulation,[],[f928,f1585]) ).
fof(f3313,plain,
( ! [X0] :
( singleton_set(d) = X0
| singleton_set(a) = X0
| ~ member(X0,ordered_pair(a,b)) )
| ~ spl0_58 ),
inference(forward_demodulation,[],[f3312,f9]) ).
fof(f3314,plain,
( ! [X0] :
( singleton_set(d) = X0
| singleton_set(d) = X0
| ~ member(X0,ordered_pair(a,b)) )
| ~ spl0_58 ),
inference(forward_demodulation,[],[f3313,f1585]) ).
fof(f3315,plain,
( ! [X0] :
( singleton_set(d) = X0
| ~ member(X0,ordered_pair(a,b)) )
| ~ spl0_58 ),
inference(duplicate_literal_removal,[],[f3314]) ).
fof(f3316,plain,
( ! [X0] :
( ~ member(X0,ordered_pair(d,b))
| singleton_set(d) = X0 )
| ~ spl0_58 ),
inference(forward_demodulation,[],[f3315,f1585]) ).
fof(f3319,plain,
( non_ordered_pair(d,b) = singleton_set(d)
| ~ spl0_58 ),
inference(resolution,[],[f3316,f200]) ).
fof(f3490,plain,
( singleton_set(d) != singleton_set(d)
| ~ little_set(b)
| ~ little_set(d)
| b = d
| ~ spl0_58 ),
inference(superposition,[],[f282,f3319]) ).
fof(f3492,plain,
( ~ little_set(b)
| ~ little_set(d)
| b = d
| ~ spl0_58 ),
inference(trivial_inequality_removal,[],[f3490]) ).
fof(f3494,plain,
( ~ little_set(d)
| b = d
| ~ spl0_58 ),
inference(forward_subsumption_resolution,[],[f3492,f166]) ).
fof(f3500,plain,
( b = d
| ~ spl0_58 ),
inference(forward_subsumption_resolution,[],[f3494,f168]) ).
fof(f3502,plain,
( $false
| ~ spl0_58 ),
inference(forward_subsumption_resolution,[],[f3500,f170]) ).
fof(f3503,plain,
~ spl0_58,
inference(avatar_contradiction_clause,[],[f3502]) ).
cnf(s17,plain,
( spl0_25
| spl0_26 ),
inference(sat_conversion,[],[f930]) ).
cnf(s54,plain,
( ~ spl0_26
| spl0_58 ),
inference(sat_conversion,[],[f1623]) ).
cnf(s58,plain,
( ~ spl0_25
| spl0_58 ),
inference(sat_conversion,[],[f1658]) ).
cnf(s91,plain,
~ spl0_58,
inference(sat_conversion,[],[f3503]) ).
cnf(s92,plain,
~ spl0_25,
inference(rat,[],[s58,s91]) ).
cnf(s93,plain,
~ spl0_26,
inference(rat,[],[s54,s91]) ).
cnf(s94,plain,
$false,
inference(rat,[],[s17,s93,s92]) ).
fof(f3504,plain,
$false,
inference(avatar_sat_refutation,[],[s94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:08:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 3.21/1.40 % (3541940)Input is clausal, will run a generic CNF schedule.
% 3.21/1.40 % (3541949)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1952778016:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.21/1.40 % (3541949)Refutation not found, incomplete strategy
% 3.21/1.40 % (3541949)------------------------------
% 3.21/1.40 % (3541949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.40 % (3541949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.40 % (3541949)CaDiCaL version: 2.1.3
% 3.21/1.40 % (3541949)Termination reason: Refutation not found, incomplete strategy
% 3.21/1.40 % (3541949)Time elapsed: 0.002 s
% 3.21/1.40 % (3541949)Peak memory usage: 88 MB
% 3.21/1.40 % (3541949)Instructions burned: 2 (million)
% 3.21/1.40 % (3541946)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=957790489:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.21/1.40 % (3541947)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2192451733:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.21/1.40 % (3541951)dis-21_1_sil=8000:lcm=predicate:random_seed=452288587: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)
% 3.21/1.40 % (3541945)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=2191295879:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.21/1.40 % (3541948)lrs+10_1_sil=8000:sp=occurrence:random_seed=618645659:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.21/1.40 % (3541950)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1567668526:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.21/1.40 % (3541948)Refutation not found, incomplete strategy
% 3.21/1.40 % (3541948)------------------------------
% 3.21/1.40 % (3541948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.40 % (3541948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.40 % (3541948)CaDiCaL version: 2.1.3
% 3.21/1.40 % (3541948)Termination reason: Refutation not found, incomplete strategy
% 3.21/1.40 % (3541948)Time elapsed: 0.002 s
% 3.21/1.40 % (3541948)Peak memory usage: 87 MB
% 3.21/1.40 % (3541948)Instructions burned: 1 (million)
% 3.21/1.40 % (3541951)Instruction limit reached!
% 3.21/1.40 % (3541951)------------------------------
% 3.21/1.40 % (3541951)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.40 % (3541951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.40 % (3541951)CaDiCaL version: 2.1.3
% 3.21/1.40 % (3541951)Termination reason: Instruction limit
% 3.21/1.40 % (3541951)Termination phase: Saturation
% 3.21/1.40 % (3541951)Time elapsed: 0.062 s
% 3.21/1.40 % (3541951)Peak memory usage: 88 MB
% 3.21/1.40 % (3541951)Instructions burned: 117 (million)
% 3.21/1.40 % (3541950)First to succeed.
% 3.21/1.40 % (3541950)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3541940"
% 3.21/1.40 % (3541949)------------------------------
% 3.21/1.40 % (3541949)------------------------------
% 3.21/1.40 % (3541959)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=467233948:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.21/1.40 % (3541959)Refutation not found, incomplete strategy
% 3.21/1.40 % (3541959)------------------------------
% 3.21/1.40 % (3541959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.21/1.40 % (3541959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.21/1.40 % (3541959)CaDiCaL version: 2.1.3
% 3.21/1.40 % (3541959)Termination reason: Refutation not found, incomplete strategy
% 3.21/1.40 % (3541959)Time elapsed: 0.002 s
% 3.21/1.40 % (3541959)Peak memory usage: 88 MB
% 3.21/1.40 % (3541959)Instructions burned: 1 (million)
% 3.21/1.40 % (3541948)------------------------------
% 3.21/1.40 % (3541948)------------------------------
% 3.21/1.40 % (3541960)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=148951839:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.21/1.40 % (3541960)Also succeeded, but the first one will report.
% 4.39/1.60 % (3541950)Refutation found. Thanks to Tanya!
% 4.39/1.60 % SZS status Unsatisfiable for theBenchmark
% 4.39/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 4.52/1.60 % (3541950)------------------------------
% 4.52/1.60 % (3541950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.52/1.60 % (3541950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.52/1.60 % (3541950)CaDiCaL version: 2.1.3
% 4.52/1.60 % (3541950)Termination reason: Refutation
% 4.52/1.60 % (3541950)Time elapsed: 0.113 s
% 4.52/1.60 % (3541950)Peak memory usage: 91 MB
% 4.52/1.60 % (3541950)Instructions burned: 160 (million)
% 4.52/1.60 % (3541950)------------------------------
% 4.52/1.60 % (3541950)------------------------------
% 4.52/1.60 % (3541940)Success in time 0.546 s
% 4.52/1.60 % Vampire exiting
%------------------------------------------------------------------------------