%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET031-4 : 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 12:39:42 PM UTC 2026
% Result : Unsatisfiable 3.62s 1.49s
% Output : Refutation 3.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 10 unt; 3 def)
% Number of atoms : 72 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 27 ~; 32 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| X0 != ordered_pair(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate4) ).
fof(f16,plain,
! [X2,X0,X1] :
( ordered_pair_predicate(X0)
| ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair(X1,X2) != X0 ),
inference(reorient_equations,[],[f15]) ).
fof(f89,axiom,
! [X0] :
( member(f18(X0),X0)
| relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation2) ).
fof(f90,axiom,
! [X0] :
( ~ ordered_pair_predicate(f18(X0))
| relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',relation3) ).
fof(f146,axiom,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| little_set(f29(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f147,axiom,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| little_set(f30(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
fof(f149,axiom,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| X0 = ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose4) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ member(X0,compose(X1,X2))
| ordered_pair(f29(X0,X1,X2),f30(X0,X1,X2)) = X0 ),
inference(reorient_equations,[],[f149]) ).
fof(f162,negated_conjecture,
~ relation(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_composition_is_a_relation) ).
fof(f164,plain,
! [X2,X1] :
( ordered_pair_predicate(ordered_pair(X1,X2))
| ~ little_set(X1)
| ~ little_set(X2) ),
inference(equality_resolution,[],[f16]) ).
fof(f167,plain,
! [X0,X1] :
( little_set(f29(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) ),
inference(resolution,[],[f146,f89]) ).
fof(f168,plain,
! [X0,X1] :
( little_set(f30(f18(compose(X0,X1)),X0,X1))
| relation(compose(X0,X1)) ),
inference(resolution,[],[f147,f89]) ).
fof(f170,plain,
! [X0,X1] :
( relation(compose(X0,X1))
| f18(compose(X0,X1)) = ordered_pair(f29(f18(compose(X0,X1)),X0,X1),f30(f18(compose(X0,X1)),X0,X1)) ),
inference(resolution,[],[f150,f89]) ).
fof(f199,plain,
f18(compose(a,b)) = ordered_pair(f29(f18(compose(a,b)),a,b),f30(f18(compose(a,b)),a,b)),
inference(resolution,[],[f170,f162]) ).
fof(f203,plain,
( ordered_pair_predicate(f18(compose(a,b)))
| ~ little_set(f29(f18(compose(a,b)),a,b))
| ~ little_set(f30(f18(compose(a,b)),a,b)) ),
inference(superposition,[],[f164,f199]) ).
fof(f205,definition,
( spl0_1
<=> little_set(f30(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f207,plain,
( ~ little_set(f30(f18(compose(a,b)),a,b))
| spl0_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f209,definition,
( spl0_2
<=> little_set(f29(f18(compose(a,b)),a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f211,plain,
( ~ little_set(f29(f18(compose(a,b)),a,b))
| spl0_2 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f213,definition,
( spl0_3
<=> ordered_pair_predicate(f18(compose(a,b))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f215,plain,
( ordered_pair_predicate(f18(compose(a,b)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f203,f213,f209,f205]) ).
fof(f243,plain,
( relation(compose(a,b))
| spl0_1 ),
inference(resolution,[],[f207,f168]) ).
fof(f244,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f243,f162]) ).
fof(f245,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f244]) ).
fof(f246,plain,
( relation(compose(a,b))
| spl0_2 ),
inference(resolution,[],[f211,f167]) ).
fof(f247,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f246,f162]) ).
fof(f248,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f249,plain,
( relation(compose(a,b))
| ~ spl0_3 ),
inference(resolution,[],[f215,f90]) ).
fof(f250,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f249,f162]) ).
fof(f251,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f250]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f216]) ).
cnf(s5,plain,
spl0_1,
inference(sat_conversion,[],[f245]) ).
cnf(s6,plain,
spl0_2,
inference(sat_conversion,[],[f248]) ).
cnf(s7,plain,
~ spl0_3,
inference(sat_conversion,[],[f251]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s7,s6,s5]) ).
fof(f252,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET031-4 : 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 00:15:48 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.62/1.49 % (3544868)Input is clausal, will run a generic CNF schedule.
% 3.62/1.49 % (3544874)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3855390230:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.62/1.49 % (3544877)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2277370802:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.62/1.49 % (3544875)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1042092668:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.62/1.49 % (3544879)dis-21_1_sil=8000:lcm=predicate:random_seed=2447100833: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)
% 3.62/1.49 % (3544876)lrs+10_1_sil=8000:sp=occurrence:random_seed=837983434:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.62/1.49 % (3544873)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=1075001730:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.62/1.49 % (3544878)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1480709412:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.62/1.49 % (3544876)First to succeed.
% 3.62/1.49 % (3544876)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3544868"
% 3.62/1.49 % (3544877)Refutation not found, incomplete strategy
% 3.62/1.49 % (3544877)------------------------------
% 3.62/1.49 % (3544877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (3544877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (3544877)CaDiCaL version: 2.1.3
% 3.62/1.49 % (3544877)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.49 % (3544877)Time elapsed: 0.013 s
% 3.62/1.49 % (3544877)Peak memory usage: 88 MB
% 3.62/1.49 % (3544877)Instructions burned: 20 (million)
% 3.62/1.49 % (3544878)Also succeeded, but the first one will report.
% 3.62/1.49 % (3544879)Instruction limit reached!
% 3.62/1.49 % (3544879)------------------------------
% 3.62/1.49 % (3544879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (3544879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (3544879)CaDiCaL version: 2.1.3
% 3.62/1.49 % (3544879)Termination reason: Instruction limit
% 3.62/1.49 % (3544879)Termination phase: Saturation
% 3.62/1.49 % (3544879)Time elapsed: 0.064 s
% 3.62/1.49 % (3544879)Peak memory usage: 89 MB
% 3.62/1.49 % (3544879)Instructions burned: 117 (million)
% 3.62/1.49 % (3544887)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=3134672444:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.62/1.49 % (3544887)Refutation not found, incomplete strategy
% 3.62/1.49 % (3544887)------------------------------
% 3.62/1.49 % (3544887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (3544887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (3544887)CaDiCaL version: 2.1.3
% 3.62/1.49 % (3544887)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.49 % (3544887)Time elapsed: 0.002 s
% 3.62/1.49 % (3544887)Peak memory usage: 88 MB
% 3.62/1.49 % (3544887)Instructions burned: 1 (million)
% 3.62/1.49 % (3544876)Refutation found. Thanks to Tanya!
% 3.62/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.62/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.62/1.49 % (3544876)------------------------------
% 3.62/1.49 % (3544876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.49 % (3544876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.49 % (3544876)CaDiCaL version: 2.1.3
% 3.62/1.49 % (3544876)Termination reason: Refutation
% 3.62/1.49 % (3544876)Time elapsed: 0.005 s
% 3.62/1.49 % (3544876)Peak memory usage: 89 MB
% 3.62/1.49 % (3544876)Instructions burned: 5 (million)
% 3.62/1.49 % (3544876)------------------------------
% 3.62/1.49 % (3544876)------------------------------
% 3.62/1.49 % (3544868)Success in time 0.435 s
% 3.62/1.49 % Vampire exiting
%------------------------------------------------------------------------------