%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n016.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 12:42:38 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 70 ( 17 unt; 5 def)
% Number of atoms : 135 ( 45 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 116 ( 51 ~; 60 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 16 !; 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(f9,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(definition_unfolding,[],[f7,f6,f6]) ).
fof(f13,plain,
! [X0] :
( ~ member(X0,unordered_pair(singleton_set(m1),unordered_pair(m1,r1)))
| singleton_set(m2) = X0
| unordered_pair(m2,r2) = X0 ),
inference(superposition,[],[f5,f9]) ).
fof(f14,plain,
member(unordered_pair(m2,r2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(superposition,[],[f4,f9]) ).
fof(f15,plain,
member(singleton_set(m2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(superposition,[],[f3,f9]) ).
fof(f16,plain,
( singleton_set(m1) = singleton_set(m2)
| unordered_pair(m1,r1) = singleton_set(m2) ),
inference(resolution,[],[f15,f5]) ).
fof(f18,definition,
( spl0_1
<=> unordered_pair(m1,r1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f20,plain,
( unordered_pair(m1,r1) = singleton_set(m2)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f18]) ).
fof(f22,definition,
( spl0_2
<=> singleton_set(m1) = singleton_set(m2) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f23,plain,
( singleton_set(m1) != singleton_set(m2)
| spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f24,plain,
( singleton_set(m1) = singleton_set(m2)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f16,f22,f18]) ).
fof(f29,plain,
( member(m2,singleton_set(m1))
| ~ spl0_2 ),
inference(superposition,[],[f1,f24]) ).
fof(f30,plain,
( singleton_set(m1) = unordered_pair(m2,r2)
| unordered_pair(m1,r1) = unordered_pair(m2,r2) ),
inference(resolution,[],[f14,f5]) ).
fof(f32,definition,
( spl0_3
<=> unordered_pair(m1,r1) = unordered_pair(m2,r2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f34,plain,
( unordered_pair(m1,r1) = unordered_pair(m2,r2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f36,definition,
( spl0_4
<=> singleton_set(m1) = unordered_pair(m2,r2) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f38,plain,
( singleton_set(m1) = unordered_pair(m2,r2)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f30,f36,f32]) ).
fof(f40,plain,
( m1 = m2
| ~ spl0_2 ),
inference(resolution,[],[f29,f2]) ).
fof(f47,plain,
( unordered_pair(m1,r1) = unordered_pair(m1,r2)
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f34,f40]) ).
fof(f54,definition,
( spl0_5
<=> unordered_pair(m1,r1) = unordered_pair(m1,r2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f56,plain,
( unordered_pair(m1,r1) = unordered_pair(m1,r2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f54]) ).
fof(f62,plain,
( spl0_5
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f47,f32,f22,f54]) ).
fof(f63,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(m1,r1))
| m1 = X0
| r2 = X0 )
| ~ spl0_5 ),
inference(superposition,[],[f5,f56]) ).
fof(f64,plain,
( member(r2,unordered_pair(m1,r1))
| ~ spl0_5 ),
inference(superposition,[],[f4,f56]) ).
fof(f66,plain,
( m1 = r2
| r1 = r2
| ~ spl0_5 ),
inference(resolution,[],[f64,f5]) ).
fof(f67,plain,
( m1 = r2
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f66,f8]) ).
fof(f73,plain,
( m1 != r1
| ~ spl0_5 ),
inference(superposition,[],[f8,f67]) ).
fof(f76,plain,
( ! [X0] :
( m1 = X0
| ~ member(X0,unordered_pair(m1,r1))
| m1 = X0 )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f63,f67]) ).
fof(f77,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(m1,r1))
| m1 = X0 )
| ~ spl0_5 ),
inference(duplicate_literal_removal,[],[f76]) ).
fof(f79,plain,
( m1 = r1
| ~ spl0_5 ),
inference(resolution,[],[f77,f4]) ).
fof(f81,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f79,f73]) ).
fof(f82,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f81]) ).
fof(f107,plain,
( singleton_set(m1) = singleton_set(m2)
| singleton_set(m1) = unordered_pair(m2,r2) ),
inference(resolution,[],[f13,f3]) ).
fof(f108,plain,
( unordered_pair(m1,r1) = singleton_set(m2)
| unordered_pair(m1,r1) = unordered_pair(m2,r2) ),
inference(resolution,[],[f13,f4]) ).
fof(f111,plain,
( spl0_3
| spl0_1 ),
inference(avatar_split_clause,[],[f108,f18,f32]) ).
fof(f112,plain,
( singleton_set(m1) = unordered_pair(m2,r2)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f107,f23]) ).
fof(f113,plain,
( spl0_4
| spl0_2 ),
inference(avatar_split_clause,[],[f112,f22,f36]) ).
fof(f118,plain,
( member(r1,singleton_set(m2))
| ~ spl0_1 ),
inference(superposition,[],[f4,f20]) ).
fof(f119,plain,
( member(m1,singleton_set(m2))
| ~ spl0_1 ),
inference(superposition,[],[f3,f20]) ).
fof(f123,plain,
( member(r2,singleton_set(m1))
| ~ spl0_4 ),
inference(superposition,[],[f4,f38]) ).
fof(f126,plain,
( r1 = m2
| ~ spl0_1 ),
inference(resolution,[],[f118,f2]) ).
fof(f142,plain,
( member(m1,singleton_set(r1))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f119,f126]) ).
fof(f145,plain,
( m1 = r2
| ~ spl0_4 ),
inference(resolution,[],[f123,f2]) ).
fof(f146,plain,
( m1 != r1
| ~ spl0_4 ),
inference(superposition,[],[f8,f145]) ).
fof(f159,plain,
( m1 = r1
| ~ spl0_1 ),
inference(resolution,[],[f142,f2]) ).
fof(f160,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f159,f146]) ).
fof(f161,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f160]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f62]) ).
cnf(s5,plain,
~ spl0_5,
inference(sat_conversion,[],[f82]) ).
cnf(s10,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f111]) ).
cnf(s11,plain,
( spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f113]) ).
cnf(s12,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f161]) ).
cnf(s13,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(rat,[],[s4,s5]) ).
cnf(s15,plain,
spl0_1,
inference(rat,[],[s13,s1,s10]) ).
cnf(s16,plain,
~ spl0_4,
inference(rat,[],[s12,s15]) ).
cnf(s17,plain,
spl0_2,
inference(rat,[],[s11,s16]) ).
cnf(s18,plain,
spl0_3,
inference(rat,[],[s2,s16]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s13,s18,s17]) ).
fof(f162,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n016.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 00:13:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.46 % (3142130)Will run a generic schedule for satisfiability detection.
% 0.18/0.46 % (3142138)dis+10_1_sil=32000:sp=arity:random_seed=4179920132:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.46 % (3142136)% WARNING: option uhcvi not known.
% 0.18/0.46 % (3142138) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3142130-3142138"...
% 0.18/0.46 % (3142138)...printing done.
% 0.18/0.46 % (3142138)Refutation found. Thanks to Tanya!
% 0.18/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.46 % (3142138)------------------------------
% 0.18/0.46 % (3142138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.46 % (3142138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.46 % (3142138)CaDiCaL version: 2.1.3
% 0.18/0.46 % (3142138)Termination reason: Refutation
% 0.18/0.46 % (3142138)Time elapsed: 0.003 s
% 0.18/0.46 % (3142138)Peak memory usage: 12 MB
% 0.18/0.46 % (3142138)Instructions burned: 6 (million)
% 0.18/0.46 % (3142130)Success in time 0.03 s
% 0.18/0.46 % Vampire exiting
%------------------------------------------------------------------------------