%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET115-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:43:10 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.50s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
fof(f177,axiom,
! [X0] :
( ordered_pair(first(X0),second(X0)) = X0
| first(X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f181,negated_conjecture,
ordered_pair(first(x),second(x)) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets3_1) ).
fof(f182,plain,
x != ordered_pair(first(x),second(x)),
inference(reorient_equations,[],[f181]) ).
fof(f183,negated_conjecture,
first(x) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).
fof(f184,plain,
x != first(x),
inference(reorient_equations,[],[f183]) ).
fof(f189,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f278,plain,
! [X0] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| first(X0) = X0 ),
inference(definition_unfolding,[],[f177,f189]) ).
fof(f282,plain,
x != unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),
inference(definition_unfolding,[],[f182,f189]) ).
fof(f1426,plain,
( x != x
| x = first(x) ),
inference(superposition,[],[f282,f278]) ).
fof(f1451,plain,
x = first(x),
inference(trivial_inequality_removal,[],[f1426]) ).
fof(f1454,plain,
$false,
inference(forward_subsumption_resolution,[],[f1451,f184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET115-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 % Computer : n010.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Mon Sep 28 00:47:48 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.43 Running first-order model finding
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.50 % (1466806)Will run a generic schedule for satisfiability detection.
% 0.16/0.50 % (1466815)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2233147204:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.50 % (1466812)% WARNING: option uhcvi not known.
% 0.16/0.50 % (1466811)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2925762143_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.50 % (1466812)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4056383003:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.50 % (1466813)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=315942432:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.50 % (1466814)dis+10_1_sil=32000:sp=arity:random_seed=3502547125:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.50 % (1466816)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4010447749:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.50 % (1466817)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4035290296:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.50 % (1466815) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1466806-1466815"...
% 0.16/0.50 % (1466815)...printing done.
% 0.16/0.50 % (1466815)Refutation found. Thanks to Tanya!
% 0.16/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.50 % (1466815)------------------------------
% 0.16/0.50 % (1466815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.50 % (1466815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.50 % (1466815)CaDiCaL version: 2.1.3
% 0.16/0.50 % (1466815)Termination reason: Refutation
% 0.16/0.50 % (1466815)Time elapsed: 0.023 s
% 0.16/0.50 % (1466815)Peak memory usage: 12 MB
% 0.16/0.50 % (1466815)Instructions burned: 66 (million)
% 0.16/0.50 % (1466806)Success in time 0.056 s
% 0.16/0.50 % Vampire exiting
%------------------------------------------------------------------------------