%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 12:43:09 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 18 unt; 0 def)
% Number of atoms : 26 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 14 !; 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(f120,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f123,axiom,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X1,X0) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f138,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f166,negated_conjecture,
unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_1) ).
fof(f167,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_2) ).
fof(f168,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_3_of_ordered_pair_3) ).
fof(f173,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(f224,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X1,X0) = unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f123,f12]) ).
fof(f235,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f254,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f166,f12,f173]) ).
fof(f312,plain,
null_class = unordered_pair(x,x),
inference(resolution,[],[f235,f167]) ).
fof(f313,plain,
null_class = unordered_pair(y,y),
inference(resolution,[],[f235,f168]) ).
fof(f331,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),
inference(superposition,[],[f254,f313]) ).
fof(f346,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(unordered_pair(x,null_class),unordered_pair(x,x)),
inference(forward_demodulation,[],[f331,f120]) ).
fof(f347,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(unordered_pair(x,null_class),null_class),
inference(forward_demodulation,[],[f346,f312]) ).
fof(f348,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(null_class,unordered_pair(x,null_class)),
inference(forward_demodulation,[],[f347,f120]) ).
fof(f349,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(null_class,unordered_pair(null_class,x)),
inference(forward_demodulation,[],[f348,f120]) ).
fof(f505,plain,
! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x),
inference(resolution,[],[f224,f167]) ).
fof(f547,plain,
unordered_pair(null_class,unordered_pair(null_class,null_class)) != unordered_pair(null_class,unordered_pair(null_class,null_class)),
inference(superposition,[],[f349,f505]) ).
fof(f550,plain,
$false,
inference(trivial_inequality_removal,[],[f547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET105-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.35 % Computer : n006.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 28 00:44:10 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.46 % (3487644)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (3487649)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1152637780_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.46 % (3487650)% WARNING: option uhcvi not known.
% 0.13/0.46 % (3487651)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1430784904:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.46 % (3487652)dis+10_1_sil=32000:sp=arity:random_seed=4247253310:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.46 % (3487653)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=118219506:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.46 % (3487654)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1965407175:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.46 % (3487655)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2402640921:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % (3487650)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4205473809:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.46 % (3487652) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3487644-3487652"...
% 0.13/0.46 % (3487650) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3487644-3487650"...
% 0.13/0.46 % (3487652)...printing done.
% 0.13/0.46 % (3487652)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.46 % (3487652)------------------------------
% 0.14/0.46 % (3487652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.46 % (3487652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.46 % (3487652)CaDiCaL version: 2.1.3
% 0.14/0.46 % (3487652)Termination reason: Refutation
% 0.14/0.46 % (3487652)Time elapsed: 0.010 s
% 0.14/0.46 % (3487652)Peak memory usage: 12 MB
% 0.14/0.46 % (3487652)Instructions burned: 14 (million)
% 0.14/0.46 % (3487644)Success in time 0.063 s
% 0.14/0.46 % Vampire exiting
%------------------------------------------------------------------------------