%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET081-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:40:00 PM UTC 2026
% Result : Unsatisfiable 3.55s 1.45s
% Output : Refutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 11 ( 7 unt; 1 def)
% Number of atoms : 17 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 12 ( 6 ~; 5 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f101,negated_conjecture,
member(y,singleton(x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_only_member_in_singleton_1) ).
fof(f102,negated_conjecture,
y != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_only_member_in_singleton_2) ).
fof(f109,plain,
member(y,unordered_pair(x,x)),
inference(definition_unfolding,[],[f101,f12]) ).
fof(f148,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f149,plain,
~ sQ0_eqProxy(y,x),
inference(equality_proxy_replacement,[],[f102,f148]) ).
fof(f164,plain,
! [X2,X0,X1] :
( sQ0_eqProxy(X0,X2)
| sQ0_eqProxy(X0,X1)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(equality_proxy_replacement,[],[f8,f148,f148]) ).
fof(f199,plain,
! [X0] :
( sQ0_eqProxy(y,X0)
| ~ member(y,unordered_pair(X0,x)) ),
inference(resolution,[],[f164,f149]) ).
fof(f201,plain,
~ member(y,unordered_pair(x,x)),
inference(resolution,[],[f199,f149]) ).
fof(f202,plain,
$false,
inference(resolution,[],[f201,f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET081-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 00:31:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.55/1.45 % (1924163)Input is clausal, will run a generic CNF schedule.
% 3.55/1.45 % (1924171)lrs+10_1_sil=8000:sp=occurrence:random_seed=4017933012:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.55/1.45 % (1924171)Refutation not found, incomplete strategy
% 3.55/1.45 % (1924171)------------------------------
% 3.55/1.45 % (1924171)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (1924171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (1924171)CaDiCaL version: 2.1.3
% 3.55/1.45 % (1924171)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.45 % (1924171)Time elapsed: 0.001 s
% 3.55/1.45 % (1924171)Peak memory usage: 87 MB
% 3.55/1.45 % (1924173)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2042052192:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.55/1.45 % (1924169)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2877203237:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.55/1.45 % (1924172)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2117395007:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.55/1.45 % (1924174)dis-21_1_sil=8000:lcm=predicate:random_seed=2991824547: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)
% 3.55/1.45 % (1924168)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=811690367:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.55/1.45 % (1924170)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1407353551:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.55/1.45 % (1924174)First to succeed.
% 3.55/1.45 % (1924174)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1924163"
% 3.55/1.45 % (1924173)Also succeeded, but the first one will report.
% 3.55/1.45 % (1924172)Instruction limit reached!
% 3.55/1.45 % (1924172)------------------------------
% 3.55/1.45 % (1924172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (1924172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (1924172)CaDiCaL version: 2.1.3
% 3.55/1.45 % (1924172)Termination reason: Instruction limit
% 3.55/1.45 % (1924172)Termination phase: Saturation
% 3.55/1.45 % (1924172)Time elapsed: 0.067 s
% 3.55/1.45 % (1924172)Peak memory usage: 89 MB
% 3.55/1.45 % (1924172)Instructions burned: 115 (million)
% 3.55/1.45 % (1924171)------------------------------
% 3.55/1.45 % (1924171)------------------------------
% 3.55/1.45 % (1924183)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=772665268: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)
% 3.55/1.45 % (1924183)Also succeeded, but the first one will report.
% 3.55/1.45 % (1924182)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=2699754472:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.55/1.45 % (1924182)Refutation not found, incomplete strategy
% 3.55/1.45 % (1924182)------------------------------
% 3.55/1.45 % (1924182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (1924182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (1924182)CaDiCaL version: 2.1.3
% 3.55/1.45 % (1924182)Termination reason: Refutation not found, incomplete strategy
% 3.55/1.45 % (1924182)Time elapsed: 0.003 s
% 3.55/1.45 % (1924182)Peak memory usage: 88 MB
% 3.55/1.45 % (1924182)Instructions burned: 3 (million)
% 3.55/1.45 % (1924174)Refutation found. Thanks to Tanya!
% 3.55/1.45 % SZS status Unsatisfiable for theBenchmark
% 3.55/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.55/1.45 % (1924174)------------------------------
% 3.55/1.45 % (1924174)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.55/1.45 % (1924174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.55/1.45 % (1924174)CaDiCaL version: 2.1.3
% 3.55/1.45 % (1924174)Termination reason: Refutation
% 3.55/1.45 % (1924174)Time elapsed: 0.004 s
% 3.55/1.45 % (1924174)Peak memory usage: 88 MB
% 3.55/1.45 % (1924174)Instructions burned: 6 (million)
% 3.55/1.45 % (1924174)------------------------------
% 3.55/1.45 % (1924174)------------------------------
% 3.55/1.45 % (1924163)Success in time 0.423 s
% 3.55/1.45 % Vampire exiting
%------------------------------------------------------------------------------