%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET958+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:45:05 PM UTC 2026
% Result : Theorem 0.09s 0.44s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 11 unt; 0 def)
% Number of atoms : 58 ( 13 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 57 ( 25 ~; 13 |; 10 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 61 ( 53 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f3,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f4,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f9,conjecture,
! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) )
=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t111_zfmisc_1) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) )
=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f12,plain,
~ ! [X0,X1] :
( ( ! [X2] :
~ ( in(X2,X0)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) )
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X0)
=> in(ordered_pair(X5,X6),X1) ) )
=> subset(X0,X1) ),
inference(rectify,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,plain,
? [X0,X1] :
( ~ subset(X0,X1)
& ! [X2] :
( ~ in(X2,X0)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
| ~ in(ordered_pair(X5,X6),X0) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f16,plain,
? [X0,X1] :
( ~ subset(X0,X1)
& ! [X2] :
( ~ in(X2,X0)
| ? [X3,X4] : ordered_pair(X3,X4) = X2 )
& ! [X5,X6] :
( in(ordered_pair(X5,X6),X1)
| ~ in(ordered_pair(X5,X6),X0) ) ),
inference(flattening,[],[f15]) ).
fof(f18,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f4]) ).
fof(f27,plain,
! [X2] :
( ordered_pair(sK5(X2),sK6(X2)) = X2
| ~ in(X2,sK3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f28,plain,
! [X6,X5] :
( ~ in(ordered_pair(X5,X6),sK3)
| in(ordered_pair(X5,X6),sK4) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
~ subset(sK3,sK4),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK4)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),sK3) ),
inference(definition_unfolding,[],[f28,f22,f22]) ).
fof(f32,plain,
! [X2] :
( ~ in(X2,sK3)
| unordered_pair(unordered_pair(sK5(X2),sK6(X2)),singleton(sK5(X2))) = X2 ),
inference(definition_unfolding,[],[f27,f22]) ).
fof(f42,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK4)
| ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3) ),
inference(superposition,[],[f31,f18]) ).
fof(f59,plain,
in(sK0(sK3,sK4),sK3),
inference(resolution,[],[f20,f29]) ).
fof(f60,plain,
sK0(sK3,sK4) = unordered_pair(unordered_pair(sK5(sK0(sK3,sK4)),sK6(sK0(sK3,sK4))),singleton(sK5(sK0(sK3,sK4)))),
inference(resolution,[],[f59,f32]) ).
fof(f63,plain,
sK0(sK3,sK4) = unordered_pair(singleton(sK5(sK0(sK3,sK4))),unordered_pair(sK5(sK0(sK3,sK4)),sK6(sK0(sK3,sK4)))),
inference(forward_demodulation,[],[f60,f18]) ).
fof(f64,plain,
~ in(sK0(sK3,sK4),sK4),
inference(resolution,[],[f21,f29]) ).
fof(f77,plain,
( in(sK0(sK3,sK4),sK4)
| ~ in(sK0(sK3,sK4),sK3) ),
inference(superposition,[],[f42,f63]) ).
fof(f101,plain,
~ in(sK0(sK3,sK4),sK3),
inference(forward_subsumption_resolution,[],[f77,f64]) ).
fof(f106,plain,
$false,
inference(forward_subsumption_resolution,[],[f101,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET958+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:16:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.39 Running first-order model finding
% 0.09/0.39 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
% 0.09/0.44 % (398688)Will run a generic schedule for satisfiability detection.
% 0.09/0.44 % (398693)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2753191999_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.44 % TRYING [1]
% 0.09/0.44 % TRYING [2]
% 0.09/0.44 % TRYING [3]
% 0.09/0.44 % (398694)% WARNING: option uhcvi not known.
% 0.09/0.44 % (398695)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3248511646:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.44 % (398696)dis+10_1_sil=32000:sp=arity:random_seed=1583342970:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.44 % (398697)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=300900535:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.44 % (398698)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1834763674:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.44 % (398699)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3491468609:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.44 % (398694)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=339554697:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.44 % (398697) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-398688-398697"...
% 0.09/0.44 % (398698) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-398688-398698"...
% 0.09/0.44 % (398696) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-398688-398696"...
% 0.09/0.44 % (398699) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-398688-398699"...
% 0.09/0.44 % (398697)...printing done.
% 0.09/0.44 % (398698)...printing done.
% 0.09/0.44 % (398696)...printing done.
% 0.09/0.44 % (398697)Refutation found. Thanks to Tanya!
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.44 % (398697)------------------------------
% 0.09/0.44 % (398697)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.44 % (398697)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.44 % (398697)CaDiCaL version: 2.1.3
% 0.09/0.44 % (398697)Termination reason: Refutation
% 0.09/0.44 % (398697)Time elapsed: 0.004 s
% 0.09/0.44 % (398697)Peak memory usage: 12 MB
% 0.09/0.44 % (398697)Instructions burned: 4 (million)
% 0.09/0.44 % (398688)Success in time 0.037 s
% 0.09/0.44 % Vampire exiting
%------------------------------------------------------------------------------