%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 12:44:57 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 8 unt; 0 def)
% Number of atoms : 48 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 40 ( 15 ~; 14 |; 1 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 48 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f4,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
fof(f5,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
| in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f13,conjecture,
! [X0,X1,X2] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).
fof(f14,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(set_union2(unordered_pair(X0,X1),X2),X2)
=> in(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( subset(X0,X1)
=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f19,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ~ in(X0,X2)
& subset(set_union2(unordered_pair(X0,X1),X2),X2) ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f31,plain,
! [X2,X3,X0,X1] :
( X0 != X3
| in(X3,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f4]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,X1)
| in(X3,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f5]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f45,plain,
subset(set_union2(unordered_pair(sK4,sK5),sK6),sK6),
inference(cnf_transformation,[],[f22]) ).
fof(f46,plain,
~ in(sK4,sK6),
inference(cnf_transformation,[],[f22]) ).
fof(f47,plain,
! [X2,X3,X1] :
( in(X3,X2)
| unordered_pair(X3,X1) != X2 ),
inference(equality_resolution,[],[f31]) ).
fof(f48,plain,
! [X3,X1] : in(X3,unordered_pair(X3,X1)),
inference(equality_resolution,[],[f47]) ).
fof(f53,plain,
! [X3,X0,X1] :
( in(X3,set_union2(X0,X1))
| ~ in(X3,X1) ),
inference(equality_resolution,[],[f36]) ).
fof(f64,plain,
subset(set_union2(sK6,unordered_pair(sK4,sK5)),sK6),
inference(superposition,[],[f45,f25]) ).
fof(f78,plain,
! [X0] :
( ~ in(X0,set_union2(sK6,unordered_pair(sK4,sK5)))
| in(X0,sK6) ),
inference(resolution,[],[f38,f64]) ).
fof(f80,plain,
! [X0] :
( ~ in(X0,unordered_pair(sK4,sK5))
| in(X0,sK6) ),
inference(resolution,[],[f78,f53]) ).
fof(f86,plain,
in(sK4,sK6),
inference(resolution,[],[f80,f48]) ).
fof(f88,plain,
$false,
inference(forward_subsumption_resolution,[],[f86,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET906+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 03:08:55 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 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
% 0.17/0.48 % (1830898)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1830903)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4048112579_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (1830904)% WARNING: option uhcvi not known.
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % (1830904)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1293921315:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (1830905)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2255080330:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (1830906)dis+10_1_sil=32000:sp=arity:random_seed=3852863505:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (1830907)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=539823083:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (1830908)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=755246935:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (1830909)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2771418015:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % (1830906) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1830898-1830906"...
% 0.17/0.48 % (1830907) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1830898-1830907"...
% 0.17/0.48 % (1830904) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1830898-1830904"...
% 0.17/0.48 % (1830909) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1830898-1830909"...
% 0.17/0.48 % (1830907)...printing done.
% 0.17/0.48 % (1830906)...printing done.
% 0.17/0.48 % (1830904)...printing done.
% 0.17/0.48 % (1830907)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1830907)------------------------------
% 0.17/0.48 % (1830907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1830907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1830907)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1830907)Termination reason: Refutation
% 0.17/0.48 % (1830907)Time elapsed: 0.003 s
% 0.17/0.48 % (1830907)Peak memory usage: 12 MB
% 0.17/0.48 % (1830907)Instructions burned: 3 (million)
% 0.17/0.48 % (1830898)Success in time 0.048 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------