%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU172+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:52:14 PM UTC 2026
% Result : Theorem 0.41s 0.48s
% Output : Refutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 93 ( 14 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 111 ( 40 ~; 37 |; 29 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 48 ( 39 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f18,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,X1) = set_difference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f96,conjecture,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,subset_complement(X0,X2))
& in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f97,negated_conjecture,
~ ! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,subset_complement(X0,X2))
& in(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f129,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f169,plain,
? [X0,X1,X2] :
( in(X1,subset_complement(X0,X2))
& in(X1,X2)
& element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f97]) ).
fof(f170,plain,
? [X0,X1,X2] :
( in(X1,subset_complement(X0,X2))
& in(X1,X2)
& element(X2,powerset(X0)) ),
inference(flattening,[],[f169]) ).
fof(f218,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f219,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f218]) ).
fof(f220,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f219]) ).
fof(f221,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK15(X0,X1,X2),X0)
| in(sK15(X0,X1,X2),X1)
| ~ in(sK15(X0,X1,X2),X2) )
& ( ( in(sK15(X0,X1,X2),X0)
& ~ in(sK15(X0,X1,X2),X1) )
| in(sK15(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X3,sK15(X0,X1,X2))],[f220]) ).
fof(f248,plain,
( in(sK26,subset_complement(sK25,sK27))
& in(sK26,sK27)
& element(sK27,powerset(sK25)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25,sK26,sK27]),skolemize(X0,sK25),skolemize(X1,sK26),skolemize(X2,sK27)],[f170]) ).
fof(f309,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f221]) ).
fof(f315,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| set_difference(X0,X1) = subset_complement(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f408,plain,
element(sK27,powerset(sK25)),
inference(cnf_transformation,[],[f248]) ).
fof(f409,plain,
in(sK26,sK27),
inference(cnf_transformation,[],[f248]) ).
fof(f410,plain,
in(sK26,subset_complement(sK25,sK27)),
inference(cnf_transformation,[],[f248]) ).
fof(f518,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f309]) ).
fof(f1577,plain,
subset_complement(sK25,sK27) = set_difference(sK25,sK27),
inference(resolution,[],[f315,f408]) ).
fof(f1893,plain,
in(sK26,set_difference(sK25,sK27)),
inference(superposition,[],[f410,f1577]) ).
fof(f1963,plain,
~ in(sK26,sK27),
inference(resolution,[],[f1893,f518]) ).
fof(f1970,plain,
$false,
inference(forward_subsumption_resolution,[],[f1963,f409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU172+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n013.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 03:52:21 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 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
% 0.41/0.48 % (786277)Will run a generic schedule for satisfiability detection.
% 0.41/0.48 % (786282)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=281832050_2999 on theBenchmark for (2999ds/0Mi)
% 0.41/0.48 % (786283)% WARNING: option uhcvi not known.
% 0.41/0.48 % TRYING [1]
% 0.41/0.48 % TRYING [2]
% 0.41/0.48 % (786284)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1386454594:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.41/0.48 % (786285)dis+10_1_sil=32000:sp=arity:random_seed=922973333:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.41/0.48 % (786286)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=699378684:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.41/0.48 % (786287)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1165656276:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.41/0.48 % (786288)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2942088308:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.41/0.48 % TRYING [3]
% 0.41/0.48 % (786283)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=429466053:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.41/0.48 % TRYING [4]
% 0.41/0.48 % (786285) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-786277-786285"...
% 0.41/0.48 % (786285)...printing done.
% 0.41/0.48 % (786285)Refutation found. Thanks to Tanya!
% 0.41/0.48 % SZS status Theorem for theBenchmark
% 0.41/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.41/0.48 % (786285)------------------------------
% 0.41/0.48 % (786285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.41/0.48 % (786285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.41/0.48 % (786285)CaDiCaL version: 2.1.3
% 0.41/0.48 % (786285)Termination reason: Refutation
% 0.41/0.48 % (786285)Time elapsed: 0.037 s
% 0.41/0.48 % (786285)Peak memory usage: 12 MB
% 0.41/0.48 % (786285)Instructions burned: 55 (million)
% 0.41/0.48 % (786277)Success in time 0.072 s
% 0.41/0.48 % Vampire exiting
%------------------------------------------------------------------------------