%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU172+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:47:34 PM UTC 2026
% Result : Theorem 3.37s 1.34s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 94 ( 13 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 113 ( 41 ~; 38 |; 29 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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(f20,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(f21,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(f22,negated_conjecture,
~ ! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,subset_complement(X0,X2))
& in(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,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(f24,plain,
? [X0,X1,X2] :
( in(X1,subset_complement(X0,X2))
& in(X1,X2)
& element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f25,plain,
? [X0,X1,X2] :
( in(X1,subset_complement(X0,X2))
& in(X1,X2)
& element(X2,powerset(X0)) ),
inference(flattening,[],[f24]) ).
fof(f29,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f20]) ).
fof(f32,plain,
( in(sK1,subset_complement(sK0,sK2))
& in(sK1,sK2)
& element(sK2,powerset(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f25]) ).
fof(f36,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,[],[f23]) ).
fof(f37,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,[],[f36]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK6(X0,X1,X2),X0)
| in(sK6(X0,X1,X2),X1)
| ~ in(sK6(X0,X1,X2),X2) )
& ( ( in(sK6(X0,X1,X2),X0)
& ~ in(sK6(X0,X1,X2),X1) )
| in(sK6(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,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f38]) ).
fof(f40,plain,
element(sK2,powerset(sK0)),
inference(cnf_transformation,[],[f32]) ).
fof(f41,plain,
in(sK1,sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f42,plain,
in(sK1,subset_complement(sK0,sK2)),
inference(cnf_transformation,[],[f32]) ).
fof(f49,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f62,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f49]) ).
fof(f67,plain,
( in(sK1,set_difference(sK0,sK2))
| ~ element(sK2,powerset(sK0)) ),
inference(superposition,[],[f42,f57]) ).
fof(f68,plain,
in(sK1,set_difference(sK0,sK2)),
inference(forward_subsumption_resolution,[],[f67,f40]) ).
fof(f73,plain,
~ in(sK1,sK2),
inference(resolution,[],[f68,f62]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[],[f73,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU172+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:55:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.37/1.34 % (2243560)Detected formulas, will run a generic FOF schedule.
% 3.37/1.34 % (2243565)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=495287769:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.37/1.34 % (2243569)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1821019158:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.37/1.34 % (2243567)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=75707792:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.37/1.34 % (2243566)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3271542325:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.37/1.34 % (2243571)dis-21_1_sil=8000:lcm=predicate:random_seed=1928491056:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.37/1.34 % (2243570)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1225903277:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.37/1.34 % (2243568)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4111168125:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.37/1.34 % (2243568)First to succeed.
% 3.37/1.34 % (2243568)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2243560"
% 3.37/1.34 % (2243570)Also succeeded, but the first one will report.
% 3.37/1.34 % (2243569)Also succeeded, but the first one will report.
% 3.37/1.34 % (2243571)Instruction limit reached!
% 3.37/1.34 % (2243571)------------------------------
% 3.37/1.34 % (2243571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.34 % (2243571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.34 % (2243571)CaDiCaL version: 2.1.3
% 3.37/1.34 % (2243571)Termination reason: Instruction limit
% 3.37/1.34 % (2243571)Termination phase: Saturation
% 3.37/1.34 % (2243571)Time elapsed: 0.074 s
% 3.37/1.34 % (2243571)Peak memory usage: 88 MB
% 3.37/1.34 % (2243571)Instructions burned: 131 (million)
% 3.37/1.34 % (2243579)lrs+10_1_sil=8000:sp=occurrence:random_seed=2809163387:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.37/1.34 % (2243579)Also succeeded, but the first one will report.
% 3.37/1.34 % (2243568)Refutation found. Thanks to Tanya!
% 3.37/1.34 % SZS status Theorem for theBenchmark
% 3.37/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.34 % (2243568)------------------------------
% 3.37/1.34 % (2243568)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.37/1.34 % (2243568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.34 % (2243568)CaDiCaL version: 2.1.3
% 3.37/1.34 % (2243568)Termination reason: Refutation
% 3.37/1.34 % (2243568)Time elapsed: 0.003 s
% 3.37/1.34 % (2243568)Peak memory usage: 89 MB
% 3.37/1.34 % (2243568)Instructions burned: 2 (million)
% 3.37/1.34 % (2243568)------------------------------
% 3.37/1.34 % (2243568)------------------------------
% 3.37/1.34 % (2243560)Success in time 0.406 s
% 3.37/1.34 % Vampire exiting
%------------------------------------------------------------------------------