%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n020.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 3.43s 1.26s
% Output : Refutation 3.43s
% 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(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(f155,plain,
? [X0,X1,X2] :
( in(X1,subset_complement(X0,X2))
& in(X1,X2)
& element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f97]) ).
fof(f156,plain,
? [X0,X1,X2] :
( in(X1,subset_complement(X0,X2))
& in(X1,X2)
& element(X2,powerset(X0)) ),
inference(flattening,[],[f155]) ).
fof(f176,plain,
! [X0,X1] :
( subset_complement(X0,X1) = set_difference(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f198,plain,
( in(sK4,subset_complement(sK3,sK5))
& in(sK4,sK5)
& element(sK5,powerset(sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f156]) ).
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(nnf_transformation,[],[f17]) ).
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) ) ) )
& ( ! [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,[],[f219]) ).
fof(f221,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,[],[f220]) ).
fof(f222,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK11(X0,X1,X2),X0)
| in(sK11(X0,X1,X2),X1)
| ~ in(sK11(X0,X1,X2),X2) )
& ( ( in(sK11(X0,X1,X2),X0)
& ~ in(sK11(X0,X1,X2),X1) )
| in(sK11(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,[sK11]),skolemize(X3,sK11(X0,X1,X2))],[f221]) ).
fof(f308,plain,
element(sK5,powerset(sK3)),
inference(cnf_transformation,[],[f198]) ).
fof(f309,plain,
in(sK4,sK5),
inference(cnf_transformation,[],[f198]) ).
fof(f310,plain,
in(sK4,subset_complement(sK3,sK5)),
inference(cnf_transformation,[],[f198]) ).
fof(f355,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f222]) ).
fof(f412,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f176]) ).
fof(f499,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f355]) ).
fof(f548,plain,
( in(sK4,set_difference(sK3,sK5))
| ~ element(sK5,powerset(sK3)) ),
inference(superposition,[],[f310,f412]) ).
fof(f549,plain,
in(sK4,set_difference(sK3,sK5)),
inference(forward_subsumption_resolution,[],[f548,f308]) ).
fof(f580,plain,
~ in(sK4,sK5),
inference(resolution,[],[f549,f499]) ).
fof(f585,plain,
$false,
inference(forward_subsumption_resolution,[],[f580,f309]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 THM
% 0.10/0.38 % Computer : n020.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:53:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 3.43/1.26 % (4008900)Detected formulas, will run a generic FOF schedule.
% 3.43/1.26 % (4008909)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3704638066:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.43/1.26 % (4008908)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3272904108:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.43/1.26 % (4008905)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=3615455131:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.43/1.26 % (4008911)dis-21_1_sil=8000:lcm=predicate:random_seed=566293898: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)
% 3.43/1.26 % (4008906)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=2796082146:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.43/1.26 % (4008907)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=1682445509:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.43/1.26 % (4008910)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4249569216:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.43/1.26 % (4008908)First to succeed.
% 3.43/1.26 % (4008908)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4008900"
% 3.43/1.26 % (4008910)Also succeeded, but the first one will report.
% 3.43/1.26 % (4008911)Instruction limit reached!
% 3.43/1.26 % (4008911)------------------------------
% 3.43/1.26 % (4008911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.26 % (4008911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.26 % (4008911)CaDiCaL version: 2.1.3
% 3.43/1.26 % (4008911)Termination reason: Instruction limit
% 3.43/1.26 % (4008911)Termination phase: Saturation
% 3.43/1.26 % (4008911)Time elapsed: 0.077 s
% 3.43/1.26 % (4008911)Peak memory usage: 89 MB
% 3.43/1.26 % (4008911)Instructions burned: 130 (million)
% 3.43/1.26 % (4008909)Instruction limit reached!
% 3.43/1.26 % (4008909)------------------------------
% 3.43/1.26 % (4008909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.26 % (4008909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.26 % (4008909)CaDiCaL version: 2.1.3
% 3.43/1.26 % (4008909)Termination reason: Instruction limit
% 3.43/1.26 % (4008909)Termination phase: Saturation
% 3.43/1.26 % (4008909)Time elapsed: 0.077 s
% 3.43/1.26 % (4008909)Peak memory usage: 89 MB
% 3.43/1.26 % (4008909)Instructions burned: 121 (million)
% 3.43/1.26 % (4008920)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3273061392:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.43/1.26 % (4008919)lrs+10_1_sil=8000:sp=occurrence:random_seed=3613951194:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.43/1.26 % (4008920)Instruction limit reached!
% 3.43/1.26 % (4008920)------------------------------
% 3.43/1.26 % (4008920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.26 % (4008920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.26 % (4008920)CaDiCaL version: 2.1.3
% 3.43/1.26 % (4008920)Termination reason: Instruction limit
% 3.43/1.26 % (4008920)Termination phase: Saturation
% 3.43/1.26 % (4008920)Time elapsed: 0.046 s
% 3.43/1.26 % (4008920)Peak memory usage: 90 MB
% 3.43/1.26 % (4008920)Instructions burned: 157 (million)
% 3.43/1.26 % (4008908)Refutation found. Thanks to Tanya!
% 3.43/1.26 % SZS status Theorem for theBenchmark
% 3.43/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.26 % (4008908)------------------------------
% 3.43/1.26 % (4008908)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.26 % (4008908)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.26 % (4008908)CaDiCaL version: 2.1.3
% 3.43/1.26 % (4008908)Termination reason: Refutation
% 3.43/1.26 % (4008908)Time elapsed: 0.010 s
% 3.43/1.26 % (4008908)Peak memory usage: 89 MB
% 3.43/1.26 % (4008908)Instructions burned: 14 (million)
% 3.43/1.26 % (4008908)------------------------------
% 3.43/1.26 % (4008908)------------------------------
% 3.43/1.26 % (4008900)Success in time 0.436 s
% 3.43/1.26 % Vampire exiting
%------------------------------------------------------------------------------