%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:47:16 PM UTC 2026
% Result : Theorem 2.68s 1.33s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 16 unt; 0 def)
% Number of atoms : 159 ( 11 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 182 ( 68 ~; 72 |; 32 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 85 ( 79 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f8,axiom,
! [X0,X1] :
( preboolean(X1)
=> ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(f9,axiom,
! [X0] : preboolean(finite_subsets(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(f11,axiom,
! [X0] :
( ~ empty(powerset(X0))
& cup_closed(powerset(X0))
& diff_closed(powerset(X0))
& preboolean(powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(f24,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f26,conjecture,
! [X0] : subset(finite_subsets(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_finsub_1) ).
fof(f27,negated_conjecture,
~ ! [X0] : subset(finite_subsets(X0),powerset(X0)),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f29,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f24]) ).
fof(f51,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f52,plain,
! [X0,X1] :
( ( X1 = finite_subsets(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ( subset(X2,X0)
& finite(X2) ) ) )
| ~ preboolean(X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f57,plain,
? [X0] : ~ subset(finite_subsets(X0),powerset(X0)),
inference(ennf_transformation,[],[f27]) ).
fof(f58,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f59,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f58]) ).
fof(f66,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f67,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK0(X0,X1),X1)
& in(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0)
| ~ finite(X2) )
& ( ( subset(X2,X0)
& finite(X2) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(nnf_transformation,[],[f52]) ).
fof(f70,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0)
| ~ finite(X2) )
& ( ( subset(X2,X0)
& finite(X2) )
| ~ in(X2,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ finite(X2)
| ~ in(X2,X1) )
& ( ( subset(X2,X0)
& finite(X2) )
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3) )
& ( ( subset(X3,X0)
& finite(X3) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( ( X1 = finite_subsets(X0)
| ( ( ~ subset(sK1(X0,X1),X0)
| ~ finite(sK1(X0,X1))
| ~ in(sK1(X0,X1),X1) )
& ( ( subset(sK1(X0,X1),X0)
& finite(sK1(X0,X1)) )
| in(sK1(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0)
| ~ finite(X3) )
& ( ( subset(X3,X0)
& finite(X3) )
| ~ in(X3,X1) ) )
| finite_subsets(X0) != X1 ) )
| ~ preboolean(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f71]) ).
fof(f83,plain,
~ subset(finite_subsets(sK12),powerset(sK12)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f57]) ).
fof(f84,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f92,plain,
! [X3,X0,X1] :
( ~ in(X3,X0)
| in(X3,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f93,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f94,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f96,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| finite_subsets(X0) != X1
| ~ preboolean(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X0] : preboolean(finite_subsets(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f106,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f11]) ).
fof(f134,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f136,plain,
~ subset(finite_subsets(sK12),powerset(sK12)),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f139,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f146,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,finite_subsets(X0))
| ~ preboolean(finite_subsets(X0)) ),
inference(equality_resolution,[],[f96]) ).
fof(f163,plain,
! [X2,X0,X1] :
( subset(X0,X1)
| ~ subset(X0,X2)
| in(sK0(X0,X1),X2) ),
inference(resolution,[],[f92,f93]) ).
fof(f170,plain,
! [X3,X0] :
( ~ in(X3,finite_subsets(X0))
| subset(X3,X0) ),
inference(forward_subsumption_resolution,[],[f146,f101]) ).
fof(f210,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| in(X0,powerset(X1)) ),
inference(resolution,[],[f137,f106]) ).
fof(f253,plain,
! [X0] :
( ~ subset(finite_subsets(sK12),X0)
| in(sK0(finite_subsets(sK12),powerset(sK12)),X0) ),
inference(resolution,[],[f163,f136]) ).
fof(f268,plain,
in(sK0(finite_subsets(sK12),powerset(sK12)),finite_subsets(sK12)),
inference(resolution,[],[f253,f134]) ).
fof(f278,plain,
subset(sK0(finite_subsets(sK12),powerset(sK12)),sK12),
inference(resolution,[],[f268,f170]) ).
fof(f310,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| in(X0,powerset(X1)) ),
inference(resolution,[],[f210,f139]) ).
fof(f644,plain,
in(sK0(finite_subsets(sK12),powerset(sK12)),powerset(sK12)),
inference(resolution,[],[f310,f278]) ).
fof(f690,plain,
subset(finite_subsets(sK12),powerset(sK12)),
inference(resolution,[],[f644,f94]) ).
fof(f695,plain,
$false,
inference(forward_subsumption_resolution,[],[f690,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU113+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:37:52 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.68/1.33 % (4125822)Detected formulas, will run a generic FOF schedule.
% 2.68/1.33 % (4125832)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1082978675:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.33 % (4125832)First to succeed.
% 2.68/1.33 % (4125832)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4125822"
% 2.68/1.33 % (4125831)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=46044836:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.33 % (4125833)dis-21_1_sil=8000:lcm=predicate:random_seed=1130197720: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)
% 2.68/1.33 % (4125830)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=507235077:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.33 % (4125828)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=1400710819:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.33 % (4125827)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=3312609135:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.33 % (4125829)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=3113528973:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.33 % (4125830)Refutation not found, incomplete strategy
% 2.68/1.33 % (4125830)------------------------------
% 2.68/1.33 % (4125830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.33 % (4125830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.33 % (4125830)CaDiCaL version: 2.1.3
% 2.68/1.33 % (4125830)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.33 % (4125830)Time elapsed: 0.001 s
% 2.68/1.33 % (4125830)Peak memory usage: 88 MB
% 2.68/1.33 % (4125831)Instruction limit reached!
% 2.68/1.33 % (4125831)------------------------------
% 2.68/1.33 % (4125831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.33 % (4125831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.33 % (4125831)CaDiCaL version: 2.1.3
% 2.68/1.33 % (4125831)Termination reason: Instruction limit
% 2.68/1.33 % (4125831)Termination phase: Saturation
% 2.68/1.33 % (4125831)Time elapsed: 0.061 s
% 2.68/1.33 % (4125831)Peak memory usage: 88 MB
% 2.68/1.33 % (4125831)Instructions burned: 121 (million)
% 2.68/1.33 % (4125833)Instruction limit reached!
% 2.68/1.33 % (4125833)------------------------------
% 2.68/1.33 % (4125833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.33 % (4125833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.33 % (4125833)CaDiCaL version: 2.1.3
% 2.68/1.33 % (4125833)Termination reason: Instruction limit
% 2.68/1.33 % (4125833)Termination phase: Saturation
% 2.68/1.33 % (4125833)Time elapsed: 0.072 s
% 2.68/1.33 % (4125833)Peak memory usage: 89 MB
% 2.68/1.33 % (4125833)Instructions burned: 130 (million)
% 2.68/1.33 % (4125832)Refutation found. Thanks to Tanya!
% 2.68/1.33 % SZS status Theorem for theBenchmark
% 2.68/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.34 % (4125832)------------------------------
% 2.68/1.34 % (4125832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (4125832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (4125832)CaDiCaL version: 2.1.3
% 2.68/1.34 % (4125832)Termination reason: Refutation
% 2.68/1.34 % (4125832)Time elapsed: 0.011 s
% 2.68/1.34 % (4125832)Peak memory usage: 89 MB
% 2.68/1.34 % (4125832)Instructions burned: 25 (million)
% 2.68/1.34 % (4125832)------------------------------
% 2.68/1.34 % (4125832)------------------------------
% 2.68/1.34 % (4125822)Success in time 0.294 s
% 2.68/1.34 % Vampire exiting
%------------------------------------------------------------------------------