%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 3.59s 1.48s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 13 unt; 0 def)
% Number of atoms : 36 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 18 ~; 11 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f30,axiom,
! [X0,X1] :
( subset(X0,X1)
=> subset(finite_subsets(X0),finite_subsets(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).
fof(f31,conjecture,
! [X0,X1] : subset(set_union2(finite_subsets(X0),finite_subsets(X1)),finite_subsets(set_union2(X0,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finsub_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] : subset(set_union2(finite_subsets(X0),finite_subsets(X1)),finite_subsets(set_union2(X0,X1))),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f39,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ( subset(X0,X1)
& subset(X2,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f67,plain,
! [X0,X1] :
( subset(finite_subsets(X0),finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f68,plain,
? [X0,X1] : ~ subset(set_union2(finite_subsets(X0),finite_subsets(X1)),finite_subsets(set_union2(X0,X1))),
inference(ennf_transformation,[],[f32]) ).
fof(f77,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f78,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X0,X1)
| ~ subset(X2,X1) ),
inference(flattening,[],[f77]) ).
fof(f89,plain,
~ subset(set_union2(finite_subsets(sK10),finite_subsets(sK11)),finite_subsets(set_union2(sK10,sK11))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f68]) ).
fof(f98,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f139,plain,
! [X0,X1] :
( subset(finite_subsets(X0),finite_subsets(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f140,plain,
~ subset(set_union2(finite_subsets(sK10),finite_subsets(sK11)),finite_subsets(set_union2(sK10,sK11))),
inference(cnf_transformation,[],[f89]) ).
fof(f148,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f39]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f162,plain,
! [X0,X1] : subset(X1,set_union2(X0,X1)),
inference(superposition,[],[f148,f98]) ).
fof(f175,plain,
! [X2,X0,X1] :
( subset(set_union2(finite_subsets(X0),X1),finite_subsets(X2))
| ~ subset(X1,finite_subsets(X2))
| ~ subset(X0,X2) ),
inference(resolution,[],[f150,f139]) ).
fof(f283,plain,
( ~ subset(finite_subsets(sK11),finite_subsets(set_union2(sK10,sK11)))
| ~ subset(sK10,set_union2(sK10,sK11)) ),
inference(resolution,[],[f175,f140]) ).
fof(f289,plain,
~ subset(finite_subsets(sK11),finite_subsets(set_union2(sK10,sK11))),
inference(forward_subsumption_resolution,[],[f283,f148]) ).
fof(f290,plain,
~ subset(sK11,set_union2(sK10,sK11)),
inference(resolution,[],[f289,f139]) ).
fof(f291,plain,
$false,
inference(forward_subsumption_resolution,[],[f290,f162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU112+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.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 03:35:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.59/1.48 % (3551727)Detected formulas, will run a generic FOF schedule.
% 3.59/1.48 % (3551734)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=4019337105:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.59/1.48 % (3551733)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=4022625904:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.59/1.48 % (3551732)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=2153847973:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.59/1.48 % (3551738)dis-21_1_sil=8000:lcm=predicate:random_seed=1503088077: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)
% 3.59/1.48 % (3551735)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3577061887:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.59/1.48 % (3551736)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=528208392:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.59/1.48 % (3551737)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3453387609:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.59/1.48 % (3551735)Refutation not found, incomplete strategy
% 3.59/1.48 % (3551735)------------------------------
% 3.59/1.48 % (3551735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.48 % (3551735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.48 % (3551735)CaDiCaL version: 2.1.3
% 3.59/1.48 % (3551735)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.48 % (3551735)Time elapsed: 0.001 s
% 3.59/1.48 % (3551735)Peak memory usage: 88 MB
% 3.59/1.48 % (3551736)Refutation not found, incomplete strategy
% 3.59/1.48 % (3551736)------------------------------
% 3.59/1.48 % (3551736)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.48 % (3551736)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.48 % (3551736)CaDiCaL version: 2.1.3
% 3.59/1.48 % (3551736)Termination reason: Refutation not found, incomplete strategy
% 3.59/1.48 % (3551736)Time elapsed: 0.002 s
% 3.59/1.48 % (3551736)Peak memory usage: 88 MB
% 3.59/1.48 % (3551736)Instructions burned: 2 (million)
% 3.59/1.48 % (3551737)First to succeed.
% 3.59/1.48 % (3551737)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3551727"
% 3.59/1.48 % (3551738)Instruction limit reached!
% 3.59/1.48 % (3551738)------------------------------
% 3.59/1.48 % (3551738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.48 % (3551738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.48 % (3551738)CaDiCaL version: 2.1.3
% 3.59/1.48 % (3551738)Termination reason: Instruction limit
% 3.59/1.48 % (3551738)Termination phase: Saturation
% 3.59/1.48 % (3551738)Time elapsed: 0.076 s
% 3.59/1.48 % (3551738)Peak memory usage: 90 MB
% 3.59/1.48 % (3551738)Instructions burned: 130 (million)
% 3.59/1.48 % (3551746)lrs+10_1_sil=8000:sp=occurrence:random_seed=2902354422:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.59/1.48 % (3551735)------------------------------
% 3.59/1.48 % (3551735)------------------------------
% 3.59/1.48 % (3551736)------------------------------
% 3.59/1.48 % (3551736)------------------------------
% 3.59/1.48 % (3551737)Refutation found. Thanks to Tanya!
% 3.59/1.48 % SZS status Theorem for theBenchmark
% 3.59/1.48 % SZS output start Proof for theBenchmark
% See solution above
% 3.59/1.48 % (3551737)------------------------------
% 3.59/1.48 % (3551737)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.59/1.48 % (3551737)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.59/1.48 % (3551737)CaDiCaL version: 2.1.3
% 3.59/1.48 % (3551737)Termination reason: Refutation
% 3.59/1.48 % (3551737)Time elapsed: 0.008 s
% 3.59/1.48 % (3551737)Peak memory usage: 89 MB
% 3.59/1.48 % (3551737)Instructions burned: 8 (million)
% 3.59/1.48 % (3551737)------------------------------
% 3.59/1.48 % (3551737)------------------------------
% 3.59/1.48 % (3551727)Success in time 0.432 s
% 3.59/1.48 % Vampire exiting
%------------------------------------------------------------------------------