%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU371+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:48:35 PM UTC 2026
% Result : Theorem 0.56s 0.93s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 19 unt; 0 def)
% Number of atoms : 145 ( 37 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 145 ( 44 ~; 43 |; 55 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 48 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0] :
( rel_str(X0)
=> bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_yellow_0) ).
fof(f22,axiom,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_yellow_1) ).
fof(f27,axiom,
! [X0] :
( strict_latt_str(boole_lattice(X0))
& latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_lattice3) ).
fof(f36,axiom,
! [X0] :
( strict_rel_str(boole_POSet(X0))
& rel_str(boole_POSet(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_yellow_1) ).
fof(f59,axiom,
! [X0] :
( ~ empty_carrier(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& lattice(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& modular_lattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0))
& complete_latt_str(boole_lattice(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_knaster) ).
fof(f103,conjecture,
! [X0] : bottom_of_relstr(boole_POSet(X0)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t18_yellow_1) ).
fof(f104,negated_conjecture,
~ ! [X0] : bottom_of_relstr(boole_POSet(X0)) = empty_set,
inference(negated_conjecture,[status(cth)],[f103]) ).
fof(f106,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) )
=> ! [X1] :
( join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1)
& meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_yellow_0) ).
fof(f109,axiom,
! [X0] :
( lower_bounded_semilattstr(boole_lattice(X0))
& bottom_of_semilattstr(boole_lattice(X0)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_lattice3) ).
fof(f112,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& complete_latt_str(X0)
& latt_str(X0) )
=> ( ~ empty_carrier(X0)
& lattice(X0)
& lower_bounded_semilattstr(X0)
& latt_str(X0)
& bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_lattice3) ).
fof(f122,plain,
! [X0] :
( ~ empty_carrier(boole_lattice(X0))
& strict_latt_str(boole_lattice(X0))
& join_commutative(boole_lattice(X0))
& join_associative(boole_lattice(X0))
& meet_commutative(boole_lattice(X0))
& meet_associative(boole_lattice(X0))
& meet_absorbing(boole_lattice(X0))
& join_absorbing(boole_lattice(X0))
& lattice(boole_lattice(X0))
& distributive_lattstr(boole_lattice(X0))
& lower_bounded_semilattstr(boole_lattice(X0))
& upper_bounded_semilattstr(boole_lattice(X0))
& bounded_lattstr(boole_lattice(X0))
& complemented_lattstr(boole_lattice(X0))
& boolean_lattstr(boole_lattice(X0))
& complete_latt_str(boole_lattice(X0)) ),
inference(pure_predicate_removal,[],[f59]) ).
fof(f160,plain,
! [X0] :
( bottom_of_relstr(X0) = join_on_relstr(X0,empty_set)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f221,plain,
? [X0] : empty_set != bottom_of_relstr(boole_POSet(X0)),
inference(ennf_transformation,[],[f104]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1)
& meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f106]) ).
fof(f224,plain,
! [X0] :
( ! [X1] :
( join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1)
& meet_of_latt_set(X0,X1) = meet_on_relstr(poset_of_lattice(X0),X1) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f223]) ).
fof(f231,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& lower_bounded_semilattstr(X0)
& latt_str(X0)
& bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0) ),
inference(ennf_transformation,[],[f112]) ).
fof(f232,plain,
! [X0] :
( ( ~ empty_carrier(X0)
& lattice(X0)
& lower_bounded_semilattstr(X0)
& latt_str(X0)
& bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set) )
| empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0) ),
inference(flattening,[],[f231]) ).
fof(f274,plain,
empty_set != bottom_of_relstr(boole_POSet(sK30)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(X0,sK30)],[f221]) ).
fof(f332,plain,
! [X0] :
( bottom_of_relstr(X0) = join_on_relstr(X0,empty_set)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f335,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f22]) ).
fof(f342,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f27]) ).
fof(f357,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[],[f36]) ).
fof(f381,plain,
! [X0] : complete_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[],[f122]) ).
fof(f388,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[],[f122]) ).
fof(f396,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[],[f122]) ).
fof(f626,plain,
empty_set != bottom_of_relstr(boole_POSet(sK30)),
inference(cnf_transformation,[],[f274]) ).
fof(f629,plain,
! [X0,X1] :
( ~ complete_latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f633,plain,
! [X0] : empty_set = bottom_of_semilattstr(boole_lattice(X0)),
inference(cnf_transformation,[],[f109]) ).
fof(f637,plain,
! [X0] :
( ~ complete_latt_str(X0)
| empty_carrier(X0)
| ~ lattice(X0)
| bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f664,plain,
! [X0,X1] :
( empty_carrier(boole_lattice(X0))
| ~ lattice(boole_lattice(X0))
| join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1)
| ~ latt_str(boole_lattice(X0)) ),
inference(resolution,[],[f381,f629]) ).
fof(f666,plain,
! [X0] :
( empty_carrier(boole_lattice(X0))
| ~ lattice(boole_lattice(X0))
| bottom_of_semilattstr(boole_lattice(X0)) = join_of_latt_set(boole_lattice(X0),empty_set)
| ~ latt_str(boole_lattice(X0)) ),
inference(resolution,[],[f381,f637]) ).
fof(f667,plain,
! [X0] :
( empty_carrier(boole_lattice(X0))
| ~ lattice(boole_lattice(X0))
| bottom_of_semilattstr(boole_lattice(X0)) = join_of_latt_set(boole_lattice(X0),empty_set) ),
inference(forward_subsumption_resolution,[],[f666,f342]) ).
fof(f669,plain,
! [X0,X1] :
( empty_carrier(boole_lattice(X0))
| ~ lattice(boole_lattice(X0))
| join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1) ),
inference(forward_subsumption_resolution,[],[f664,f342]) ).
fof(f670,plain,
! [X0] :
( empty_set = join_of_latt_set(boole_lattice(X0),empty_set)
| empty_carrier(boole_lattice(X0))
| ~ lattice(boole_lattice(X0)) ),
inference(forward_demodulation,[],[f667,f633]) ).
fof(f672,plain,
! [X0,X1] :
( join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1)
| empty_carrier(boole_lattice(X0))
| ~ lattice(boole_lattice(X0)) ),
inference(forward_demodulation,[],[f669,f335]) ).
fof(f1002,plain,
! [X0] :
( empty_set = join_of_latt_set(boole_lattice(X0),empty_set)
| ~ lattice(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f670,f396]) ).
fof(f1003,plain,
! [X0] : empty_set = join_of_latt_set(boole_lattice(X0),empty_set),
inference(forward_subsumption_resolution,[],[f1002,f388]) ).
fof(f1059,plain,
! [X0,X1] :
( join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1)
| ~ lattice(boole_lattice(X0)) ),
inference(forward_subsumption_resolution,[],[f672,f396]) ).
fof(f1060,plain,
! [X0,X1] : join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1),
inference(forward_subsumption_resolution,[],[f1059,f388]) ).
fof(f1062,plain,
! [X0] :
( bottom_of_relstr(boole_POSet(X0)) = join_of_latt_set(boole_lattice(X0),empty_set)
| ~ rel_str(boole_POSet(X0)) ),
inference(superposition,[],[f332,f1060]) ).
fof(f1065,plain,
! [X0] : bottom_of_relstr(boole_POSet(X0)) = join_of_latt_set(boole_lattice(X0),empty_set),
inference(forward_subsumption_resolution,[],[f1062,f357]) ).
fof(f1067,plain,
! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
inference(forward_demodulation,[],[f1065,f1003]) ).
fof(f1069,plain,
empty_set != empty_set,
inference(superposition,[],[f626,f1067]) ).
fof(f1071,plain,
$false,
inference(trivial_inequality_removal,[],[f1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU371+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 04:58:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.56/0.93 % (442990)Detected formulas, will run a generic FOF schedule.
% 0.56/0.93 % (443000)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2106934193:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.56/0.93 % (442999)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1287805432:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.56/0.93 % (442998)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2901151663:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.56/0.93 % (443001)dis-21_1_sil=8000:lcm=predicate:random_seed=2727492764: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)
% 0.56/0.93 % (442995)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=1123905096:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.56/0.93 % (442996)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=3383539582:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.56/0.93 % (442997)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=1183557058:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.56/0.93 % (442998)Refutation not found, incomplete strategy
% 0.56/0.93 % (442998)------------------------------
% 0.56/0.93 % (442998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.56/0.93 % (442998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.93 % (442998)CaDiCaL version: 2.1.3
% 0.56/0.93 % (442998)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.93 % (442998)Time elapsed: 0.002 s
% 0.56/0.93 % (442998)Peak memory usage: 88 MB
% 0.56/0.93 % (442998)Instructions burned: 1 (million)
% 0.56/0.93 % (442999)Refutation not found, incomplete strategy
% 0.56/0.93 % (442999)------------------------------
% 0.56/0.93 % (442999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.56/0.93 % (442999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.93 % (442999)CaDiCaL version: 2.1.3
% 0.56/0.93 % (442999)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.93 % (442999)Time elapsed: 0.003 s
% 0.56/0.93 % (442999)Peak memory usage: 88 MB
% 0.56/0.93 % (442999)Instructions burned: 4 (million)
% 0.56/0.93 % (443000)First to succeed.
% 0.56/0.93 % (443000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-442990"
% 0.56/0.93 % (443001)Instruction limit reached!
% 0.56/0.93 % (443001)------------------------------
% 0.56/0.93 % (443001)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.56/0.93 % (443001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.56/0.93 % (443001)CaDiCaL version: 2.1.3
% 0.56/0.93 % (443001)Termination reason: Instruction limit
% 0.56/0.93 % (443001)Termination phase: Saturation
% 0.56/0.93 % (443001)Time elapsed: 0.066 s
% 0.56/0.93 % (443001)Peak memory usage: 92 MB
% 0.56/0.93 % (443001)Instructions burned: 130 (million)
% 0.56/0.93 % (443000)Refutation found. Thanks to Tanya!
% 0.56/0.93 % SZS status Theorem for theBenchmark
% 0.56/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.13 % (443000)------------------------------
% 2.78/1.13 % (443000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.13 % (443000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.13 % (443000)CaDiCaL version: 2.1.3
% 2.78/1.13 % (443000)Termination reason: Refutation
% 2.78/1.13 % (443000)Time elapsed: 0.015 s
% 2.78/1.13 % (443000)Peak memory usage: 89 MB
% 2.78/1.13 % (443000)Instructions burned: 37 (million)
% 2.78/1.13 % (443000)------------------------------
% 2.78/1.13 % (443000)------------------------------
% 2.78/1.13 % (442990)Success in time 0.332 s
% 2.78/1.13 % Vampire exiting
%------------------------------------------------------------------------------