%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU344+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 : Sun Sep 27 08:45:52 AM UTC 2026
% Result : Theorem 2.83s 0.81s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 14 unt; 0 def)
% Number of atoms : 116 ( 24 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 117 ( 44 ~; 48 |; 11 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 53 ( 4 sgn 19 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_lattices,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below(A,B,C)
<=> join(A,B,C) = C ) ) ) ),
file('theBenchmark.p',d3_lattices) ).
fof(dt_k1_lattice3,axiom,
! [A] :
( latt_str(boole_lattice(A))
& strict_latt_str(boole_lattice(A)) ),
file('theBenchmark.p',dt_k1_lattice3) ).
fof(dt_l3_lattices,axiom,
! [A] :
( latt_str(A)
=> ( join_semilatt_str(A)
& meet_semilatt_str(A) ) ),
file('theBenchmark.p',dt_l3_lattices) ).
fof(fc1_lattice3,axiom,
! [A] :
( strict_latt_str(boole_lattice(A))
& ~ empty_carrier(boole_lattice(A)) ),
file('theBenchmark.p',fc1_lattice3) ).
fof(t12_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t1_lattice3,axiom,
! [A,B] :
( element(B,the_carrier(boole_lattice(A)))
=> ! [C] :
( element(C,the_carrier(boole_lattice(A)))
=> ( meet(boole_lattice(A),B,C) = set_intersection2(B,C)
& join(boole_lattice(A),B,C) = set_union2(B,C) ) ) ),
file('theBenchmark.p',t1_lattice3) ).
fof(t7_xboole_1,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t2_lattice3,conjecture,
! [A,B] :
( element(B,the_carrier(boole_lattice(A)))
=> ! [C] :
( element(C,the_carrier(boole_lattice(A)))
=> ( below(boole_lattice(A),B,C)
<=> subset(B,C) ) ) ),
file('theBenchmark.p',t2_lattice3) ).
fof(t2_lattice3_neg,negated_conjecture,
~ ! [A,B] :
( element(B,the_carrier(boole_lattice(A)))
=> ! [C] :
( element(C,the_carrier(boole_lattice(A)))
=> ( below(boole_lattice(A),B,C)
<=> subset(B,C) ) ) ),
inference(assume_negation,[status(cth)],[t2_lattice3]) ).
cnf(c_83,plain,
latt_str(boole_lattice(A)),
inference(clausify,[status(thm)],[dt_k1_lattice3]) ).
cnf(c_85,plain,
( join_semilatt_str(A)
| ~ latt_str(A) ),
inference(clausify,[status(thm)],[dt_l3_lattices]) ).
cnf(c_97,plain,
( join(A,B,C) != C
| below(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[d3_lattices]) ).
cnf(c_98,plain,
( join(A,B,C) = C
| ~ below(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[d3_lattices]) ).
cnf(c_100,plain,
join_semilatt_str(boole_lattice(A)),
inference(resolve,[status(thm)],[c_85,c_83]) ).
cnf(c_219,plain,
~ empty_carrier(boole_lattice(A)),
inference(clausify,[status(thm)],[fc1_lattice3]) ).
cnf(c_245,plain,
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t12_xboole_1]) ).
cnf(c_247,plain,
( join(boole_lattice(B),A,C) = set_union2(A,C)
| ~ element(C,the_carrier(boole_lattice(B)))
| ~ element(A,the_carrier(boole_lattice(B))) ),
inference(clausify,[status(thm)],[t1_lattice3]) ).
cnf(c_258,plain,
subset(A,set_union2(A,B)),
inference(clausify,[status(thm)],[t7_xboole_1]) ).
fof(nnf_80,plain,
? [A,B] :
( ? [C] :
( ( ~ subset(B,C)
| ~ below(boole_lattice(A),B,C) )
& ( subset(B,C)
| below(boole_lattice(A),B,C) )
& element(C,the_carrier(boole_lattice(A))) )
& element(B,the_carrier(boole_lattice(A))) ),
inference(fof_nnf,[status(thm)],[t2_lattice3_neg]) ).
fof(sk_t2_lattice3_neg,plain,
( ( ~ subset(sK0,sK2)
| ~ below(boole_lattice(sK1),sK0,sK2) )
& ( subset(sK0,sK2)
| below(boole_lattice(sK1),sK0,sK2) )
& element(sK2,the_carrier(boole_lattice(sK1)))
& element(sK0,the_carrier(boole_lattice(sK1))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2)],[nnf_80]) ).
cnf(c_260,negated_conjecture,
element(sK0,the_carrier(boole_lattice(sK1))),
inference(split_conjunct,[status(thm)],[sk_t2_lattice3_neg]) ).
cnf(c_261,negated_conjecture,
element(sK2,the_carrier(boole_lattice(sK1))),
inference(split_conjunct,[status(thm)],[sk_t2_lattice3_neg]) ).
cnf(c_262,negated_conjecture,
( subset(sK0,sK2)
| below(boole_lattice(sK1),sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t2_lattice3_neg]) ).
cnf(c_263,negated_conjecture,
( ~ subset(sK0,sK2)
| ~ below(boole_lattice(sK1),sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t2_lattice3_neg]) ).
cnf(c_282,plain,
( join(boole_lattice(A),B,C) != C
| below(boole_lattice(A),B,C)
| ~ element(C,the_carrier(boole_lattice(A)))
| ~ element(B,the_carrier(boole_lattice(A)))
| empty_carrier(boole_lattice(A)) ),
inference(resolve,[status(thm)],[c_100,c_97]) ).
cnf(c_283,plain,
( join(boole_lattice(B),A,C) != C
| below(boole_lattice(B),A,C)
| ~ element(C,the_carrier(boole_lattice(B)))
| ~ element(A,the_carrier(boole_lattice(B))) ),
inference(resolve,[status(thm)],[c_219,c_282]) ).
cnf(c_284,plain,
( join(boole_lattice(A),B,C) = C
| ~ below(boole_lattice(A),B,C)
| ~ element(C,the_carrier(boole_lattice(A)))
| ~ element(B,the_carrier(boole_lattice(A)))
| empty_carrier(boole_lattice(A)) ),
inference(resolve,[status(thm)],[c_100,c_98]) ).
cnf(c_285,plain,
( join(boole_lattice(B),A,C) = C
| ~ below(boole_lattice(B),A,C)
| ~ element(C,the_carrier(boole_lattice(B)))
| ~ element(A,the_carrier(boole_lattice(B))) ),
inference(resolve,[status(thm)],[c_219,c_284]) ).
cnf(c_1912,negated_conjecture,
( join(boole_lattice(sK1),sK0,A) = set_union2(sK0,A)
| ~ element(A,the_carrier(boole_lattice(sK1))) ),
inference(resolve,[status(thm)],[c_247,c_260]) ).
cnf(c_715,negated_conjecture,
join(boole_lattice(sK1),sK0,sK2) = set_union2(sK0,sK2),
inference(resolve,[status(thm)],[c_1912,c_261]) ).
cnf(c_1913,negated_conjecture,
( subset(sK0,sK2)
| join(boole_lattice(sK1),sK0,sK2) = sK2
| ~ element(sK2,the_carrier(boole_lattice(sK1)))
| ~ element(sK0,the_carrier(boole_lattice(sK1))) ),
inference(resolve,[status(thm)],[c_285,c_262]) ).
cnf(c_1914,negated_conjecture,
( subset(sK0,sK2)
| set_union2(sK0,sK2) = sK2
| ~ element(sK2,the_carrier(boole_lattice(sK1)))
| ~ element(sK0,the_carrier(boole_lattice(sK1))) ),
inference(paramod,[status(thm)],[c_715,c_1913]) ).
cnf(c_1915,negated_conjecture,
( subset(sK0,sK2)
| set_union2(sK0,sK2) = sK2
| ~ element(sK2,the_carrier(boole_lattice(sK1))) ),
inference(resolve,[status(thm)],[c_260,c_1914]) ).
cnf(c_860,negated_conjecture,
( subset(sK0,sK2)
| set_union2(sK0,sK2) = sK2 ),
inference(resolve,[status(thm)],[c_261,c_1915]) ).
cnf(c_1916,plain,
( set_union2(sK0,sK2) = sK2
| set_union2(sK0,sK2) = sK2 ),
inference(resolve,[status(thm)],[c_860,c_245]) ).
cnf(c_1621,plain,
set_union2(sK0,sK2) = sK2,
inference(copy,[status(thm)],[c_1916]) ).
cnf(c_1627,negated_conjecture,
join(boole_lattice(sK1),sK0,sK2) = sK2,
inference(paramod,[status(thm)],[c_1621,c_715]) ).
cnf(c_1629,plain,
subset(sK0,sK2),
inference(paramod,[status(thm)],[c_1621,c_258]) ).
cnf(c_1630,negated_conjecture,
~ below(boole_lattice(sK1),sK0,sK2),
inference(resolve,[status(thm)],[c_1629,c_263]) ).
cnf(c_1917,negated_conjecture,
( join(boole_lattice(sK1),sK0,A) != A
| below(boole_lattice(sK1),sK0,A)
| ~ element(A,the_carrier(boole_lattice(sK1))) ),
inference(resolve,[status(thm)],[c_283,c_260]) ).
cnf(c_1918,negated_conjecture,
( join(boole_lattice(sK1),sK0,sK2) != sK2
| below(boole_lattice(sK1),sK0,sK2) ),
inference(resolve,[status(thm)],[c_1917,c_261]) ).
cnf(c_1919,negated_conjecture,
below(boole_lattice(sK1),sK0,sK2),
inference(resolve,[status(thm)],[c_1918,c_1627]) ).
cnf(c_1911,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1630,c_1919]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU344+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.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 : Sat Sep 26 09:11:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 354620 was started by sandbox2 on n017,
% 0.09/0.37 % Sat Sep 26 09:11:34 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.39
% 0.09/0.39 % From the command line: assign(max_seconds, 300).
% 2.83/0.81
% 2.83/0.81 % SZS status Theorem for theBenchmark
% 2.83/0.81
% 2.83/0.81 % Proof 1 at 0.33 (+ 0.07) seconds.
% 2.83/0.81 % Length of proof is 32.
% 2.83/0.81 % Level of proof is 9.
% 2.83/0.81 % Maximum clause weight is 37.000.
% 2.83/0.81 % Given clauses 403.
% 2.83/0.81
% 2.83/0.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------