%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU348+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 0.15s 5.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 12 unt; 0 def)
% Number of atoms : 158 ( 12 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 181 ( 72 ~; 72 |; 23 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> cast_to_el_of_LattPOSet(A,B) = B ) ),
file('theBenchmark.p',d3_lattice3) ).
fof(d4_lattice3,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(poset_of_lattice(A)))
=> cast_to_el_of_lattice(A,B) = B ) ),
file('theBenchmark.p',d4_lattice3) ).
fof(dt_k5_lattice3,axiom,
! [A,B] :
( ( element(B,the_carrier(poset_of_lattice(A)))
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> element(cast_to_el_of_lattice(A,B),the_carrier(A)) ),
file('theBenchmark.p',dt_k5_lattice3) ).
fof(t28_lattice3,axiom,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(B))
=> ( latt_set_smaller(B,C,A)
<=> relstr_element_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) ) ) ),
file('theBenchmark.p',t28_lattice3) ).
fof(t29_lattice3,conjecture,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
file('theBenchmark.p',t29_lattice3) ).
fof(t29_lattice3_neg,negated_conjecture,
~ ! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_element_smaller(poset_of_lattice(B),A,C)
<=> latt_set_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
inference(assume_negation,[status(cth)],[t29_lattice3]) ).
fof(nnf_64,plain,
? [A,B] :
( ? [C] :
( ( ~ latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
| ~ relstr_element_smaller(poset_of_lattice(B),A,C) )
& ( latt_set_smaller(B,cast_to_el_of_lattice(B,C),A)
| relstr_element_smaller(poset_of_lattice(B),A,C) )
& element(C,the_carrier(poset_of_lattice(B))) )
& latt_str(B)
& lattice(B)
& ~ empty_carrier(B) ),
inference(fof_nnf,[status(thm)],[t29_lattice3_neg]) ).
fof(sk_t29_lattice3_neg,plain,
( ( ~ latt_set_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2) )
& ( latt_set_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2) )
& element(sK2,the_carrier(poset_of_lattice(sK0)))
& latt_str(sK0)
& lattice(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(A,sK1),skolemize(B,sK0),skolemize(C,sK2)],[nnf_64]) ).
cnf(c_78,negated_conjecture,
latt_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t29_lattice3_neg]) ).
cnf(c_87,plain,
( ~ relstr_element_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B))
| latt_set_smaller(A,B,C)
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[t28_lattice3]) ).
cnf(c_88,plain,
( relstr_element_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B))
| ~ latt_set_smaller(A,B,C)
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[t28_lattice3]) ).
cnf(c_99,plain,
( element(cast_to_el_of_lattice(A,B),the_carrier(A))
| ~ element(B,the_carrier(poset_of_lattice(A)))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[dt_k5_lattice3]) ).
cnf(c_110,plain,
( cast_to_el_of_lattice(A,B) = B
| ~ element(B,the_carrier(poset_of_lattice(A)))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[d4_lattice3]) ).
cnf(c_111,plain,
( cast_to_el_of_LattPOSet(A,B) = B
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[d3_lattice3]) ).
cnf(c_241,negated_conjecture,
( ~ latt_set_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t29_lattice3_neg]) ).
cnf(c_242,negated_conjecture,
( latt_set_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t29_lattice3_neg]) ).
cnf(c_243,negated_conjecture,
element(sK2,the_carrier(poset_of_lattice(sK0))),
inference(split_conjunct,[status(thm)],[sk_t29_lattice3_neg]) ).
cnf(c_244,negated_conjecture,
lattice(sK0),
inference(split_conjunct,[status(thm)],[sk_t29_lattice3_neg]) ).
cnf(c_245,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t29_lattice3_neg]) ).
cnf(c_285,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| latt_set_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_87,c_78]) ).
cnf(c_624,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| latt_set_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0) ),
inference(resolve,[status(thm)],[c_245,c_285]) ).
cnf(c_286,negated_conjecture,
( ~ relstr_element_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| latt_set_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_244,c_624]) ).
cnf(c_287,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| ~ latt_set_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_88,c_78]) ).
cnf(c_625,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| ~ latt_set_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0) ),
inference(resolve,[status(thm)],[c_245,c_287]) ).
cnf(c_288,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| ~ latt_set_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_244,c_625]) ).
cnf(c_314,negated_conjecture,
( element(cast_to_el_of_lattice(sK0,A),the_carrier(sK0))
| ~ element(A,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_99,c_78]) ).
cnf(c_626,negated_conjecture,
( element(cast_to_el_of_lattice(sK0,A),the_carrier(sK0))
| ~ element(A,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0) ),
inference(resolve,[status(thm)],[c_245,c_314]) ).
cnf(c_315,negated_conjecture,
( element(cast_to_el_of_lattice(sK0,A),the_carrier(sK0))
| ~ element(A,the_carrier(poset_of_lattice(sK0))) ),
inference(resolve,[status(thm)],[c_244,c_626]) ).
cnf(c_329,negated_conjecture,
( cast_to_el_of_lattice(sK0,A) = A
| ~ element(A,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_110,c_78]) ).
cnf(c_627,negated_conjecture,
( cast_to_el_of_lattice(sK0,A) = A
| ~ element(A,the_carrier(poset_of_lattice(sK0)))
| ~ lattice(sK0) ),
inference(resolve,[status(thm)],[c_245,c_329]) ).
cnf(c_330,negated_conjecture,
( cast_to_el_of_lattice(sK0,A) = A
| ~ element(A,the_carrier(poset_of_lattice(sK0))) ),
inference(resolve,[status(thm)],[c_244,c_627]) ).
cnf(c_332,negated_conjecture,
( cast_to_el_of_LattPOSet(sK0,A) = A
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_111,c_78]) ).
cnf(c_628,negated_conjecture,
( cast_to_el_of_LattPOSet(sK0,A) = A
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0) ),
inference(resolve,[status(thm)],[c_245,c_332]) ).
cnf(c_333,negated_conjecture,
( cast_to_el_of_LattPOSet(sK0,A) = A
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_244,c_628]) ).
cnf(c_498,plain,
element(cast_to_el_of_lattice(sK0,sK2),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_315,c_243]) ).
cnf(c_503,plain,
cast_to_el_of_lattice(sK0,sK2) = sK2,
inference(resolve,[status(thm)],[c_330,c_243]) ).
cnf(c_505,plain,
element(sK2,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_503,c_498]) ).
cnf(c_506,negated_conjecture,
( latt_set_smaller(sK0,sK2,sK1)
| relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(paramod,[status(thm)],[c_503,c_242]) ).
cnf(c_507,negated_conjecture,
( ~ latt_set_smaller(sK0,sK2,sK1)
| ~ relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(paramod,[status(thm)],[c_503,c_241]) ).
cnf(c_527,plain,
cast_to_el_of_LattPOSet(sK0,sK2) = sK2,
inference(resolve,[status(thm)],[c_505,c_333]) ).
cnf(c_629,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),A,sK2)
| latt_set_smaller(sK0,sK2,A)
| ~ element(sK2,the_carrier(sK0)) ),
inference(paramod,[status(thm)],[c_527,c_286]) ).
cnf(c_537,plain,
( ~ relstr_element_smaller(poset_of_lattice(sK0),A,sK2)
| latt_set_smaller(sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_505,c_629]) ).
cnf(c_630,negated_conjecture,
( latt_set_smaller(sK0,sK2,sK1)
| latt_set_smaller(sK0,sK2,sK1) ),
inference(resolve,[status(thm)],[c_537,c_506]) ).
cnf(c_621,negated_conjecture,
latt_set_smaller(sK0,sK2,sK1),
inference(copy,[status(thm)],[c_630]) ).
cnf(c_622,negated_conjecture,
~ relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2),
inference(resolve,[status(thm)],[c_621,c_507]) ).
cnf(c_631,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(sK0),sK1,cast_to_el_of_LattPOSet(sK0,sK2))
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_621,c_288]) ).
cnf(c_632,negated_conjecture,
( relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2)
| ~ element(sK2,the_carrier(sK0)) ),
inference(paramod,[status(thm)],[c_527,c_631]) ).
cnf(c_633,negated_conjecture,
relstr_element_smaller(poset_of_lattice(sK0),sK1,sK2),
inference(resolve,[status(thm)],[c_505,c_632]) ).
cnf(c_623,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_622,c_633]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU348+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n015.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 09:20:18 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 3678693 was started by sandbox on n015,
% 0.11/5.39 % Sat Sep 26 09:20:18 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.40
% 0.15/5.40 % From the command line: assign(max_seconds, 300).
% 0.15/5.51
% 0.15/5.51 % SZS status Theorem for theBenchmark
% 0.15/5.51
% 0.15/5.51 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.15/5.51 % Length of proof is 36.
% 0.15/5.51 % Level of proof is 10.
% 0.15/5.51 % Maximum clause weight is 15.000.
% 0.15/5.51 % Given clauses 289.
% 0.15/5.51
% 0.15/5.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------