%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU350+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 : 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 : Sun Sep 27 08:45:53 AM UTC 2026
% Result : Theorem 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 12 unt; 0 def)
% Number of atoms : 157 ( 12 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 179 ( 71 ~; 71 |; 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 : 55 ( 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(t30_lattice3,axiom,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(B))
=> ( latt_element_smaller(B,C,A)
<=> relstr_set_smaller(poset_of_lattice(B),A,cast_to_el_of_LattPOSet(B,C)) ) ) ),
file('theBenchmark.p',t30_lattice3) ).
fof(t31_lattice3,conjecture,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_set_smaller(poset_of_lattice(B),A,C)
<=> latt_element_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
file('theBenchmark.p',t31_lattice3) ).
fof(t31_lattice3_neg,negated_conjecture,
~ ! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ! [C] :
( element(C,the_carrier(poset_of_lattice(B)))
=> ( relstr_set_smaller(poset_of_lattice(B),A,C)
<=> latt_element_smaller(B,cast_to_el_of_lattice(B,C),A) ) ) ),
inference(assume_negation,[status(cth)],[t31_lattice3]) ).
fof(nnf_64,plain,
? [A,B] :
( ? [C] :
( ( ~ latt_element_smaller(B,cast_to_el_of_lattice(B,C),A)
| ~ relstr_set_smaller(poset_of_lattice(B),A,C) )
& ( latt_element_smaller(B,cast_to_el_of_lattice(B,C),A)
| relstr_set_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)],[t31_lattice3_neg]) ).
fof(sk_t31_lattice3_neg,plain,
( ( ~ latt_element_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,sK2) )
& ( latt_element_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| relstr_set_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_t31_lattice3_neg]) ).
cnf(c_87,plain,
( ~ relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B))
| latt_element_smaller(A,B,C)
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[t30_lattice3]) ).
cnf(c_88,plain,
( relstr_set_smaller(poset_of_lattice(A),C,cast_to_el_of_LattPOSet(A,B))
| ~ latt_element_smaller(A,B,C)
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[t30_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_element_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t31_lattice3_neg]) ).
cnf(c_242,negated_conjecture,
( latt_element_smaller(sK0,cast_to_el_of_lattice(sK0,sK2),sK1)
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(split_conjunct,[status(thm)],[sk_t31_lattice3_neg]) ).
cnf(c_243,negated_conjecture,
element(sK2,the_carrier(poset_of_lattice(sK0))),
inference(split_conjunct,[status(thm)],[sk_t31_lattice3_neg]) ).
cnf(c_244,negated_conjecture,
lattice(sK0),
inference(split_conjunct,[status(thm)],[sk_t31_lattice3_neg]) ).
cnf(c_245,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t31_lattice3_neg]) ).
cnf(c_285,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| latt_element_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_87,c_78]) ).
cnf(c_617,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| latt_element_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_set_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| latt_element_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_244,c_617]) ).
cnf(c_287,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| ~ latt_element_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0))
| ~ lattice(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_88,c_78]) ).
cnf(c_618,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| ~ latt_element_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_set_smaller(poset_of_lattice(sK0),B,cast_to_el_of_LattPOSet(sK0,A))
| ~ latt_element_smaller(sK0,A,B)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_244,c_618]) ).
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_619,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_619]) ).
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_620,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_620]) ).
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_621,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_621]) ).
cnf(c_522,plain,
element(cast_to_el_of_lattice(sK0,sK2),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_315,c_243]) ).
cnf(c_527,plain,
cast_to_el_of_lattice(sK0,sK2) = sK2,
inference(resolve,[status(thm)],[c_330,c_243]) ).
cnf(c_529,plain,
element(sK2,the_carrier(sK0)),
inference(paramod,[status(thm)],[c_527,c_522]) ).
cnf(c_530,negated_conjecture,
( latt_element_smaller(sK0,sK2,sK1)
| relstr_set_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(paramod,[status(thm)],[c_527,c_242]) ).
cnf(c_531,negated_conjecture,
( ~ latt_element_smaller(sK0,sK2,sK1)
| ~ relstr_set_smaller(poset_of_lattice(sK0),sK1,sK2) ),
inference(paramod,[status(thm)],[c_527,c_241]) ).
cnf(c_575,plain,
cast_to_el_of_LattPOSet(sK0,sK2) = sK2,
inference(resolve,[status(thm)],[c_529,c_333]) ).
cnf(c_622,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(sK0),A,cast_to_el_of_LattPOSet(sK0,sK2))
| ~ latt_element_smaller(sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_529,c_288]) ).
cnf(c_576,negated_conjecture,
( relstr_set_smaller(poset_of_lattice(sK0),A,sK2)
| ~ latt_element_smaller(sK0,sK2,A) ),
inference(paramod,[status(thm)],[c_575,c_622]) ).
cnf(c_623,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(sK0),A,cast_to_el_of_LattPOSet(sK0,sK2))
| latt_element_smaller(sK0,sK2,A) ),
inference(resolve,[status(thm)],[c_529,c_286]) ).
cnf(c_577,negated_conjecture,
( ~ relstr_set_smaller(poset_of_lattice(sK0),A,sK2)
| latt_element_smaller(sK0,sK2,A) ),
inference(paramod,[status(thm)],[c_575,c_623]) ).
cnf(c_624,negated_conjecture,
( latt_element_smaller(sK0,sK2,sK1)
| latt_element_smaller(sK0,sK2,sK1) ),
inference(resolve,[status(thm)],[c_577,c_530]) ).
cnf(c_614,negated_conjecture,
latt_element_smaller(sK0,sK2,sK1),
inference(copy,[status(thm)],[c_624]) ).
cnf(c_615,negated_conjecture,
~ relstr_set_smaller(poset_of_lattice(sK0),sK1,sK2),
inference(resolve,[status(thm)],[c_614,c_531]) ).
cnf(c_625,plain,
relstr_set_smaller(poset_of_lattice(sK0),sK1,sK2),
inference(resolve,[status(thm)],[c_614,c_576]) ).
cnf(c_616,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_615,c_625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU350+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 09:16:55 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 916388 was started by sandbox on n006,
% 0.10/0.35 % Sat Sep 26 09:16:55 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.43
% 0.12/0.43 % SZS status Theorem for theBenchmark
% 0.12/0.43
% 0.12/0.43 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.12/0.43 % Length of proof is 37.
% 0.12/0.43 % Level of proof is 10.
% 0.12/0.43 % Maximum clause weight is 26.000.
% 0.12/0.43 % Given clauses 241.
% 0.12/0.43
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------