%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU305+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 08:45:45 AM UTC 2026
% Result : Theorem 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 150 ( 39 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 167 ( 64 ~; 60 |; 29 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 44 ( 0 sgn 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join_commut(A,C,B) ),
file('theBenchmark.p',commutativity_k3_lattices) ).
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(redefinition_k3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join(A,B,C) ),
file('theBenchmark.p',redefinition_k3_lattices) ).
fof(t26_lattices,conjecture,
! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( below(A,C,B)
& below(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t26_lattices) ).
fof(t26_lattices_neg,negated_conjecture,
~ ! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( below(A,C,B)
& below(A,B,C) )
=> B = C ) ) ) ),
inference(assume_negation,[status(cth)],[t26_lattices]) ).
cnf(c_47,plain,
( join(A,B,C) = join_commut(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[redefinition_k3_lattices]) ).
fof(nnf_42,plain,
? [A] :
( ? [B] :
( ? [C] :
( C != B
& below(A,C,B)
& below(A,B,C)
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t26_lattices_neg]) ).
fof(sk_t26_lattices_neg,plain,
( sK2 != sK1
& below(sK0,sK2,sK1)
& below(sK0,sK1,sK2)
& element(sK2,the_carrier(sK0))
& element(sK1,the_carrier(sK0))
& join_semilatt_str(sK0)
& join_commutative(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK1),skolemize(C,sK2)],[nnf_42]) ).
cnf(c_48,negated_conjecture,
join_commutative(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_50,plain,
( join_commut(A,C,B) = join_commut(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[commutativity_k3_lattices]) ).
cnf(c_52,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_53,negated_conjecture,
below(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_54,negated_conjecture,
below(sK0,sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_82,negated_conjecture,
( join(sK0,sK2,sK1) = sK1
| ~ element(sK1,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_54,c_52]) ).
cnf(c_83,negated_conjecture,
( join(sK0,sK1,sK2) = sK2
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_53,c_52]) ).
cnf(c_84,negated_conjecture,
sK2 != sK1,
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_85,negated_conjecture,
element(sK2,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_86,negated_conjecture,
element(sK1,the_carrier(sK0)),
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_87,negated_conjecture,
join_semilatt_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_88,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t26_lattices_neg]) ).
cnf(c_105,negated_conjecture,
( join(sK0,A,B) = join_commut(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_47,c_48]) ).
cnf(c_201,negated_conjecture,
( join_commut(sK0,A,B) = join(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0) ),
inference(copy,[status(thm)],[c_105]) ).
cnf(c_202,negated_conjecture,
( join_commut(sK0,A,B) = join(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0))
| ~ join_semilatt_str(sK0) ),
inference(resolve,[status(thm)],[c_88,c_201]) ).
cnf(c_106,negated_conjecture,
( join_commut(sK0,A,B) = join(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_87,c_202]) ).
cnf(c_109,negated_conjecture,
( join_commut(sK0,B,A) = join_commut(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_50,c_48]) ).
cnf(c_203,negated_conjecture,
( join_commut(sK0,B,A) = join_commut(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0))
| ~ join_semilatt_str(sK0) ),
inference(resolve,[status(thm)],[c_88,c_109]) ).
cnf(c_110,negated_conjecture,
( join_commut(sK0,B,A) = join_commut(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_87,c_203]) ).
cnf(c_204,negated_conjecture,
( join(sK0,sK1,sK2) = sK2
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| ~ join_semilatt_str(sK0) ),
inference(resolve,[status(thm)],[c_88,c_83]) ).
cnf(c_205,negated_conjecture,
( join(sK0,sK1,sK2) = sK2
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_87,c_204]) ).
cnf(c_206,negated_conjecture,
( join(sK0,sK1,sK2) = sK2
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_86,c_205]) ).
cnf(c_119,negated_conjecture,
join(sK0,sK1,sK2) = sK2,
inference(resolve,[status(thm)],[c_85,c_206]) ).
cnf(c_207,negated_conjecture,
( join(sK0,sK2,sK1) = sK1
| ~ element(sK1,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ join_semilatt_str(sK0) ),
inference(resolve,[status(thm)],[c_88,c_82]) ).
cnf(c_208,negated_conjecture,
( join(sK0,sK2,sK1) = sK1
| ~ element(sK1,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_87,c_207]) ).
cnf(c_209,negated_conjecture,
( join(sK0,sK2,sK1) = sK1
| ~ element(sK1,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_85,c_208]) ).
cnf(c_120,negated_conjecture,
join(sK0,sK2,sK1) = sK1,
inference(resolve,[status(thm)],[c_86,c_209]) ).
cnf(c_210,negated_conjecture,
( join_commut(sK0,sK1,A) = join(sK0,sK1,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_106,c_86]) ).
cnf(c_211,negated_conjecture,
join_commut(sK0,sK1,sK2) = join(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_210,c_85]) ).
cnf(c_185,negated_conjecture,
join_commut(sK0,sK1,sK2) = sK2,
inference(paramod,[status(thm)],[c_119,c_211]) ).
cnf(c_212,negated_conjecture,
( join_commut(sK0,sK2,A) = join(sK0,sK2,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_106,c_85]) ).
cnf(c_213,negated_conjecture,
join_commut(sK0,sK2,sK1) = join(sK0,sK2,sK1),
inference(resolve,[status(thm)],[c_212,c_86]) ).
cnf(c_187,negated_conjecture,
join_commut(sK0,sK2,sK1) = sK1,
inference(paramod,[status(thm)],[c_120,c_213]) ).
cnf(c_214,negated_conjecture,
( join_commut(sK0,A,sK1) = join_commut(sK0,sK1,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_110,c_86]) ).
cnf(c_215,negated_conjecture,
join_commut(sK0,sK2,sK1) = join_commut(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_214,c_85]) ).
cnf(c_216,negated_conjecture,
sK1 = join_commut(sK0,sK1,sK2),
inference(paramod,[status(thm)],[c_187,c_215]) ).
cnf(c_217,negated_conjecture,
sK1 = sK2,
inference(paramod,[status(thm)],[c_185,c_216]) ).
cnf(c_218,negated_conjecture,
sK2 = sK1,
inference(copy,[status(thm)],[c_217]) ).
cnf(c_200,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_84,c_218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU305+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 09:12:28 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 3668067 was started by sandbox on n015,
% 0.09/0.37 % Sat Sep 26 09:12:28 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.43 % Length of proof is 26.
% 0.09/0.43 % Level of proof is 5.
% 0.09/0.43 % Maximum clause weight is 28.000.
% 0.09/0.43 % Given clauses 31.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------