%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU305+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:11:25 PM UTC 2026
% Result : Theorem 11.47s 9.38s
% Output : CNFRefutation 11.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 121 ( 24 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 134 ( 44 ~; 38 |; 32 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 45 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(redefinition_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(t26_lattices,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
fof(d3_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(commutativity_k3_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k3_lattices]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( ( below(X1,X2,X3)
& below(X1,X3,X2) )
=> X2 = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t26_lattices])]) ).
fof(c_0_6,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& join_semilatt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ( below(X1,X2,X3)
<=> join(X1,X2,X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[d3_lattices]) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& join_commutative(X1)
& join_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> join_commut(X1,X2,X3) = join_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k3_lattices]) ).
fof(c_0_8,plain,
! [X1904,X1905,X1906] :
( empty_carrier(X1904)
| ~ join_commutative(X1904)
| ~ join_semilatt_str(X1904)
| ~ element(X1905,the_carrier(X1904))
| ~ element(X1906,the_carrier(X1904))
| join_commut(X1904,X1905,X1906) = join(X1904,X1905,X1906) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])]) ).
fof(c_0_9,negated_conjecture,
( ~ empty_carrier(esk290_0)
& join_commutative(esk290_0)
& join_semilatt_str(esk290_0)
& element(esk291_0,the_carrier(esk290_0))
& element(esk292_0,the_carrier(esk290_0))
& below(esk290_0,esk291_0,esk292_0)
& below(esk290_0,esk292_0,esk291_0)
& esk291_0 != esk292_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_10,plain,
! [X1492,X1493,X1494] :
( ( ~ below(X1492,X1493,X1494)
| join(X1492,X1493,X1494) = X1494
| ~ element(X1494,the_carrier(X1492))
| ~ element(X1493,the_carrier(X1492))
| empty_carrier(X1492)
| ~ join_semilatt_str(X1492) )
& ( join(X1492,X1493,X1494) != X1494
| below(X1492,X1493,X1494)
| ~ element(X1494,the_carrier(X1492))
| ~ element(X1493,the_carrier(X1492))
| empty_carrier(X1492)
| ~ join_semilatt_str(X1492) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X1241,X1242,X1243] :
( empty_carrier(X1241)
| ~ join_commutative(X1241)
| ~ join_semilatt_str(X1241)
| ~ element(X1242,the_carrier(X1241))
| ~ element(X1243,the_carrier(X1241))
| join_commut(X1241,X1242,X1243) = join_commut(X1241,X1243,X1242) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_12,plain,
( empty_carrier(X1)
| join_commut(X1,X2,X3) = join(X1,X2,X3)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
element(esk292_0,the_carrier(esk290_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
join_semilatt_str(esk290_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
join_commutative(esk290_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,negated_conjecture,
~ empty_carrier(esk290_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( join(X1,X2,X3) = X3
| empty_carrier(X1)
| ~ below(X1,X2,X3)
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
below(esk290_0,esk291_0,esk292_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
element(esk291_0,the_carrier(esk290_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_20,negated_conjecture,
below(esk290_0,esk292_0,esk291_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
( empty_carrier(X1)
| join_commut(X1,X2,X3) = join_commut(X1,X3,X2)
| ~ join_commutative(X1)
| ~ join_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( join_commut(esk290_0,X1,esk292_0) = join(esk290_0,X1,esk292_0)
| ~ element(X1,the_carrier(esk290_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_23,negated_conjecture,
join(esk290_0,esk291_0,esk292_0) = esk292_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14]),c_0_13]),c_0_19])]),c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( join_commut(esk290_0,X1,esk291_0) = join(esk290_0,X1,esk291_0)
| ~ element(X1,the_carrier(esk290_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_19]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_25,negated_conjecture,
join(esk290_0,esk292_0,esk291_0) = esk291_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_14]),c_0_19]),c_0_13])]),c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( join_commut(esk290_0,X1,esk292_0) = join_commut(esk290_0,esk292_0,X1)
| ~ element(X1,the_carrier(esk290_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_13]),c_0_14]),c_0_15])]),c_0_16]) ).
cnf(c_0_27,negated_conjecture,
join_commut(esk290_0,esk291_0,esk292_0) = esk292_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
join_commut(esk290_0,esk292_0,esk291_0) = esk291_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_13]),c_0_25]) ).
cnf(c_0_29,negated_conjecture,
esk291_0 != esk292_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_27]),c_0_28]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : SEU305+2 : TPTP v9.2.1. Released v3.3.0.
% 0.02/0.21 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.42 % Computer : n014.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8042.1875MB
% 0.12/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Tue May 5 02:56:21 EDT 2026
% 0.12/0.44 % CPUTime :
% 0.14/0.46 % start to proof: theBenchmark
% 11.47/9.38 % Version : CSE_E---1.7
% 11.47/9.38 % Problem : theBenchmark.p
% 11.47/9.38 % SZS status Theorem for theBenchmark.p
% 11.47/9.38 % SZS output start CNFRefutation
% See solution above
% 11.57/9.42 % Total time : 7.605s
%------------------------------------------------------------------------------