%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU304+1 : 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 : n019.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 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 11 unt; 0 def)
% Number of atoms : 187 ( 21 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 222 ( 76 ~; 73 |; 44 &)
% ( 4 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 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 : 73 ( 0 sgn 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_lattices,conjecture,
! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_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(dt_l3_lattices,axiom,
! [X1] :
( latt_str(X1)
=> ( meet_semilatt_str(X1)
& join_semilatt_str(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(commutativity_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(redefinition_k4_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(d8_lattices,axiom,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( meet_absorbing(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,meet(X1,X2,X3),X3) = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattices) ).
fof(dt_k2_lattices,axiom,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_lattices) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_absorbing(X1)
& latt_str(X1) )
=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> below(X1,meet_commut(X1,X2,X3),X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t23_lattices])]) ).
fof(c_0_8,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_9,plain,
! [X138] :
( ( meet_semilatt_str(X138)
| ~ latt_str(X138) )
& ( join_semilatt_str(X138)
| ~ latt_str(X138) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_l3_lattices])])]) ).
fof(c_0_10,negated_conjecture,
( ~ empty_carrier(esk12_0)
& meet_commutative(esk12_0)
& meet_absorbing(esk12_0)
& latt_str(esk12_0)
& element(esk13_0,the_carrier(esk12_0))
& element(esk14_0,the_carrier(esk12_0))
& ~ below(esk12_0,meet_commut(esk12_0,esk13_0,esk14_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2) ),
inference(fof_simplification,[status(thm)],[commutativity_k4_lattices]) ).
fof(c_0_12,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_commutative(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> meet_commut(X1,X2,X3) = meet(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k4_lattices]) ).
fof(c_0_13,plain,
! [X113,X114,X115] :
( ( ~ below(X113,X114,X115)
| join(X113,X114,X115) = X115
| ~ element(X115,the_carrier(X113))
| ~ element(X114,the_carrier(X113))
| empty_carrier(X113)
| ~ join_semilatt_str(X113) )
& ( join(X113,X114,X115) != X115
| below(X113,X114,X115)
| ~ element(X115,the_carrier(X113))
| ~ element(X114,the_carrier(X113))
| empty_carrier(X113)
| ~ join_semilatt_str(X113) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_14,plain,
( join_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
latt_str(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X104,X105,X106] :
( empty_carrier(X104)
| ~ meet_commutative(X104)
| ~ meet_semilatt_str(X104)
| ~ element(X105,the_carrier(X104))
| ~ element(X106,the_carrier(X104))
| meet_commut(X104,X105,X106) = meet_commut(X104,X106,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_17,plain,
! [X167,X168,X169] :
( empty_carrier(X167)
| ~ meet_commutative(X167)
| ~ meet_semilatt_str(X167)
| ~ element(X168,the_carrier(X167))
| ~ element(X169,the_carrier(X167))
| meet_commut(X167,X168,X169) = meet(X167,X168,X169) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_18,negated_conjecture,
~ below(esk12_0,meet_commut(esk12_0,esk13_0,esk14_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( below(X1,X2,X3)
| empty_carrier(X1)
| join(X1,X2,X3) != X3
| ~ element(X3,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,negated_conjecture,
element(esk13_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
~ empty_carrier(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
join_semilatt_str(esk12_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet_commut(X1,X3,X2)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( empty_carrier(X1)
| meet_commut(X1,X2,X3) = meet(X1,X2,X3)
| ~ meet_commutative(X1)
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( meet_semilatt_str(X1)
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_26,plain,
! [X1] :
( ( ~ empty_carrier(X1)
& latt_str(X1) )
=> ( meet_absorbing(X1)
<=> ! [X2] :
( element(X2,the_carrier(X1))
=> ! [X3] :
( element(X3,the_carrier(X1))
=> join(X1,meet(X1,X2,X3),X3) = X3 ) ) ) ),
inference(fof_simplification,[status(thm)],[d8_lattices]) ).
cnf(c_0_27,negated_conjecture,
( join(esk12_0,meet_commut(esk12_0,esk13_0,esk14_0),esk13_0) != esk13_0
| ~ element(meet_commut(esk12_0,esk13_0,esk14_0),the_carrier(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]),c_0_21]),c_0_22])]) ).
cnf(c_0_28,plain,
( meet_commut(X1,X2,X3) = meet(X1,X3,X2)
| empty_carrier(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
element(esk14_0,the_carrier(esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_30,negated_conjecture,
meet_semilatt_str(esk12_0),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_31,negated_conjecture,
meet_commutative(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_32,plain,
! [X116,X117,X118] :
( ( ~ meet_absorbing(X116)
| ~ element(X117,the_carrier(X116))
| ~ element(X118,the_carrier(X116))
| join(X116,meet(X116,X117,X118),X118) = X118
| empty_carrier(X116)
| ~ latt_str(X116) )
& ( element(esk1_1(X116),the_carrier(X116))
| meet_absorbing(X116)
| empty_carrier(X116)
| ~ latt_str(X116) )
& ( element(esk2_1(X116),the_carrier(X116))
| meet_absorbing(X116)
| empty_carrier(X116)
| ~ latt_str(X116) )
& ( join(X116,meet(X116,esk1_1(X116),esk2_1(X116)),esk2_1(X116)) != esk2_1(X116)
| meet_absorbing(X116)
| empty_carrier(X116)
| ~ latt_str(X116) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])]) ).
fof(c_0_33,plain,
! [X1,X2,X3] :
( ( ~ empty_carrier(X1)
& meet_semilatt_str(X1)
& element(X2,the_carrier(X1))
& element(X3,the_carrier(X1)) )
=> element(meet(X1,X2,X3),the_carrier(X1)) ),
inference(fof_simplification,[status(thm)],[dt_k2_lattices]) ).
cnf(c_0_34,negated_conjecture,
( join(esk12_0,meet(esk12_0,esk14_0,esk13_0),esk13_0) != esk13_0
| ~ element(meet(esk12_0,esk14_0,esk13_0),the_carrier(esk12_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]),c_0_29]),c_0_30]),c_0_31])]),c_0_21]) ).
cnf(c_0_35,plain,
( join(X1,meet(X1,X2,X3),X3) = X3
| empty_carrier(X1)
| ~ meet_absorbing(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1))
| ~ latt_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
meet_absorbing(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_37,plain,
! [X130,X131,X132] :
( empty_carrier(X130)
| ~ meet_semilatt_str(X130)
| ~ element(X131,the_carrier(X130))
| ~ element(X132,the_carrier(X130))
| element(meet(X130,X131,X132),the_carrier(X130)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_38,negated_conjecture,
~ element(meet(esk12_0,esk14_0,esk13_0),the_carrier(esk12_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_15]),c_0_20]),c_0_29])]),c_0_21]) ).
cnf(c_0_39,plain,
( empty_carrier(X1)
| element(meet(X1,X2,X3),the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X3,the_carrier(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
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_38,c_0_39]),c_0_20]),c_0_29]),c_0_30])]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU304+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:56:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------