%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU304+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 : Fri Sep 25 02:56:34 PM UTC 2026
% Result : Theorem 2.83s 1.18s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 103 ( 28 unt; 2 def)
% Number of atoms : 425 ( 73 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 498 ( 207 ~; 219 |; 50 &)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 4 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 168 ( 0 sgn 158 !; 10 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& meet_semilatt_str(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k4_lattices) ).
fof(f7,axiom,
! [X0] :
( ( join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(f8,axiom,
! [X0] :
( ( latt_str(X0)
& ~ empty_carrier(X0) )
=> ( meet_absorbing(X0)
<=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattices) ).
fof(f16,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& meet_semilatt_str(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> element(meet_commut(X0,X1,X2),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_lattices) ).
fof(f20,axiom,
! [X0] :
( latt_str(X0)
=> ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l3_lattices) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& meet_semilatt_str(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> meet_commut(X0,X1,X2) = meet(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k4_lattices) ).
fof(f43,conjecture,
! [X0] :
( ( latt_str(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> below(X0,meet_commut(X0,X1,X2),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_lattices) ).
fof(f44,negated_conjecture,
~ ! [X0] :
( ( latt_str(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> below(X0,meet_commut(X0,X1,X2),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1) ),
inference(flattening,[],[f58]) ).
fof(f64,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f65,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ),
inference(flattening,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( meet_absorbing(X0)
<=> ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f67,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( meet_absorbing(X0)
<=> ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| join(X0,meet(X0,X1,X2),X2) = X2 ) ) ) ),
inference(flattening,[],[f66]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| element(meet_commut(X0,X1,X2),the_carrier(X0)) ),
inference(ennf_transformation,[],[f16]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| element(meet_commut(X0,X1,X2),the_carrier(X0)) ),
inference(flattening,[],[f74]) ).
fof(f78,plain,
! [X0] :
( ~ latt_str(X0)
| ( join_semilatt_str(X0)
& meet_semilatt_str(X0) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| meet_commut(X0,X1,X2) = meet(X0,X1,X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| meet_commut(X0,X1,X2) = meet(X0,X1,X2) ),
inference(flattening,[],[f88]) ).
fof(f91,plain,
? [X0] :
( latt_str(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& ~ below(X0,meet_commut(X0,X1,X2),X1) ) ) ),
inference(ennf_transformation,[],[f44]) ).
fof(f92,plain,
? [X0] :
( latt_str(X0)
& meet_absorbing(X0)
& meet_commutative(X0)
& ~ empty_carrier(X0)
& ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& ~ below(X0,meet_commut(X0,X1,X2),X1) ) ) ),
inference(flattening,[],[f91]) ).
fof(f102,plain,
! [X0] :
( ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ below(X0,X1,X2)
| join(X0,X1,X2) = X2 )
& ( join(X0,X1,X2) != X2
| below(X0,X1,X2) ) ) ) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f103,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( ( ~ meet_absorbing(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ! [X2] :
( ~ element(X2,the_carrier(X0))
| join(X0,meet(X0,X1,X2),X2) = X2 ) ) )
& ( ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& join(X0,meet(X0,X1,X2),X2) != X2 ) )
| meet_absorbing(X0) ) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f104,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( ( ~ meet_absorbing(X0)
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| join(X0,meet(X0,X3,X4),X4) = X4 ) ) )
& ( ? [X1] :
( element(X1,the_carrier(X0))
& ? [X2] :
( element(X2,the_carrier(X0))
& join(X0,meet(X0,X1,X2),X2) != X2 ) )
| meet_absorbing(X0) ) ) ),
inference(rectify,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ( ( ~ meet_absorbing(X0)
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| join(X0,meet(X0,X3,X4),X4) = X4 ) ) )
& ( ( element(sK0(X0),the_carrier(X0))
& element(sK1(X0),the_carrier(X0))
& sK1(X0) != join(X0,meet(X0,sK0(X0),sK1(X0)),sK1(X0)) )
| meet_absorbing(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0))],[f104]) ).
fof(f116,plain,
( latt_str(sK11)
& meet_absorbing(sK11)
& meet_commutative(sK11)
& ~ empty_carrier(sK11)
& element(sK12,the_carrier(sK11))
& element(sK13,the_carrier(sK11))
& ~ below(sK11,meet_commut(sK11,sK12,sK13),sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f92]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| join(X0,X1,X2) != X2
| below(X0,X1,X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f126,plain,
! [X3,X0,X4] :
( ~ latt_str(X0)
| empty_carrier(X0)
| ~ meet_absorbing(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X4,the_carrier(X0))
| join(X0,meet(X0,X3,X4),X4) = X4 ),
inference(cnf_transformation,[],[f105]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| element(meet_commut(X0,X1,X2),the_carrier(X0)) ),
inference(cnf_transformation,[],[f75]) ).
fof(f136,plain,
! [X0] :
( ~ latt_str(X0)
| join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f137,plain,
! [X0] :
( ~ latt_str(X0)
| meet_semilatt_str(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0)
| meet_commut(X0,X1,X2) = meet(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f167,plain,
latt_str(sK11),
inference(cnf_transformation,[],[f116]) ).
fof(f168,plain,
meet_absorbing(sK11),
inference(cnf_transformation,[],[f116]) ).
fof(f169,plain,
meet_commutative(sK11),
inference(cnf_transformation,[],[f116]) ).
fof(f170,plain,
~ empty_carrier(sK11),
inference(cnf_transformation,[],[f116]) ).
fof(f171,plain,
element(sK12,the_carrier(sK11)),
inference(cnf_transformation,[],[f116]) ).
fof(f172,plain,
element(sK13,the_carrier(sK11)),
inference(cnf_transformation,[],[f116]) ).
fof(f173,plain,
~ below(sK11,meet_commut(sK11,sK12,sK13),sK12),
inference(cnf_transformation,[],[f116]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| ( meet_commut(X1,X0,X2) = meet_commut(X1,X2,X0) )
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| below(X0,X1,X2)
| ~ join_semilatt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( join(X0,X1,X2) != X2 ) ),
inference(cnf_transformation,[],[f125]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| ( join(X1,meet(X1,X0,X2),X2) = X2 )
| ~ latt_str(X1)
| ~ meet_absorbing(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| element(meet_commut(X1,X0,X2),the_carrier(X1))
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_68,plain,
! [X0: $i] :
( meet_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_69,plain,
! [X0: $i] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X1)
| ( meet_commut(X1,X0,X2) = meet(X1,X0,X2) )
| ~ meet_semilatt_str(X1)
| ~ meet_commutative(X1)
| ~ element(X2,the_carrier(X1))
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_99,negated_conjecture,
~ below(sK11,meet_commut(sK11,sK12,sK13),sK12),
inference(cnf_transformation,[],[f173]) ).
tcf(c_100,negated_conjecture,
element(sK13,the_carrier(sK11)),
inference(cnf_transformation,[],[f172]) ).
tcf(c_101,negated_conjecture,
element(sK12,the_carrier(sK11)),
inference(cnf_transformation,[],[f171]) ).
tcf(c_102,negated_conjecture,
~ empty_carrier(sK11),
inference(cnf_transformation,[],[f170]) ).
tcf(c_103,negated_conjecture,
meet_commutative(sK11),
inference(cnf_transformation,[],[f169]) ).
tcf(c_104,negated_conjecture,
meet_absorbing(sK11),
inference(cnf_transformation,[],[f168]) ).
tcf(c_105,negated_conjecture,
latt_str(sK11),
inference(cnf_transformation,[],[f167]) ).
tcf(c_119,plain,
( join_semilatt_str(sK11)
| ~ latt_str(sK11) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_120,plain,
( meet_semilatt_str(sK11)
| ~ latt_str(sK11) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1072,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| ( meet_commut(X0,X1,X2) = meet(X0,X1,X2) )
| ~ meet_semilatt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_103]) ).
tcf(c_1073,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK11)
| ( meet_commut(sK11,X0,X1) = meet(sK11,X0,X1) )
| ~ meet_semilatt_str(sK11)
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(unflattening,[status(thm)],[c_1072]) ).
tcf(c_1075,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11))
| ( meet_commut(sK11,X0,X1) = meet(sK11,X0,X1) ) ),
inference(global_subsumption_just,[status(thm)],[c_1073,c_105,c_102,c_120,c_1073]) ).
tcf(c_1076,plain,
! [X0: $i,X1: $i] :
( ( meet_commut(sK11,X0,X1) = meet(sK11,X0,X1) )
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(renaming,[status(thm)],[c_1075]) ).
tcf(c_1087,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| element(meet_commut(X0,X1,X2),the_carrier(X0))
| ~ meet_semilatt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_103]) ).
tcf(c_1088,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK11)
| element(meet_commut(sK11,X0,X1),the_carrier(sK11))
| ~ meet_semilatt_str(sK11)
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(unflattening,[status(thm)],[c_1087]) ).
tcf(c_1090,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11))
| element(meet_commut(sK11,X0,X1),the_carrier(sK11)) ),
inference(global_subsumption_just,[status(thm)],[c_1088,c_105,c_102,c_120,c_1088]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i] :
( element(meet_commut(sK11,X0,X1),the_carrier(sK11))
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(renaming,[status(thm)],[c_1090]) ).
tcf(c_1102,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| ( meet_commut(X0,X1,X2) = meet_commut(X0,X2,X1) )
| ~ meet_semilatt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_103]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK11)
| ( meet_commut(sK11,X0,X1) = meet_commut(sK11,X1,X0) )
| ~ meet_semilatt_str(sK11)
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(unflattening,[status(thm)],[c_1102]) ).
tcf(c_1105,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11))
| ( meet_commut(sK11,X0,X1) = meet_commut(sK11,X1,X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_1103,c_105,c_102,c_120,c_1103]) ).
tcf(c_1106,plain,
! [X0: $i,X1: $i] :
( ( meet_commut(sK11,X0,X1) = meet_commut(sK11,X1,X0) )
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(renaming,[status(thm)],[c_1105]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| ~ join_semilatt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X2 != sK12 )
| ( X0 != sK11 )
| ( meet_commut(sK11,sK12,sK13) != X1 )
| ( join(X0,X1,X2) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_99]) ).
tcf(c_1129,plain,
( empty_carrier(sK11)
| ~ join_semilatt_str(sK11)
| ~ element(sK12,the_carrier(sK11))
| ~ element(meet_commut(sK11,sK12,sK13),the_carrier(sK11))
| ( join(sK11,meet_commut(sK11,sK12,sK13),sK12) != sK12 ) ),
inference(unflattening,[status(thm)],[c_1128]) ).
tcf(c_1130,plain,
( ( join(sK11,meet_commut(sK11,sK12,sK13),sK12) != sK12 )
| ~ element(meet_commut(sK11,sK12,sK13),the_carrier(sK11)) ),
inference(global_subsumption_just,[status(thm)],[c_1129,c_105,c_102,c_101,c_119,c_1129]) ).
tcf(c_1131,plain,
( ~ element(meet_commut(sK11,sK12,sK13),the_carrier(sK11))
| ( join(sK11,meet_commut(sK11,sK12,sK13),sK12) != sK12 ) ),
inference(renaming,[status(thm)],[c_1130]) ).
tcf(c_1203,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| ( join(X0,meet(X0,X1,X2),X2) = X2 )
| ~ latt_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_104]) ).
tcf(c_1204,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK11)
| ( join(sK11,meet(sK11,X0,X1),X1) = X1 )
| ~ latt_str(sK11)
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(unflattening,[status(thm)],[c_1203]) ).
tcf(c_1206,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11))
| ( join(sK11,meet(sK11,X0,X1),X1) = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_1204,c_105,c_102,c_1204]) ).
tcf(c_1207,plain,
! [X0: $i,X1: $i] :
( ( join(sK11,meet(sK11,X0,X1),X1) = X1 )
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(renaming,[status(thm)],[c_1206]) ).
tcf(c_1401,plain,
! [X0: $i,X1: $i,X2: $i] :
( empty_carrier(X0)
| ( join(X0,meet(X0,X1,X2),X2) = X2 )
| ~ meet_absorbing(X0)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK11 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_105]) ).
tcf(c_1402,plain,
! [X0: $i,X1: $i] :
( empty_carrier(sK11)
| ( join(sK11,meet(sK11,X0,X1),X1) = X1 )
| ~ meet_absorbing(sK11)
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(unflattening,[status(thm)],[c_1401]) ).
tcf(c_1403,plain,
! [X0: $i,X1: $i] :
( ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11))
| ( join(sK11,meet(sK11,X0,X1),X1) = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_1402,c_1207]) ).
tcf(c_1404,plain,
! [X0: $i,X1: $i] :
( ( join(sK11,meet(sK11,X0,X1),X1) = X1 )
| ~ element(X1,the_carrier(sK11))
| ~ element(X0,the_carrier(sK11)) ),
inference(renaming,[status(thm)],[c_1403]) ).
tcf(c_4407,definition,
iPr_def_19 = meet_commut(sK11,sK12,sK13),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_4408,definition,
iPr_def_20 = join(sK11,iPr_def_19,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_4424,plain,
! [X0: $i,X1: $i] :
( ( join(sK11,meet(sK11,X0,X1),X1) = X1 )
| ~ element(X1,iPr_def_11)
| ~ element(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_1404]) ).
tcf(c_4425,plain,
( ~ element(iPr_def_19,iPr_def_11)
| ( iPr_def_20 != sK12 ) ),
inference(demodulation,[status(thm)],[c_1131,c_4407,c_4408]) ).
tcf(c_4426,plain,
! [X0: $i,X1: $i] :
( ( meet_commut(sK11,X0,X1) = meet_commut(sK11,X1,X0) )
| ~ element(X1,iPr_def_11)
| ~ element(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_1106]) ).
tcf(c_4427,plain,
! [X0: $i,X1: $i] :
( element(meet_commut(sK11,X0,X1),iPr_def_11)
| ~ element(X1,iPr_def_11)
| ~ element(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_1091]) ).
tcf(c_4428,plain,
! [X0: $i,X1: $i] :
( ( meet_commut(sK11,X0,X1) = meet(sK11,X0,X1) )
| ~ element(X1,iPr_def_11)
| ~ element(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_1076]) ).
tcf(c_4431,negated_conjecture,
element(sK12,iPr_def_11),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_4432,negated_conjecture,
element(sK13,iPr_def_11),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_5500,plain,
! [X0: $i] :
( ( join(sK11,meet(sK11,sK13,X0),X0) = X0 )
| ~ element(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4432,c_4424]) ).
tcf(c_5534,plain,
join(sK11,meet(sK11,sK13,sK12),sK12) = sK12,
inference(superposition,[status(thm)],[c_4431,c_5500]) ).
tcf(c_5548,plain,
! [X0: $i] :
( ( meet_commut(sK11,X0,sK12) = meet_commut(sK11,sK12,X0) )
| ~ element(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4431,c_4426]) ).
tcf(c_5575,plain,
meet_commut(sK11,sK12,sK13) = meet_commut(sK11,sK13,sK12),
inference(superposition,[status(thm)],[c_4432,c_5548]) ).
tcf(c_5576,plain,
meet_commut(sK11,sK13,sK12) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_5575,c_4407]) ).
tcf(c_5593,plain,
( element(iPr_def_19,iPr_def_11)
| ~ element(sK13,iPr_def_11)
| ~ element(sK12,iPr_def_11) ),
inference(superposition,[status(thm)],[c_5576,c_4427]) ).
tcf(c_5594,plain,
element(iPr_def_19,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_5593,c_4432,c_4431]) ).
tcf(c_5595,plain,
sK12 != iPr_def_20,
inference(backward_subsumption_resolution,[status(thm)],[c_4425,c_5594]) ).
tcf(c_6424,plain,
! [X0: $i] :
( ( meet_commut(sK11,sK13,X0) = meet(sK11,sK13,X0) )
| ~ element(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_4432,c_4428]) ).
tcf(c_6571,plain,
meet_commut(sK11,sK13,sK12) = meet(sK11,sK13,sK12),
inference(superposition,[status(thm)],[c_4431,c_6424]) ).
tcf(c_6583,plain,
meet(sK11,sK13,sK12) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_6571,c_5576]) ).
tcf(c_6598,plain,
join(sK11,iPr_def_19,sK12) = sK12,
inference(demodulation,[status(thm)],[c_5534,c_6583]) ).
tcf(c_6599,plain,
sK12 = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_6598,c_4408]) ).
tcf(c_6600,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6599,c_5595]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU304+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.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
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:37:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.83/1.18 % SZS status Started for theBenchmark.p
% 2.83/1.18 % SZS status Theorem for theBenchmark.p
% 2.83/1.18
% 2.83/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.83/1.18
% 2.83/1.18 % ------ iProver source info
% 2.83/1.18
% 2.83/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 2.83/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.83/1.18 % git: non_committed_changes: false
% 2.83/1.18
% 2.83/1.18 % ------ Parsing...
% 2.83/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.83/1.18
% 2.83/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 10 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e %
% 2.83/1.18
% 2.83/1.18 % ------ Preprocessing... gs_s sp: 1 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.83/1.18
% 2.83/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.83/1.18 % ------ Proving...
% 2.83/1.18 % ------ Problem Properties
% 2.83/1.18
% 2.83/1.18 %
% 2.83/1.18 % clauses 96
% 2.83/1.18 % conjectures 4
% 2.83/1.18 % EPR 24
% 2.83/1.18 % Horn 77
% 2.83/1.18 % unary 51
% 2.83/1.18 % binary 18
% 2.83/1.18 % lits 187
% 2.83/1.18 % lits eq 25
% 2.83/1.18 % fd_pure 0
% 2.83/1.18 % fd_pseudo 0
% 2.83/1.18 % fd_cond 1
% 2.83/1.18 % fd_pseudo_cond 1
% 2.83/1.18 % AC symbols 0
% 2.83/1.18
% 2.83/1.18 % ------ Schedule dynamic 5 is on
% 2.83/1.18
% 2.83/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.83/1.18
% 2.83/1.18
% 2.83/1.18 % ------
% 2.83/1.18 % Current options:
% 2.83/1.18 % ------
% 2.83/1.18
% 2.83/1.18
% 2.83/1.18 %
% 2.83/1.18
% 2.83/1.18 % ------ Proving...
% 2.83/1.18 %
% 2.83/1.18
% 2.83/1.18 % SZS status Theorem for theBenchmark.p
% 2.83/1.18
% 2.83/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.83/1.18
% 2.83/1.18
%------------------------------------------------------------------------------