%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU413+1 : TPTP v9.2.1. Released v3.4.0.
% 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 : n027.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 05:12:13 PM UTC 2026
% Result : Theorem 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 117 ( 41 ~; 37 |; 21 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t23_latsum_1,conjecture,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
& r1_orders_2(k1_latsum_1(X1,X2),X3,X4)
& r2_hidden(X4,u1_struct_0(X1)) )
=> r2_hidden(X3,u1_struct_0(X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_latsum_1) ).
fof(t21_latsum_1,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3,X4] :
( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
& r2_hidden(k4_tarski(X3,X4),u1_orders_2(k1_latsum_1(X1,X2)))
& r2_hidden(X4,u1_struct_0(X1)) )
=> r2_hidden(X3,u1_struct_0(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_latsum_1) ).
fof(d9_orders_2,axiom,
! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( m1_subset_1(X2,u1_struct_0(X1))
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(X1))
=> ( r1_orders_2(X1,X2,X3)
<=> r2_hidden(k4_tarski(X2,X3),u1_orders_2(X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_orders_2) ).
fof(dt_k1_latsum_1,axiom,
! [X1,X2] :
( ( l1_orders_2(X1)
& l1_orders_2(X2) )
=> ( v1_orders_2(k1_latsum_1(X1,X2))
& l1_orders_2(k1_latsum_1(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_latsum_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( l1_orders_2(X1)
=> ! [X2] :
( l1_orders_2(X2)
=> ! [X3] :
( m1_subset_1(X3,u1_struct_0(k1_latsum_1(X1,X2)))
=> ! [X4] :
( m1_subset_1(X4,u1_struct_0(k1_latsum_1(X1,X2)))
=> ( ( v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
& m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
& r1_orders_2(k1_latsum_1(X1,X2),X3,X4)
& r2_hidden(X4,u1_struct_0(X1)) )
=> r2_hidden(X3,u1_struct_0(X1)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t23_latsum_1]) ).
fof(c_0_5,plain,
! [X121,X122,X123,X124] :
( ~ l1_orders_2(X121)
| ~ l1_orders_2(X122)
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X121),u1_struct_0(X122)),X122)
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X121),u1_struct_0(X122)),k1_zfmisc_1(u1_struct_0(X122)))
| ~ r2_hidden(k4_tarski(X123,X124),u1_orders_2(k1_latsum_1(X121,X122)))
| ~ r2_hidden(X124,u1_struct_0(X121))
| r2_hidden(X123,u1_struct_0(X121)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_latsum_1])])]) ).
fof(c_0_6,negated_conjecture,
( l1_orders_2(esk1_0)
& l1_orders_2(esk2_0)
& m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
& m1_subset_1(esk4_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
& v12_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0)
& m1_subset_1(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),k1_zfmisc_1(u1_struct_0(esk2_0)))
& r1_orders_2(k1_latsum_1(esk1_0,esk2_0),esk3_0,esk4_0)
& r2_hidden(esk4_0,u1_struct_0(esk1_0))
& ~ r2_hidden(esk3_0,u1_struct_0(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( r2_hidden(X3,u1_struct_0(X1))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2)
| ~ v12_waybel_0(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),X2)
| ~ m1_subset_1(k3_xboole_0(u1_struct_0(X1),u1_struct_0(X2)),k1_zfmisc_1(u1_struct_0(X2)))
| ~ r2_hidden(k4_tarski(X3,X4),u1_orders_2(k1_latsum_1(X1,X2)))
| ~ r2_hidden(X4,u1_struct_0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
m1_subset_1(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),k1_zfmisc_1(u1_struct_0(esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
v12_waybel_0(k3_xboole_0(u1_struct_0(esk1_0),u1_struct_0(esk2_0)),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
l1_orders_2(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
l1_orders_2(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_12,plain,
! [X86,X87,X88] :
( ( ~ r1_orders_2(X86,X87,X88)
| r2_hidden(k4_tarski(X87,X88),u1_orders_2(X86))
| ~ m1_subset_1(X88,u1_struct_0(X86))
| ~ m1_subset_1(X87,u1_struct_0(X86))
| ~ l1_orders_2(X86) )
& ( ~ r2_hidden(k4_tarski(X87,X88),u1_orders_2(X86))
| r1_orders_2(X86,X87,X88)
| ~ m1_subset_1(X88,u1_struct_0(X86))
| ~ m1_subset_1(X87,u1_struct_0(X86))
| ~ l1_orders_2(X86) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d9_orders_2])])])]) ).
cnf(c_0_13,negated_conjecture,
( r2_hidden(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(k4_tarski(X1,X2),u1_orders_2(k1_latsum_1(esk1_0,esk2_0)))
| ~ r2_hidden(X2,u1_struct_0(esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]),c_0_10]),c_0_11])]) ).
cnf(c_0_14,plain,
( r2_hidden(k4_tarski(X2,X3),u1_orders_2(X1))
| ~ r1_orders_2(X1,X2,X3)
| ~ m1_subset_1(X3,u1_struct_0(X1))
| ~ m1_subset_1(X2,u1_struct_0(X1))
| ~ l1_orders_2(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( r2_hidden(X1,u1_struct_0(esk1_0))
| ~ r2_hidden(X2,u1_struct_0(esk1_0))
| ~ r1_orders_2(k1_latsum_1(esk1_0,esk2_0),X1,X2)
| ~ m1_subset_1(X2,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| ~ m1_subset_1(X1,u1_struct_0(k1_latsum_1(esk1_0,esk2_0)))
| ~ l1_orders_2(k1_latsum_1(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
r1_orders_2(k1_latsum_1(esk1_0,esk2_0),esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
r2_hidden(esk4_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
m1_subset_1(esk4_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
m1_subset_1(esk3_0,u1_struct_0(k1_latsum_1(esk1_0,esk2_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
~ r2_hidden(esk3_0,u1_struct_0(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_21,plain,
! [X91,X92] :
( ( v1_orders_2(k1_latsum_1(X91,X92))
| ~ l1_orders_2(X91)
| ~ l1_orders_2(X92) )
& ( l1_orders_2(k1_latsum_1(X91,X92))
| ~ l1_orders_2(X91)
| ~ l1_orders_2(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k1_latsum_1])])]) ).
cnf(c_0_22,negated_conjecture,
~ l1_orders_2(k1_latsum_1(esk1_0,esk2_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_15,c_0_16]),c_0_17]),c_0_18]),c_0_19])]),c_0_20]) ).
cnf(c_0_23,plain,
( l1_orders_2(k1_latsum_1(X1,X2))
| ~ l1_orders_2(X1)
| ~ l1_orders_2(X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_10]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SEU413+1 : TPTP v9.2.1. Released v3.4.0.
% 0.13/0.13 % 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
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 03:06:20 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.36 % start to proof: theBenchmark
% 1.31/1.74 % Version : CSE_E---1.7
% 1.31/1.74 % Problem : theBenchmark.p
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74 % SZS output start CNFRefutation
% See solution above
% 1.31/1.74 % Total time : 1.375s
%------------------------------------------------------------------------------