%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU131+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 : n031.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 05:10:43 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 100 ( 26 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 104 ( 38 ~; 48 |; 10 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 72 ( 7 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_boole) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(l32_xboole_1,conjecture,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_5,plain,
! [X38,X39,X40,X41,X42,X43,X44,X45] :
( ( in(X41,X38)
| ~ in(X41,X40)
| X40 != set_difference(X38,X39) )
& ( ~ in(X41,X39)
| ~ in(X41,X40)
| X40 != set_difference(X38,X39) )
& ( ~ in(X42,X38)
| in(X42,X39)
| in(X42,X40)
| X40 != set_difference(X38,X39) )
& ( ~ in(esk2_3(X43,X44,X45),X45)
| ~ in(esk2_3(X43,X44,X45),X43)
| in(esk2_3(X43,X44,X45),X44)
| X45 = set_difference(X43,X44) )
& ( in(esk2_3(X43,X44,X45),X43)
| in(esk2_3(X43,X44,X45),X45)
| X45 = set_difference(X43,X44) )
& ( ~ in(esk2_3(X43,X44,X45),X44)
| in(esk2_3(X43,X44,X45),X45)
| X45 = set_difference(X43,X44) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])])]) ).
cnf(c_0_6,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_7,plain,
! [X56] : set_difference(empty_set,X56) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(c_0_8,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X32,X33,X34,X35,X36] :
( ( ~ subset(X32,X33)
| ~ in(X34,X32)
| in(X34,X33) )
& ( in(esk1_2(X35,X36),X35)
| subset(X35,X36) )
& ( ~ in(esk1_2(X35,X36),X36)
| subset(X35,X36) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(c_0_11,plain,
( ~ in(X1,empty_set)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
inference(assume_negation,[status(cth)],[l32_xboole_1]) ).
cnf(c_0_14,plain,
( subset(empty_set,X1)
| ~ in(esk1_2(empty_set,X1),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,negated_conjecture,
( ( set_difference(esk3_0,esk4_0) != empty_set
| ~ subset(esk3_0,esk4_0) )
& ( set_difference(esk3_0,esk4_0) = empty_set
| subset(esk3_0,esk4_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
cnf(c_0_16,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
subset(empty_set,X1),
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( set_difference(esk3_0,esk4_0) = empty_set
| subset(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
~ in(X1,empty_set),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_11]) ).
cnf(c_0_20,plain,
( in(esk2_3(X1,X2,X3),X1)
| in(esk2_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( set_difference(esk3_0,esk4_0) = empty_set
| in(X1,esk4_0)
| ~ in(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_23,plain,
( set_difference(X1,X2) = empty_set
| in(esk2_3(X1,X2,empty_set),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
( in(esk2_3(X1,X2,X3),X3)
| X3 = set_difference(X1,X2)
| ~ in(esk2_3(X1,X2,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,negated_conjecture,
( set_difference(esk3_0,esk4_0) = empty_set
| set_difference(esk3_0,X1) = empty_set
| in(esk2_3(esk3_0,X1,empty_set),esk4_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( subset(X1,X2)
| in(esk1_2(X1,X2),set_difference(X1,X3))
| in(esk1_2(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_12]) ).
cnf(c_0_28,negated_conjecture,
set_difference(esk3_0,esk4_0) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).
cnf(c_0_29,negated_conjecture,
( set_difference(esk3_0,esk4_0) != empty_set
| ~ subset(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_30,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_31,negated_conjecture,
( subset(esk3_0,X1)
| in(esk1_2(esk3_0,X1),esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_19]) ).
cnf(c_0_32,negated_conjecture,
~ subset(esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU131+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n031.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:46:53 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % 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 : 1.371s
%------------------------------------------------------------------------------