%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU107+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n025.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 05:10:38 PM UTC 2026
% Result : Theorem 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 90 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 93 ( 35 ~; 33 |; 17 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 53 ( 2 sgn 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_finsub_1) ).
fof(redefinition_k2_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(t37_xboole_1,axiom,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t18_finsub_1,conjecture,
! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_finsub_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_difference(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[dt_k2_finsub_1]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_difference(X1,X2,X3) = set_difference(X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k2_finsub_1]) ).
fof(c_0_9,plain,
! [X67,X68,X69] :
( empty(X67)
| ~ preboolean(X67)
| ~ element(X68,X67)
| ~ element(X69,X67)
| element(prebool_difference(X67,X68,X69),X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
fof(c_0_10,plain,
! [X89,X90,X91] :
( empty(X89)
| ~ preboolean(X89)
| ~ element(X90,X89)
| ~ element(X91,X89)
| prebool_difference(X89,X90,X91) = set_difference(X90,X91) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_11,plain,
! [X98,X99] :
( ( set_difference(X98,X99) != empty_set
| subset(X98,X99) )
& ( ~ subset(X98,X99)
| set_difference(X98,X99) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t37_xboole_1])]) ).
fof(c_0_12,plain,
! [X92] : subset(X92,X92),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& preboolean(X1) )
=> in(empty_set,X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t18_finsub_1])]) ).
cnf(c_0_14,plain,
( empty(X1)
| element(prebool_difference(X1,X2,X3),X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( empty(X1)
| prebool_difference(X1,X2,X3) = set_difference(X2,X3)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,negated_conjecture,
( ~ empty(esk11_0)
& preboolean(esk11_0)
& ~ in(empty_set,esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_19,plain,
! [X96,X97] :
( ~ element(X96,X97)
| empty(X97)
| in(X96,X97) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_20,plain,
( element(set_difference(X1,X2),X3)
| empty(X3)
| ~ element(X2,X3)
| ~ element(X1,X3)
| ~ preboolean(X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
set_difference(X1,X1) = empty_set,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X70] : element(esk1_1(X70),X70),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_23,negated_conjecture,
~ in(empty_set,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,negated_conjecture,
~ empty(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( element(empty_set,X1)
| empty(X1)
| ~ element(X2,X1)
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,negated_conjecture,
~ element(empty_set,esk11_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_29,plain,
( element(empty_set,X1)
| empty(X1)
| ~ preboolean(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
preboolean(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU107+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.16/0.32 % Computer : n025.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:43:43 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------