%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU102+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 05:10:37 PM UTC 2026
% Result : Theorem 1.15s 1.62s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 11 unt; 0 def)
% Number of atoms : 71 ( 7 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 76 ( 28 ~; 20 |; 20 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 39 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t13_finsub_1,conjecture,
! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(set_intersection2(X1,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finsub_1) ).
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',redefinition_k2_finsub_1) ).
fof(t48_xboole_1,axiom,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(set_intersection2(X1,X2),X3) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t13_finsub_1])]) ).
fof(c_0_5,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_6,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_7,negated_conjecture,
( ~ empty(esk13_0)
& preboolean(esk13_0)
& element(esk11_0,esk13_0)
& element(esk12_0,esk13_0)
& ~ element(set_intersection2(esk11_0,esk12_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X122,X123] : set_difference(X122,set_difference(X122,X123)) = set_intersection2(X122,X123),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_9,plain,
! [X80,X81,X82] :
( empty(X80)
| ~ preboolean(X80)
| ~ element(X81,X80)
| ~ element(X82,X80)
| element(prebool_difference(X80,X81,X82),X80) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
fof(c_0_10,plain,
! [X107,X108,X109] :
( empty(X107)
| ~ preboolean(X107)
| ~ element(X108,X107)
| ~ element(X109,X107)
| prebool_difference(X107,X108,X109) = set_difference(X108,X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
cnf(c_0_11,negated_conjecture,
~ element(set_intersection2(esk11_0,esk12_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,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_14,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_15,negated_conjecture,
~ element(set_difference(esk11_0,set_difference(esk11_0,esk12_0)),esk13_0),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( element(set_difference(X1,X2),X3)
| empty(X3)
| ~ element(X2,X3)
| ~ element(X1,X3)
| ~ preboolean(X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
element(esk11_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
preboolean(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
~ empty(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
~ element(set_difference(esk11_0,esk12_0),esk13_0),
inference(sr,[status(thm)],[inference(cn,[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]) ).
cnf(c_0_21,negated_conjecture,
element(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_22,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_20,c_0_16]),c_0_21]),c_0_17]),c_0_18])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU102+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue May 5 02:43:32 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.15/1.62 % Version : CSE_E---1.7
% 1.15/1.62 % Problem : theBenchmark.p
% 1.15/1.62 % SZS status Theorem for theBenchmark.p
% 1.15/1.62 % SZS output start CNFRefutation
% See solution above
% 1.15/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------