%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU308+2 : 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 : n024.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 05:11:26 PM UTC 2026
% Result : Theorem 33.89s 19.97s
% Output : CNFRefutation 34.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 47 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 14 ~; 9 |; 3 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t17_pre_topc,conjecture,
! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(d3_pre_topc,axiom,
! [X1] :
( one_sorted_str(X1)
=> cast_as_carrier_subset(X1) = the_carrier(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(redefinition_k6_subset_1,axiom,
! [X1,X2,X3] :
( ( element(X2,powerset(X1))
& element(X3,powerset(X1)) )
=> subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(dt_k2_subset_1,axiom,
! [X1] : element(cast_to_subset(X1),powerset(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(d4_subset_1,axiom,
! [X1] : cast_to_subset(X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( one_sorted_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> subset_complement(the_carrier(X1),X2) = subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X2) ) ),
inference(assume_negation,[status(cth)],[t17_pre_topc]) ).
fof(c_0_7,plain,
! [X1604] :
( ~ one_sorted_str(X1604)
| cast_as_carrier_subset(X1604) = the_carrier(X1604) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_pre_topc])]) ).
fof(c_0_8,negated_conjecture,
( one_sorted_str(esk286_0)
& element(esk287_0,powerset(the_carrier(esk286_0)))
& subset_complement(the_carrier(esk286_0),esk287_0) != subset_difference(the_carrier(esk286_0),cast_as_carrier_subset(esk286_0),esk287_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_9,plain,
( cast_as_carrier_subset(X1) = the_carrier(X1)
| ~ one_sorted_str(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
one_sorted_str(esk286_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X1706,X1707] :
( ~ element(X1707,powerset(X1706))
| subset_complement(X1706,X1707) = set_difference(X1706,X1707) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(c_0_12,plain,
! [X2065,X2066,X2067] :
( ~ element(X2066,powerset(X2065))
| ~ element(X2067,powerset(X2065))
| subset_difference(X2065,X2066,X2067) = set_difference(X2066,X2067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).
fof(c_0_13,plain,
! [X1798] : element(cast_to_subset(X1798),powerset(X1798)),
inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).
fof(c_0_14,plain,
! [X1654] : cast_to_subset(X1654) = X1654,
inference(variable_rename,[status(thm)],[d4_subset_1]) ).
cnf(c_0_15,negated_conjecture,
subset_complement(the_carrier(esk286_0),esk287_0) != subset_difference(the_carrier(esk286_0),cast_as_carrier_subset(esk286_0),esk287_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
cast_as_carrier_subset(esk286_0) = the_carrier(esk286_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
element(esk287_0,powerset(the_carrier(esk286_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( subset_difference(X2,X1,X3) = set_difference(X1,X3)
| ~ element(X1,powerset(X2))
| ~ element(X3,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
element(cast_to_subset(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
cast_to_subset(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
subset_difference(the_carrier(esk286_0),the_carrier(esk286_0),esk287_0) != subset_complement(the_carrier(esk286_0),esk287_0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
subset_complement(the_carrier(esk286_0),esk287_0) = set_difference(the_carrier(esk286_0),esk287_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( subset_difference(the_carrier(esk286_0),X1,esk287_0) = set_difference(X1,esk287_0)
| ~ element(X1,powerset(the_carrier(esk286_0))) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_25,plain,
element(X1,powerset(X1)),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
subset_difference(the_carrier(esk286_0),the_carrier(esk286_0),esk287_0) != set_difference(the_carrier(esk286_0),esk287_0),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU308+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.07/0.26 % Computer : n024.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon May 4 21:55:56 EDT 2026
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % start to proof: theBenchmark
% 33.89/19.97 % Version : CSE_E---1.7
% 33.89/19.97 % Problem : theBenchmark.p
% 33.89/19.97 % SZS status Theorem for theBenchmark.p
% 33.89/19.97 % SZS output start CNFRefutation
% See solution above
% 34.00/20.08 % Total time : 15.486s
%------------------------------------------------------------------------------