%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU103+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 : n007.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 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 118 ( 11 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 134 ( 49 ~; 41 |; 32 &)
% ( 0 <=>; 12 =>; 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 : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t14_finsub_1,conjecture,
! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(symmetric_difference(X1,X2),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finsub_1) ).
fof(dt_k1_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_union2(X1,X2,X3),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_finsub_1) ).
fof(redefinition_k1_finsub_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_finsub_1) ).
fof(d6_xboole_0,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
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(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ empty(X3)
& preboolean(X3) )
=> ( ( element(X1,X3)
& element(X2,X3) )
=> element(symmetric_difference(X1,X2),X3) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t14_finsub_1])]) ).
fof(c_0_7,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> element(prebool_union2(X1,X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[dt_k1_finsub_1]) ).
fof(c_0_8,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& preboolean(X1)
& element(X2,X1)
& element(X3,X1) )
=> prebool_union2(X1,X2,X3) = set_union2(X2,X3) ),
inference(fof_simplification,[status(thm)],[redefinition_k1_finsub_1]) ).
fof(c_0_9,negated_conjecture,
( ~ empty(esk13_0)
& preboolean(esk13_0)
& element(esk11_0,esk13_0)
& element(esk12_0,esk13_0)
& ~ element(symmetric_difference(esk11_0,esk12_0),esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X104,X105] : symmetric_difference(X104,X105) = set_union2(set_difference(X104,X105),set_difference(X105,X104)),
inference(variable_rename,[status(thm)],[d6_xboole_0]) ).
fof(c_0_11,plain,
! [X106,X107,X108] :
( empty(X106)
| ~ preboolean(X106)
| ~ element(X107,X106)
| ~ element(X108,X106)
| element(prebool_union2(X106,X107,X108),X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
fof(c_0_12,plain,
! [X143,X144,X145] :
( empty(X143)
| ~ preboolean(X143)
| ~ element(X144,X143)
| ~ element(X145,X143)
| prebool_union2(X143,X144,X145) = set_union2(X144,X145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_13,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_14,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]) ).
cnf(c_0_15,negated_conjecture,
~ element(symmetric_difference(esk11_0,esk12_0),esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( empty(X1)
| element(prebool_union2(X1,X2,X3),X1)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
( empty(X1)
| prebool_union2(X1,X2,X3) = set_union2(X2,X3)
| ~ preboolean(X1)
| ~ element(X2,X1)
| ~ element(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_19,plain,
! [X109,X110,X111] :
( empty(X109)
| ~ preboolean(X109)
| ~ element(X110,X109)
| ~ element(X111,X109)
| element(prebool_difference(X109,X110,X111),X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])]) ).
fof(c_0_20,plain,
! [X146,X147,X148] :
( empty(X146)
| ~ preboolean(X146)
| ~ element(X147,X146)
| ~ element(X148,X146)
| prebool_difference(X146,X147,X148) = set_difference(X147,X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
~ element(set_union2(set_difference(esk11_0,esk12_0),set_difference(esk12_0,esk11_0)),esk13_0),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( element(set_union2(X1,X2),X3)
| empty(X3)
| ~ element(X2,X3)
| ~ element(X1,X3)
| ~ preboolean(X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
preboolean(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
~ empty(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,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_19]) ).
cnf(c_0_26,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_20]) ).
cnf(c_0_27,negated_conjecture,
( ~ element(set_difference(esk12_0,esk11_0),esk13_0)
| ~ element(set_difference(esk11_0,esk12_0),esk13_0) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]),c_0_24]) ).
cnf(c_0_28,plain,
( element(set_difference(X1,X2),X3)
| empty(X3)
| ~ element(X2,X3)
| ~ element(X1,X3)
| ~ preboolean(X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
element(esk11_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
element(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_23])]),c_0_24]) ).
cnf(c_0_32,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_31,c_0_28]),c_0_30]),c_0_29]),c_0_23])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU103+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n007.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:42:54 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------