%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET014+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n029.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 05:06:49 PM UTC 2026
% Result : Theorem 1.37s 1.73s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 5 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 119 ( 48 ~; 56 |; 9 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 2 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI45,conjecture,
! [X1,X3,X5] :
( ( subset(X3,X1)
& subset(X5,X1) )
<=> subset(union(X3,X5),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI45) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(union,axiom,
! [X3,X1,X2] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',union) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X3,X5] :
( ( subset(X3,X1)
& subset(X5,X1) )
<=> subset(union(X3,X5),X1) ),
inference(assume_negation,[status(cth)],[thI45]) ).
fof(c_0_5,plain,
! [X37,X38,X39,X40,X41] :
( ( ~ subset(X37,X38)
| ~ member(X39,X37)
| member(X39,X38) )
& ( member(esk1_2(X40,X41),X40)
| subset(X40,X41) )
& ( ~ member(esk1_2(X40,X41),X41)
| subset(X40,X41) ) ),
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)],[subset])])])])])]) ).
fof(c_0_6,negated_conjecture,
( ( ~ subset(esk5_0,esk4_0)
| ~ subset(esk6_0,esk4_0)
| ~ subset(union(esk5_0,esk6_0),esk4_0) )
& ( subset(esk5_0,esk4_0)
| subset(union(esk5_0,esk6_0),esk4_0) )
& ( subset(esk6_0,esk4_0)
| subset(union(esk5_0,esk6_0),esk4_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_7,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( subset(esk6_0,esk4_0)
| subset(union(esk5_0,esk6_0),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X50,X51,X52] :
( ( ~ member(X50,union(X51,X52))
| member(X50,X51)
| member(X50,X52) )
& ( ~ member(X50,X51)
| member(X50,union(X51,X52)) )
& ( ~ member(X50,X52)
| member(X50,union(X51,X52)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union])])]) ).
fof(c_0_10,plain,
! [X45,X46] :
( ( ~ member(X45,power_set(X46))
| subset(X45,X46) )
& ( ~ subset(X45,X46)
| member(X45,power_set(X46)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
cnf(c_0_11,negated_conjecture,
( ~ subset(esk5_0,esk4_0)
| ~ subset(esk6_0,esk4_0)
| ~ subset(union(esk5_0,esk6_0),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( member(X1,esk4_0)
| subset(esk6_0,esk4_0)
| ~ member(X1,union(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( member(esk1_2(union(esk5_0,esk6_0),esk4_0),union(esk5_0,esk6_0))
| ~ subset(esk5_0,esk4_0)
| ~ subset(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk6_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_7]) ).
cnf(c_0_20,plain,
( member(esk1_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_21,negated_conjecture,
( subset(esk5_0,esk4_0)
| subset(union(esk5_0,esk6_0),esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( member(esk1_2(union(esk5_0,esk6_0),esk4_0),union(esk5_0,esk6_0))
| ~ member(esk6_0,power_set(esk4_0))
| ~ subset(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
( member(X1,power_set(X2))
| ~ member(esk1_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( member(esk1_2(esk6_0,X1),esk4_0)
| member(esk6_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,esk4_0)
| subset(esk5_0,esk4_0)
| ~ member(X1,union(esk5_0,esk6_0)) ),
inference(spm,[status(thm)],[c_0_7,c_0_21]) ).
cnf(c_0_26,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk4_0)
| ~ subset(esk5_0,esk4_0)
| ~ subset(esk6_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_28,negated_conjecture,
( member(esk1_2(union(esk5_0,esk6_0),esk4_0),union(esk5_0,esk6_0))
| ~ member(esk6_0,power_set(esk4_0))
| ~ member(esk5_0,power_set(esk4_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_29,negated_conjecture,
member(esk6_0,power_set(esk4_0)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk5_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_7]) ).
cnf(c_0_31,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk4_0)
| ~ member(esk6_0,power_set(esk4_0))
| ~ subset(esk5_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_32,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,negated_conjecture,
( member(esk1_2(union(esk5_0,esk6_0),esk4_0),union(esk5_0,esk6_0))
| ~ member(esk5_0,power_set(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]) ).
cnf(c_0_34,negated_conjecture,
( member(esk1_2(esk5_0,X1),esk4_0)
| member(esk5_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk4_0)
| ~ member(esk6_0,power_set(esk4_0))
| ~ member(esk5_0,power_set(esk4_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_36,negated_conjecture,
( member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk5_0)
| member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk6_0)
| ~ member(esk5_0,power_set(esk4_0)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
member(esk5_0,power_set(esk4_0)),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( ~ member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk4_0)
| ~ member(esk5_0,power_set(esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_29])]) ).
cnf(c_0_39,negated_conjecture,
( member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk6_0)
| member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk5_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37])]) ).
cnf(c_0_40,negated_conjecture,
~ member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_37])]) ).
cnf(c_0_41,negated_conjecture,
member(esk1_2(union(esk5_0,esk6_0),esk4_0),esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_39]),c_0_40]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_41]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET014+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n029.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 02:04:14 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.33 % start to proof: theBenchmark
% 1.37/1.73 % Version : CSE_E---1.7
% 1.37/1.73 % Problem : theBenchmark.p
% 1.37/1.73 % SZS status Theorem for theBenchmark.p
% 1.37/1.73 % SZS output start CNFRefutation
% See solution above
% 1.37/1.74 % Total time : 1.368s
%------------------------------------------------------------------------------