%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET347+4 : TPTP v9.2.1. Released v2.2.0.
% 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 : n017.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 05:07:45 PM UTC 2026
% Result : Theorem 1.20s 1.71s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 54 ( 24 ~; 18 |; 8 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 31 ( 2 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thI38,conjecture,
equal_set(sum(empty_set),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI38) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(c_0_5,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[thI38])]) ).
fof(c_0_6,plain,
! [X40,X41] :
( ( subset(X40,X41)
| ~ equal_set(X40,X41) )
& ( subset(X41,X40)
| ~ equal_set(X40,X41) )
& ( ~ subset(X40,X41)
| ~ subset(X41,X40)
| equal_set(X40,X41) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_7,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X34,X35,X36,X37,X38] :
( ( ~ subset(X34,X35)
| ~ member(X36,X34)
| member(X36,X35) )
& ( member(esk1_2(X37,X38),X37)
| subset(X37,X38) )
& ( ~ member(esk1_2(X37,X38),X38)
| subset(X37,X38) ) ),
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_10,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
cnf(c_0_11,negated_conjecture,
( ~ subset(empty_set,sum(empty_set))
| ~ subset(sum(empty_set),empty_set) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X50] : ~ member(X50,empty_set),
inference(variable_rename,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X59,X60,X62,X63,X64] :
( ( member(esk2_2(X59,X60),X60)
| ~ member(X59,sum(X60)) )
& ( member(X59,esk2_2(X59,X60))
| ~ member(X59,sum(X60)) )
& ( ~ member(X64,X63)
| ~ member(X62,X64)
| member(X62,sum(X63)) ) ),
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)],[sum])])])])])]) ).
cnf(c_0_15,negated_conjecture,
( member(esk1_2(sum(empty_set),empty_set),sum(empty_set))
| ~ subset(empty_set,sum(empty_set)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
member(esk1_2(sum(empty_set),empty_set),sum(empty_set)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_16]) ).
cnf(c_0_19,plain,
~ member(X1,sum(empty_set)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_18,c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET347+4 : TPTP v9.2.1. Released v2.2.0.
% 0.10/0.13 % 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
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 5 02:18:29 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.20/1.71 % Version : CSE_E---1.7
% 1.20/1.71 % Problem : theBenchmark.p
% 1.20/1.71 % SZS status Theorem for theBenchmark.p
% 1.20/1.71 % SZS output start CNFRefutation
% See solution above
% 1.20/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------