%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET588+3 : 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 : n019.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 05:08:03 PM UTC 2026
% Result : Theorem 1.62s 1.87s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 4 unt; 0 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 59 ( 22 ~; 24 |; 7 &)
% ( 3 <=>; 3 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 2 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_difference_subset1,conjecture,
! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X1,X3),difference(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_subset1) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(X1,X2)
=> subset(difference(X1,X3),difference(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_difference_subset1]) ).
fof(c_0_4,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_5,plain,
! [X17,X18,X19,X20,X21] :
( ( ~ subset(X17,X18)
| ~ member(X19,X17)
| member(X19,X18) )
& ( member(esk1_2(X20,X21),X20)
| subset(X20,X21) )
& ( ~ member(esk1_2(X20,X21),X21)
| subset(X20,X21) ) ),
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_defn])])])])])]) ).
fof(c_0_6,negated_conjecture,
( subset(esk2_0,esk3_0)
& ~ subset(difference(esk2_0,esk4_0),difference(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_7,plain,
! [X14,X15,X16] :
( ( member(X16,X14)
| ~ member(X16,difference(X14,X15)) )
& ( ~ member(X16,X15)
| ~ member(X16,difference(X14,X15)) )
& ( ~ member(X16,X14)
| member(X16,X15)
| member(X16,difference(X14,X15)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
subset(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( member(X1,esk3_0)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,difference(esk3_0,X2))
| member(X1,X2)
| ~ member(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( subset(difference(X1,X2),X3)
| member(esk1_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
( subset(difference(esk2_0,X1),X2)
| member(esk1_2(difference(esk2_0,X1),X2),difference(esk3_0,X3))
| member(esk1_2(difference(esk2_0,X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_20,negated_conjecture,
( subset(difference(esk2_0,X1),difference(esk3_0,X2))
| member(esk1_2(difference(esk2_0,X1),difference(esk3_0,X2)),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ subset(difference(esk2_0,esk4_0),difference(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
subset(difference(esk2_0,X1),difference(esk3_0,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET588+3 : TPTP v9.2.1. Released v2.2.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n019.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 02:28:44 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.62/1.87 % Version : CSE_E---1.7
% 1.62/1.87 % Problem : theBenchmark.p
% 1.62/1.87 % SZS status Theorem for theBenchmark.p
% 1.62/1.87 % SZS output start CNFRefutation
% See solution above
% 1.62/1.87 % Total time : 1.371s
%------------------------------------------------------------------------------