%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET928+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n002.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 05:08:59 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 57 ( 16 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 65 ( 33 ~; 19 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t72_zfmisc_1,conjecture,
! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_zfmisc_1) ).
fof(t55_zfmisc_1,axiom,
! [X1,X2,X3] :
~ ( disjoint(unordered_pair(X1,X2),X3)
& in(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_zfmisc_1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(t83_xboole_1,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t57_zfmisc_1,axiom,
! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( set_difference(unordered_pair(X1,X2),X3) = unordered_pair(X1,X2)
<=> ( ~ in(X1,X3)
& ~ in(X2,X3) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t72_zfmisc_1])]) ).
fof(c_0_6,plain,
! [X31,X32,X33] :
( ~ disjoint(unordered_pair(X31,X32),X33)
| ~ in(X31,X33) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t55_zfmisc_1])]) ).
fof(c_0_7,plain,
! [X25,X26] : unordered_pair(X25,X26) = unordered_pair(X26,X25),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
fof(c_0_8,negated_conjecture,
( ( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0)
| in(esk3_0,esk5_0)
| in(esk4_0,esk5_0) )
& ( ~ in(esk3_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0) )
& ( ~ in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
fof(c_0_9,plain,
! [X40,X41] :
( ( ~ disjoint(X40,X41)
| set_difference(X40,X41) = X40 )
& ( set_difference(X40,X41) != X40
| disjoint(X40,X41) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
cnf(c_0_10,plain,
( ~ disjoint(unordered_pair(X1,X2),X3)
| ~ in(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X1,X2,X3] :
~ ( ~ in(X1,X2)
& ~ in(X3,X2)
& ~ disjoint(unordered_pair(X1,X3),X2) ),
inference(fof_simplification,[status(thm)],[t57_zfmisc_1]) ).
cnf(c_0_13,negated_conjecture,
( in(esk3_0,esk5_0)
| in(esk4_0,esk5_0)
| set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) != unordered_pair(esk3_0,esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( ~ disjoint(unordered_pair(X1,X2),X3)
| ~ in(X2,X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_16,plain,
! [X34,X35,X36] :
( in(X34,X35)
| in(X36,X35)
| disjoint(unordered_pair(X34,X36),X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_17,plain,
( disjoint(X1,X2)
| set_difference(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0)
| ~ in(esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,negated_conjecture,
~ disjoint(unordered_pair(esk3_0,esk4_0),esk5_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( set_difference(unordered_pair(esk3_0,esk4_0),esk5_0) = unordered_pair(esk3_0,esk4_0)
| ~ in(esk3_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| in(X3,X2)
| disjoint(unordered_pair(X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
~ in(esk4_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
~ in(esk3_0,esk5_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_21]),c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET928+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.32 % Computer : n002.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:40:31 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------