%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM385+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 : n028.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 04:57:13 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 15 unt; 0 def)
% Number of atoms : 85 ( 33 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 86 ( 33 ~; 36 |; 9 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_ordinal1,conjecture,
! [X1,X2] :
( succ(X1) = succ(X2)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_ordinal1) ).
fof(t10_ordinal1,axiom,
! [X1] : in(X1,succ(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(d1_ordinal1,axiom,
! [X1] : succ(X1) = set_union2(X1,singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( succ(X1) = succ(X2)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t12_ordinal1]) ).
fof(c_0_7,plain,
! [X98] : in(X98,succ(X98)),
inference(variable_rename,[status(thm)],[t10_ordinal1]) ).
fof(c_0_8,plain,
! [X61] : succ(X61) = set_union2(X61,singleton(X61)),
inference(variable_rename,[status(thm)],[d1_ordinal1]) ).
fof(c_0_9,negated_conjecture,
( succ(esk14_0) = succ(esk15_0)
& esk14_0 != esk15_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X69,X70,X71,X72,X73,X74,X75,X76] :
( ( ~ in(X72,X71)
| in(X72,X69)
| in(X72,X70)
| X71 != set_union2(X69,X70) )
& ( ~ in(X73,X69)
| in(X73,X71)
| X71 != set_union2(X69,X70) )
& ( ~ in(X73,X70)
| in(X73,X71)
| X71 != set_union2(X69,X70) )
& ( ~ in(esk2_3(X74,X75,X76),X74)
| ~ in(esk2_3(X74,X75,X76),X76)
| X76 = set_union2(X74,X75) )
& ( ~ in(esk2_3(X74,X75,X76),X75)
| ~ in(esk2_3(X74,X75,X76),X76)
| X76 = set_union2(X74,X75) )
& ( in(esk2_3(X74,X75,X76),X76)
| in(esk2_3(X74,X75,X76),X74)
| in(esk2_3(X74,X75,X76),X75)
| X76 = set_union2(X74,X75) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_11,plain,
in(X1,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
succ(X1) = set_union2(X1,singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
succ(esk14_0) = succ(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,plain,
! [X62,X63,X64,X65,X66,X67] :
( ( ~ in(X64,X63)
| X64 = X62
| X63 != singleton(X62) )
& ( X65 != X62
| in(X65,X63)
| X63 != singleton(X62) )
& ( ~ in(esk1_2(X66,X67),X67)
| esk1_2(X66,X67) != X66
| X67 = singleton(X66) )
& ( in(esk1_2(X66,X67),X67)
| esk1_2(X66,X67) = X66
| X67 = singleton(X66) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_15,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
in(X1,set_union2(X1,singleton(X1))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
set_union2(esk15_0,singleton(esk15_0)) = set_union2(esk14_0,singleton(esk14_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_12]) ).
fof(c_0_18,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_19,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
in(esk14_0,set_union2(esk15_0,singleton(esk15_0))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X54,X55] :
( ~ in(X54,X55)
| ~ in(X55,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( in(esk14_0,singleton(esk15_0))
| in(esk14_0,esk15_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
esk14_0 != esk15_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,negated_conjecture,
in(esk14_0,esk15_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( in(X1,singleton(esk14_0))
| in(X1,esk14_0)
| ~ in(X1,set_union2(esk15_0,singleton(esk15_0))) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_29,negated_conjecture,
~ in(esk15_0,esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
in(esk15_0,singleton(esk14_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_16]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM385+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.32 % Computer : n028.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 00:31:30 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------