%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM383+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 : n010.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 1.18s 2.04s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 72 ( 35 ~; 25 |; 7 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 51 ( 3 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(t7_ordinal1,conjecture,
! [X1,X2] :
~ ( in(X1,X2)
& subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
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,plain,
! [X69,X70,X71] :
( ~ in(X69,X70)
| ~ element(X70,powerset(X71))
| ~ empty(X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(c_0_7,plain,
! [X64,X65] :
( ( ~ element(X64,powerset(X65))
| subset(X64,X65) )
& ( ~ subset(X64,X65)
| element(X64,powerset(X65)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
~ ( in(X1,X2)
& subset(X2,X1) ),
inference(assume_negation,[status(cth)],[t7_ordinal1]) ).
fof(c_0_9,plain,
! [X66,X67,X68] :
( ~ in(X66,X67)
| ~ element(X67,powerset(X68))
| element(X66,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
cnf(c_0_10,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
( in(esk12_0,esk13_0)
& subset(esk13_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_13,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
subset(esk13_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X62,X63] :
( ~ element(X62,X63)
| empty(X63)
| in(X62,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
cnf(c_0_17,plain,
( element(X1,X2)
| ~ subset(X3,X2)
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( ~ empty(esk12_0)
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
in(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_21,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( element(X1,esk12_0)
| ~ in(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
~ empty(esk12_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_24,plain,
! [X42,X43] :
( ~ in(X42,X43)
| ~ in(X43,X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
cnf(c_0_25,negated_conjecture,
( in(X1,esk12_0)
| ~ in(X1,esk13_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_27,negated_conjecture,
in(esk12_0,esk12_0),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.31 % Problem : NUM383+1 : TPTP v9.2.1. Released v3.2.0.
% 0.05/0.31 % 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
% 0.10/0.59 % Computer : n010.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8042.1875MB
% 0.10/0.59 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Tue May 5 00:31:21 EDT 2026
% 0.10/0.60 % CPUTime :
% 0.10/0.61 % start to proof: theBenchmark
% 1.18/2.04 % Version : CSE_E---1.7
% 1.18/2.04 % Problem : theBenchmark.p
% 1.18/2.04 % SZS status Theorem for theBenchmark.p
% 1.18/2.04 % SZS output start CNFRefutation
% See solution above
% 1.18/2.04 % Total time : 1.419s
%------------------------------------------------------------------------------