%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO085+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n024.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 04:19:16 PM UTC 2026
% Result : Theorem 1.12s 1.61s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 52 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 55 ( 24 ~; 17 |; 9 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 35 ( 1 sgn 16 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(theorem_2_7_1,conjecture,
! [X1] :
( open(X1)
=> ? [X3,X5] :
( X3 != X5
& end_point(X3,X1)
& end_point(X5,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_2_7_1) ).
fof(closed_defn,axiom,
! [X1] :
( closed(X1)
<=> ~ ? [X3] : end_point(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',closed_defn) ).
fof(open_defn,axiom,
! [X1] :
( open(X1)
<=> ? [X3] : end_point(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',open_defn) ).
fof(c6,axiom,
! [X1,X3] :
( end_point(X3,X1)
=> ? [X5] :
( end_point(X5,X1)
& X3 != X5 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c6) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( open(X1)
=> ? [X3,X5] :
( X3 != X5
& end_point(X3,X1)
& end_point(X5,X1) ) ),
inference(assume_negation,[status(cth)],[theorem_2_7_1]) ).
fof(c_0_5,negated_conjecture,
! [X138,X139] :
( open(esk14_0)
& ( X138 = X139
| ~ end_point(X138,esk14_0)
| ~ end_point(X139,esk14_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_6,plain,
! [X97,X98,X99] :
( ( ~ closed(X97)
| ~ end_point(X98,X97) )
& ( end_point(esk6_1(X99),X99)
| closed(X99) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[closed_defn])])])])]) ).
cnf(c_0_7,negated_conjecture,
( X1 = X2
| ~ end_point(X1,esk14_0)
| ~ end_point(X2,esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( end_point(esk6_1(X1),X1)
| closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ closed(X1)
| ~ end_point(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X101,X103,X104] :
( ( ~ open(X101)
| end_point(esk7_1(X101),X101) )
& ( ~ end_point(X104,X103)
| open(X103) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[open_defn])])])])]) ).
fof(c_0_11,plain,
! [X122,X123] :
( ( end_point(esk11_2(X122,X123),X122)
| ~ end_point(X123,X122) )
& ( X123 != esk11_2(X122,X123)
| ~ end_point(X123,X122) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c6])])])]) ).
cnf(c_0_12,negated_conjecture,
( X1 = esk6_1(esk14_0)
| ~ end_point(X1,esk14_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_13,plain,
( end_point(esk7_1(X1),X1)
| ~ open(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
open(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,plain,
( end_point(esk11_2(X1,X2),X1)
| ~ end_point(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
esk7_1(esk14_0) = esk6_1(esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]) ).
cnf(c_0_17,plain,
( X1 != esk11_2(X2,X1)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( esk11_2(esk14_0,X1) = esk6_1(esk14_0)
| ~ end_point(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
end_point(esk6_1(esk14_0),esk14_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_16]),c_0_14])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18])]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GEO085+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 12:40:41 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.12/1.61 % Version : CSE_E---1.7
% 1.12/1.61 % Problem : theBenchmark.p
% 1.12/1.61 % SZS status Theorem for theBenchmark.p
% 1.12/1.61 % SZS output start CNFRefutation
% See solution above
% 1.12/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------