%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO093+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 : 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 04:19:18 PM UTC 2026
% Result : Theorem 23.57s 15.55s
% Output : CNFRefutation 23.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 11 unt; 0 def)
% Number of atoms : 233 ( 46 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 228 ( 74 ~; 116 |; 25 &)
% ( 8 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 168 ( 12 sgn 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_defn,axiom,
! [X1,X2,X4] :
( X1 = sum(X2,X4)
<=> ! [X5] :
( incident_c(X5,X1)
<=> ( incident_c(X5,X2)
| incident_c(X5,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',sum_defn) ).
fof(inner_point_defn,axiom,
! [X3,X1] :
( inner_point(X3,X1)
<=> ( incident_c(X3,X1)
& ~ end_point(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(part_of_defn,axiom,
! [X1,X2] :
( part_of(X2,X1)
<=> ! [X3] :
( incident_c(X3,X2)
=> incident_c(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(closed_defn,axiom,
! [X1] :
( closed(X1)
<=> ~ ? [X3] : end_point(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',closed_defn) ).
fof(c1,axiom,
! [X1,X2] :
( ( part_of(X2,X1)
& X2 != X1 )
=> open(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c1) ).
fof(open_defn,axiom,
! [X1] :
( open(X1)
<=> ? [X3] : end_point(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',open_defn) ).
fof(proposition_2_14_2,conjecture,
! [X1,X2,X4,X3] :
( ( open(X1)
& part_of(X2,X1)
& part_of(X4,X1)
& meet(X3,X2,X4) )
=> open(sum(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_2) ).
fof(c9,axiom,
! [X1,X2] :
( ! [X3] :
( incident_c(X3,X1)
<=> incident_c(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c9) ).
fof(c_0_8,plain,
! [X71,X72,X73,X74,X75,X76,X77,X78] :
( ( ~ incident_c(X74,X71)
| incident_c(X74,X72)
| incident_c(X74,X73)
| X71 != sum(X72,X73) )
& ( ~ incident_c(X75,X72)
| incident_c(X75,X71)
| X71 != sum(X72,X73) )
& ( ~ incident_c(X75,X73)
| incident_c(X75,X71)
| X71 != sum(X72,X73) )
& ( ~ incident_c(esk2_3(X76,X77,X78),X77)
| ~ incident_c(esk2_3(X76,X77,X78),X76)
| X76 = sum(X77,X78) )
& ( ~ incident_c(esk2_3(X76,X77,X78),X78)
| ~ incident_c(esk2_3(X76,X77,X78),X76)
| X76 = sum(X77,X78) )
& ( incident_c(esk2_3(X76,X77,X78),X76)
| incident_c(esk2_3(X76,X77,X78),X77)
| incident_c(esk2_3(X76,X77,X78),X78)
| X76 = sum(X77,X78) ) ),
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)],[sum_defn])])])])])]) ).
fof(c_0_9,plain,
! [X3,X1] :
( inner_point(X3,X1)
<=> ( incident_c(X3,X1)
& ~ end_point(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[inner_point_defn]) ).
fof(c_0_10,plain,
! [X65,X66,X67,X68,X69] :
( ( ~ part_of(X66,X65)
| ~ incident_c(X67,X66)
| incident_c(X67,X65) )
& ( incident_c(esk1_2(X68,X69),X69)
| part_of(X69,X68) )
& ( ~ incident_c(esk1_2(X68,X69),X68)
| part_of(X69,X68) ) ),
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)],[part_of_defn])])])])])]) ).
cnf(c_0_11,plain,
( incident_c(X1,X3)
| ~ incident_c(X1,X2)
| X3 != sum(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( incident_c(X1,X3)
| ~ incident_c(X1,X2)
| X3 != sum(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X88,X89] :
( ( incident_c(X88,X89)
| ~ inner_point(X88,X89) )
& ( ~ end_point(X88,X89)
| ~ inner_point(X88,X89) )
& ( ~ incident_c(X88,X89)
| end_point(X88,X89)
| inner_point(X88,X89) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_14,plain,
( part_of(X2,X1)
| ~ incident_c(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X2) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X3) ),
inference(er,[status(thm)],[c_0_12]) ).
fof(c_0_17,plain,
! [X98,X99,X100] :
( ( ~ closed(X98)
| ~ end_point(X99,X98) )
& ( end_point(esk6_1(X100),X100)
| closed(X100) ) ),
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_18,plain,
( end_point(X1,X2)
| inner_point(X1,X2)
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X106,X107] :
( ~ part_of(X107,X106)
| X107 = X106
| open(X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c1])]) ).
cnf(c_0_20,plain,
( part_of(X1,sum(X2,X3))
| ~ incident_c(esk1_2(sum(X2,X3),X1),X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( incident_c(esk1_2(X1,X2),X2)
| part_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_22,plain,
! [X102,X104,X105] :
( ( ~ open(X102)
| end_point(esk7_1(X102),X102) )
& ( ~ end_point(X105,X104)
| open(X104) ) ),
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_23,negated_conjecture,
~ ! [X1,X2,X4,X3] :
( ( open(X1)
& part_of(X2,X1)
& part_of(X4,X1)
& meet(X3,X2,X4) )
=> open(sum(X2,X4)) ),
inference(assume_negation,[status(cth)],[proposition_2_14_2]) ).
cnf(c_0_24,plain,
( part_of(X1,sum(X2,X3))
| ~ incident_c(esk1_2(sum(X2,X3),X1),X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
fof(c_0_25,plain,
! [X135,X136] :
( ( ~ incident_c(esk13_2(X135,X136),X135)
| ~ incident_c(esk13_2(X135,X136),X136)
| X135 = X136 )
& ( incident_c(esk13_2(X135,X136),X135)
| incident_c(esk13_2(X135,X136),X136)
| X135 = X136 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c9])])])]) ).
cnf(c_0_26,plain,
( ~ closed(X1)
| ~ end_point(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
( inner_point(X1,sum(X2,X3))
| end_point(X1,sum(X2,X3))
| ~ incident_c(X1,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_28,plain,
( X1 = X2
| open(X1)
| ~ part_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_29,plain,
part_of(X1,sum(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,plain,
( open(X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( end_point(esk6_1(X1),X1)
| closed(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_32,negated_conjecture,
( open(esk14_0)
& part_of(esk15_0,esk14_0)
& part_of(esk16_0,esk14_0)
& meet(esk17_0,esk15_0,esk16_0)
& ~ open(sum(esk15_0,esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])]) ).
cnf(c_0_33,plain,
( incident_c(esk2_3(X1,X2,X3),X1)
| incident_c(esk2_3(X1,X2,X3),X2)
| incident_c(esk2_3(X1,X2,X3),X3)
| X1 = sum(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,plain,
part_of(X1,sum(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_35,plain,
( X1 = X2
| ~ incident_c(esk13_2(X1,X2),X1)
| ~ incident_c(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
( incident_c(esk13_2(X1,X2),X1)
| incident_c(esk13_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
( inner_point(X1,sum(X2,X3))
| ~ closed(sum(X2,X3))
| ~ incident_c(X1,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_38,plain,
( sum(X1,X2) = X1
| open(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
( open(X1)
| closed(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( incident_c(X3,X2)
| ~ part_of(X1,X2)
| ~ incident_c(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_41,negated_conjecture,
part_of(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,negated_conjecture,
part_of(esk16_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,plain,
( X1 = sum(X2,X3)
| ~ incident_c(esk2_3(X1,X2,X3),X2)
| ~ incident_c(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_44,plain,
( sum(X1,X2) = X1
| incident_c(esk2_3(X1,X1,X2),X2)
| incident_c(esk2_3(X1,X1,X2),X1) ),
inference(ef,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( sum(X1,X2) = X2
| open(X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_34]) ).
cnf(c_0_46,plain,
( X1 = sum(X2,X3)
| ~ incident_c(esk13_2(X1,sum(X2,X3)),X1)
| ~ incident_c(esk13_2(X1,sum(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_16]) ).
cnf(c_0_47,plain,
( incident_c(X1,X2)
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_48,plain,
( X1 = X2
| inner_point(esk13_2(X1,X2),X1)
| end_point(esk13_2(X1,X2),X1)
| incident_c(esk13_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_36]) ).
cnf(c_0_49,plain,
( open(X1)
| inner_point(X2,X1)
| ~ incident_c(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_50,negated_conjecture,
( incident_c(X1,esk14_0)
| ~ incident_c(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
( incident_c(X1,esk14_0)
| ~ incident_c(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_42]) ).
cnf(c_0_52,plain,
( sum(X1,X2) = X1
| incident_c(esk2_3(X1,X1,X2),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_44]) ).
cnf(c_0_53,plain,
( incident_c(X1,X3)
| incident_c(X1,X4)
| ~ incident_c(X1,X2)
| X2 != sum(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_54,plain,
( open(X1)
| part_of(X2,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_55,plain,
( X1 = sum(X2,X3)
| ~ inner_point(esk13_2(X1,sum(X2,X3)),X1)
| ~ incident_c(esk13_2(X1,sum(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,plain,
( X1 = X2
| open(X1)
| inner_point(esk13_2(X1,X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_48]),c_0_49]) ).
cnf(c_0_57,plain,
( X1 = sum(X2,X3)
| ~ incident_c(esk2_3(X1,X2,X3),X3)
| ~ incident_c(esk2_3(X1,X2,X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_58,plain,
( sum(X1,X1) = X1
| incident_c(esk2_3(X1,X1,X1),X1) ),
inference(ef,[status(thm)],[c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( X1 = sum(esk14_0,X2)
| ~ incident_c(esk2_3(X1,esk14_0,X2),esk15_0)
| ~ incident_c(esk2_3(X1,esk14_0,X2),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_60,negated_conjecture,
( sum(X1,esk16_0) = X1
| incident_c(esk2_3(X1,X1,esk16_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_61,plain,
( incident_c(X1,X2)
| incident_c(X1,X3)
| ~ incident_c(X1,sum(X3,X2)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_62,negated_conjecture,
~ open(sum(esk15_0,esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_63,plain,
( X1 = X2
| open(X2)
| open(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_54]) ).
cnf(c_0_64,plain,
( X1 = sum(X2,X3)
| open(X1)
| ~ incident_c(esk13_2(X1,sum(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
sum(X1,X1) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( sum(esk14_0,esk15_0) = esk14_0
| ~ incident_c(esk2_3(esk14_0,esk14_0,esk15_0),esk14_0) ),
inference(spm,[status(thm)],[c_0_59,c_0_52]) ).
cnf(c_0_67,negated_conjecture,
sum(esk14_0,esk16_0) = esk14_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_60]),c_0_60]) ).
cnf(c_0_68,plain,
( sum(X1,X2) = X3
| incident_c(esk13_2(sum(X1,X2),X3),X3)
| incident_c(esk13_2(sum(X1,X2),X3),X1)
| incident_c(esk13_2(sum(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_61,c_0_36]) ).
cnf(c_0_69,negated_conjecture,
( sum(esk15_0,esk16_0) = X1
| open(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
( X1 = X2
| open(X1)
| ~ incident_c(esk13_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
sum(esk14_0,esk15_0) = esk14_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50]),c_0_52]) ).
cnf(c_0_72,negated_conjecture,
( X1 = esk14_0
| open(X1)
| ~ incident_c(esk13_2(X1,esk14_0),esk16_0) ),
inference(spm,[status(thm)],[c_0_64,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( X1 = X2
| open(X1)
| incident_c(esk13_2(X1,X2),esk16_0)
| incident_c(esk13_2(X1,X2),esk15_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]) ).
cnf(c_0_74,negated_conjecture,
( X1 = esk14_0
| open(X1)
| ~ incident_c(esk13_2(X1,esk14_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_64,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( X1 = esk14_0
| open(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]) ).
cnf(c_0_76,negated_conjecture,
sum(esk15_0,esk16_0) = esk14_0,
inference(spm,[status(thm)],[c_0_62,c_0_75]) ).
cnf(c_0_77,negated_conjecture,
open(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_76]),c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO093+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.11 % 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
% 0.14/0.32 % 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 : Mon May 4 17:40:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 23.57/15.55 % Version : CSE_E---1.7
% 23.57/15.55 % Problem : theBenchmark.p
% 23.57/15.55 % SZS status Theorem for theBenchmark.p
% 23.57/15.55 % SZS output start CNFRefutation
% See solution above
% 23.67/15.62 % Total time : 12.393s
%------------------------------------------------------------------------------