%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO111+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 : n016.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 04:19:20 PM UTC 2026
% Result : Theorem 1.67s 1.83s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 58 ( 9 unt; 0 def)
% Number of atoms : 254 ( 39 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 315 ( 119 ~; 128 |; 54 &)
% ( 8 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 177 ( 18 sgn 72 !; 3 ?)
% 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(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(c4,axiom,
! [X1,X3] :
( inner_point(X3,X1)
=> ? [X2,X4] :
( meet(X3,X2,X4)
& X1 = sum(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c4) ).
fof(meet_defn,axiom,
! [X3,X1,X2] :
( meet(X3,X1,X2)
<=> ( incident_c(X3,X1)
& incident_c(X3,X2)
& ! [X5] :
( ( incident_c(X5,X1)
& incident_c(X5,X2) )
=> ( end_point(X5,X1)
& end_point(X5,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',meet_defn) ).
fof(between_c_defn,axiom,
! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
<=> ( X3 != X7
& ? [X8] :
( part_of(X8,X1)
& end_point(X3,X8)
& end_point(X7,X8)
& inner_point(X5,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+1.ax',between_c_defn) ).
fof(end_point_defn,axiom,
! [X3,X1] :
( end_point(X3,X1)
<=> ( incident_c(X3,X1)
& ! [X2,X4] :
( ( part_of(X2,X1)
& part_of(X4,X1)
& incident_c(X3,X2)
& incident_c(X3,X4) )
=> ( part_of(X2,X4)
| part_of(X4,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).
fof(theorem_3_8_1,conjecture,
! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
=> ( incident_c(X3,X1)
& incident_c(X5,X1)
& incident_c(X7,X1)
& X3 != X5
& X5 != X7
& X3 != X7 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_3_8_1) ).
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(c_0_8,plain,
! [X77,X78,X79,X80,X81,X82,X83,X84] :
( ( ~ incident_c(X80,X77)
| incident_c(X80,X78)
| incident_c(X80,X79)
| X77 != sum(X78,X79) )
& ( ~ incident_c(X81,X78)
| incident_c(X81,X77)
| X77 != sum(X78,X79) )
& ( ~ incident_c(X81,X79)
| incident_c(X81,X77)
| X77 != sum(X78,X79) )
& ( ~ incident_c(esk2_3(X82,X83,X84),X83)
| ~ incident_c(esk2_3(X82,X83,X84),X82)
| X82 = sum(X83,X84) )
& ( ~ incident_c(esk2_3(X82,X83,X84),X84)
| ~ incident_c(esk2_3(X82,X83,X84),X82)
| X82 = sum(X83,X84) )
& ( incident_c(esk2_3(X82,X83,X84),X82)
| incident_c(esk2_3(X82,X83,X84),X83)
| incident_c(esk2_3(X82,X83,X84),X84)
| X82 = sum(X83,X84) ) ),
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,
! [X71,X72,X73,X74,X75] :
( ( ~ part_of(X72,X71)
| ~ incident_c(X73,X72)
| incident_c(X73,X71) )
& ( incident_c(esk1_2(X74,X75),X75)
| part_of(X75,X74) )
& ( ~ incident_c(esk1_2(X74,X75),X74)
| part_of(X75,X74) ) ),
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_10,plain,
( incident_c(X1,X3)
| ~ incident_c(X1,X2)
| X3 != sum(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( incident_c(X3,X2)
| ~ part_of(X1,X2)
| ~ incident_c(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X3) ),
inference(er,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X121,X122] :
( ( meet(X122,esk9_2(X121,X122),esk10_2(X121,X122))
| ~ inner_point(X122,X121) )
& ( X121 = sum(esk9_2(X121,X122),esk10_2(X121,X122))
| ~ inner_point(X122,X121) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c4])])])]) ).
fof(c_0_14,plain,
! [X96,X97,X98,X99,X100,X101,X102] :
( ( incident_c(X96,X97)
| ~ meet(X96,X97,X98) )
& ( incident_c(X96,X98)
| ~ meet(X96,X97,X98) )
& ( end_point(X99,X97)
| ~ incident_c(X99,X97)
| ~ incident_c(X99,X98)
| ~ meet(X96,X97,X98) )
& ( end_point(X99,X98)
| ~ incident_c(X99,X97)
| ~ incident_c(X99,X98)
| ~ meet(X96,X97,X98) )
& ( incident_c(esk5_3(X100,X101,X102),X101)
| ~ incident_c(X100,X101)
| ~ incident_c(X100,X102)
| meet(X100,X101,X102) )
& ( incident_c(esk5_3(X100,X101,X102),X102)
| ~ incident_c(X100,X101)
| ~ incident_c(X100,X102)
| meet(X100,X101,X102) )
& ( ~ end_point(esk5_3(X100,X101,X102),X101)
| ~ end_point(esk5_3(X100,X101,X102),X102)
| ~ incident_c(X100,X101)
| ~ incident_c(X100,X102)
| meet(X100,X101,X102) ) ),
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)],[meet_defn])])])])])]) ).
cnf(c_0_15,plain,
( incident_c(X1,X2)
| ~ incident_c(X1,X3)
| ~ part_of(sum(X4,X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( X1 = sum(esk9_2(X1,X2),esk10_2(X1,X2))
| ~ inner_point(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( incident_c(X1,X2)
| ~ meet(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( meet(X1,esk9_2(X2,X1),esk10_2(X2,X1))
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( incident_c(X1,X2)
| ~ inner_point(X3,X4)
| ~ incident_c(X1,esk10_2(X4,X3))
| ~ part_of(X4,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( incident_c(X1,esk10_2(X2,X1))
| ~ inner_point(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_21,plain,
! [X144,X145,X146,X147,X149,X150,X151,X152,X153] :
( ( X145 != X147
| ~ between_c(X144,X145,X146,X147) )
& ( part_of(esk14_4(X144,X145,X146,X147),X144)
| ~ between_c(X144,X145,X146,X147) )
& ( end_point(X145,esk14_4(X144,X145,X146,X147))
| ~ between_c(X144,X145,X146,X147) )
& ( end_point(X147,esk14_4(X144,X145,X146,X147))
| ~ between_c(X144,X145,X146,X147) )
& ( inner_point(X146,esk14_4(X144,X145,X146,X147))
| ~ between_c(X144,X145,X146,X147) )
& ( X150 = X152
| ~ part_of(X153,X149)
| ~ end_point(X150,X153)
| ~ end_point(X152,X153)
| ~ inner_point(X151,X153)
| between_c(X149,X150,X151,X152) ) ),
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)],[between_c_defn])])])])])]) ).
fof(c_0_22,plain,
! [X86,X87,X88,X89,X90,X91] :
( ( incident_c(X86,X87)
| ~ end_point(X86,X87) )
& ( ~ part_of(X88,X87)
| ~ part_of(X89,X87)
| ~ incident_c(X86,X88)
| ~ incident_c(X86,X89)
| part_of(X88,X89)
| part_of(X89,X88)
| ~ end_point(X86,X87) )
& ( part_of(esk3_2(X90,X91),X91)
| ~ incident_c(X90,X91)
| end_point(X90,X91) )
& ( part_of(esk4_2(X90,X91),X91)
| ~ incident_c(X90,X91)
| end_point(X90,X91) )
& ( incident_c(X90,esk3_2(X90,X91))
| ~ incident_c(X90,X91)
| end_point(X90,X91) )
& ( incident_c(X90,esk4_2(X90,X91))
| ~ incident_c(X90,X91)
| end_point(X90,X91) )
& ( ~ part_of(esk3_2(X90,X91),esk4_2(X90,X91))
| ~ incident_c(X90,X91)
| end_point(X90,X91) )
& ( ~ part_of(esk4_2(X90,X91),esk3_2(X90,X91))
| ~ incident_c(X90,X91)
| end_point(X90,X91) ) ),
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)],[end_point_defn])])])])])]) ).
cnf(c_0_23,plain,
( incident_c(X1,X2)
| ~ inner_point(X1,X3)
| ~ part_of(X3,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( inner_point(X1,esk14_4(X2,X3,X1,X4))
| ~ between_c(X2,X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,negated_conjecture,
~ ! [X1,X3,X5,X7] :
( between_c(X1,X3,X5,X7)
=> ( incident_c(X3,X1)
& incident_c(X5,X1)
& incident_c(X7,X1)
& X3 != X5
& X5 != X7
& X3 != X7 ) ),
inference(assume_negation,[status(cth)],[theorem_3_8_1]) ).
cnf(c_0_26,plain,
( incident_c(X1,X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( end_point(X1,esk14_4(X2,X3,X4,X1))
| ~ between_c(X2,X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( incident_c(X1,X2)
| ~ between_c(X3,X4,X1,X5)
| ~ part_of(esk14_4(X3,X4,X1,X5),X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( part_of(esk14_4(X1,X2,X3,X4),X1)
| ~ between_c(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_30,negated_conjecture,
( between_c(esk15_0,esk16_0,esk17_0,esk18_0)
& ( ~ incident_c(esk16_0,esk15_0)
| ~ incident_c(esk17_0,esk15_0)
| ~ incident_c(esk18_0,esk15_0)
| esk16_0 = esk17_0
| esk17_0 = esk18_0
| esk16_0 = esk18_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])]) ).
cnf(c_0_31,plain,
( incident_c(X1,esk14_4(X2,X3,X4,X1))
| ~ between_c(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
( end_point(X1,esk14_4(X2,X1,X3,X4))
| ~ between_c(X2,X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
( incident_c(X1,X2)
| ~ between_c(X2,X3,X1,X4) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
between_c(esk15_0,esk16_0,esk17_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( incident_c(X1,X2)
| ~ between_c(X3,X4,X5,X1)
| ~ part_of(esk14_4(X3,X4,X5,X1),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_31]) ).
cnf(c_0_36,plain,
( incident_c(X1,esk14_4(X2,X1,X3,X4))
| ~ between_c(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_32]) ).
fof(c_0_37,plain,
! [X3,X1] :
( inner_point(X3,X1)
<=> ( incident_c(X3,X1)
& ~ end_point(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[inner_point_defn]) ).
cnf(c_0_38,negated_conjecture,
( esk16_0 = esk17_0
| esk17_0 = esk18_0
| esk16_0 = esk18_0
| ~ incident_c(esk16_0,esk15_0)
| ~ incident_c(esk17_0,esk15_0)
| ~ incident_c(esk18_0,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,negated_conjecture,
incident_c(esk17_0,esk15_0),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,plain,
( incident_c(X1,X2)
| ~ between_c(X2,X3,X4,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_41,plain,
( incident_c(X1,X2)
| ~ between_c(X3,X1,X4,X5)
| ~ part_of(esk14_4(X3,X1,X4,X5),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_36]) ).
fof(c_0_42,plain,
! [X94,X95] :
( ( incident_c(X94,X95)
| ~ inner_point(X94,X95) )
& ( ~ end_point(X94,X95)
| ~ inner_point(X94,X95) )
& ( ~ incident_c(X94,X95)
| end_point(X94,X95)
| inner_point(X94,X95) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_37])])]) ).
cnf(c_0_43,negated_conjecture,
( esk18_0 = esk17_0
| esk18_0 = esk16_0
| esk17_0 = esk16_0
| ~ incident_c(esk16_0,esk15_0)
| ~ incident_c(esk18_0,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]) ).
cnf(c_0_44,negated_conjecture,
incident_c(esk18_0,esk15_0),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_45,plain,
( incident_c(X1,X2)
| ~ between_c(X2,X1,X3,X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_46,plain,
( ~ end_point(X1,X2)
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( esk17_0 = esk16_0
| esk18_0 = esk16_0
| esk18_0 = esk17_0
| ~ incident_c(esk16_0,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]) ).
cnf(c_0_48,negated_conjecture,
incident_c(esk16_0,esk15_0),
inference(spm,[status(thm)],[c_0_45,c_0_34]) ).
cnf(c_0_49,plain,
( ~ between_c(X1,X2,X3,X4)
| ~ end_point(X3,esk14_4(X1,X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_46,c_0_24]) ).
cnf(c_0_50,negated_conjecture,
( esk18_0 = esk17_0
| esk18_0 = esk16_0
| esk17_0 = esk16_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]) ).
cnf(c_0_51,plain,
~ between_c(X1,X2,X3,X3),
inference(spm,[status(thm)],[c_0_49,c_0_27]) ).
cnf(c_0_52,plain,
( X1 != X2
| ~ between_c(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_53,negated_conjecture,
( esk17_0 = esk16_0
| esk18_0 = esk16_0 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_50]),c_0_51]) ).
cnf(c_0_54,plain,
~ between_c(X1,X2,X3,X2),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_55,negated_conjecture,
esk17_0 = esk16_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_53]),c_0_54]) ).
cnf(c_0_56,plain,
~ between_c(X1,X2,X2,X3),
inference(spm,[status(thm)],[c_0_49,c_0_32]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_55]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO111+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n016.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:42:21 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.67/1.83 % Version : CSE_E---1.7
% 1.67/1.83 % Problem : theBenchmark.p
% 1.67/1.83 % SZS status Theorem for theBenchmark.p
% 1.67/1.83 % SZS output start CNFRefutation
% See solution above
% 1.67/1.84 % Total time : 1.368s
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