%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO086+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 : n006.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 0.27s 1.61s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 43)
% Comments :
%------------------------------------------------------------------------------
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(theorem_2_7_2,conjecture,
! [X1,X8] :
( ( open(X1)
& part_of(X8,X1) )
=> open(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theorem_2_7_2) ).
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(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(c2,axiom,
! [X1,X2,X4,X6] :
( ( part_of(X2,X1)
& part_of(X4,X1)
& part_of(X6,X1)
& ? [X3] :
( end_point(X3,X2)
& end_point(X3,X4)
& end_point(X3,X6) ) )
=> ( part_of(X4,X6)
| part_of(X6,X4)
| part_of(X2,X4)
| part_of(X4,X2)
| part_of(X2,X6)
| part_of(X6,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c2) ).
fof(c7,axiom,
! [X1,X2,X4,X3] :
( ( closed(X1)
& meet(X3,X2,X4)
& X1 = sum(X2,X4) )
=> ! [X5] :
( end_point(X5,X2)
=> meet(X5,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c7) ).
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(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(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(c8,axiom,
! [X2,X4] :
( ? [X3] : meet(X3,X2,X4)
=> ? [X1] : X1 = sum(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c8) ).
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(c5,axiom,
! [X1,X3,X5,X7] :
( ( end_point(X3,X1)
& end_point(X5,X1)
& end_point(X7,X1) )
=> ( X3 = X5
| X3 = X7
| X5 = X7 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c5) ).
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(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(c3,axiom,
! [X1] :
? [X3] : inner_point(X3,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax',c3) ).
fof(i_0_17,plain,
! [X3,X1] :
( inner_point(X3,X1)
<=> ( incident_c(X3,X1)
& ~ end_point(X3,X1) ) ),
inference(fof_simplification,[status(thm)],[inner_point_defn]) ).
fof(i_0_18,negated_conjecture,
~ ! [X1,X8] :
( ( open(X1)
& part_of(X8,X1) )
=> open(X8) ),
inference(assume_negation,[status(cth)],[theorem_2_7_2]) ).
fof(i_0_19,plain,
! [X89,X90,X91,X92,X93,X94,X95] :
( ( incident_c(X89,X90)
| ~ meet(X89,X90,X91) )
& ( incident_c(X89,X91)
| ~ meet(X89,X90,X91) )
& ( end_point(X92,X90)
| ~ incident_c(X92,X90)
| ~ incident_c(X92,X91)
| ~ meet(X89,X90,X91) )
& ( end_point(X92,X91)
| ~ incident_c(X92,X90)
| ~ incident_c(X92,X91)
| ~ meet(X89,X90,X91) )
& ( incident_c(esk5_3(X93,X94,X95),X94)
| ~ incident_c(X93,X94)
| ~ incident_c(X93,X95)
| meet(X93,X94,X95) )
& ( incident_c(esk5_3(X93,X94,X95),X95)
| ~ incident_c(X93,X94)
| ~ incident_c(X93,X95)
| meet(X93,X94,X95) )
& ( ~ end_point(esk5_3(X93,X94,X95),X94)
| ~ end_point(esk5_3(X93,X94,X95),X95)
| ~ incident_c(X93,X94)
| ~ incident_c(X93,X95)
| meet(X93,X94,X95) ) ),
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])])])])])]) ).
fof(i_0_20,plain,
! [X70,X71,X72,X73,X74,X75,X76,X77] :
( ( ~ incident_c(X73,X70)
| incident_c(X73,X71)
| incident_c(X73,X72)
| X70 != sum(X71,X72) )
& ( ~ incident_c(X74,X71)
| incident_c(X74,X70)
| X70 != sum(X71,X72) )
& ( ~ incident_c(X74,X72)
| incident_c(X74,X70)
| X70 != sum(X71,X72) )
& ( ~ incident_c(esk2_3(X75,X76,X77),X76)
| ~ incident_c(esk2_3(X75,X76,X77),X75)
| X75 = sum(X76,X77) )
& ( ~ incident_c(esk2_3(X75,X76,X77),X77)
| ~ incident_c(esk2_3(X75,X76,X77),X75)
| X75 = sum(X76,X77) )
& ( incident_c(esk2_3(X75,X76,X77),X75)
| incident_c(esk2_3(X75,X76,X77),X76)
| incident_c(esk2_3(X75,X76,X77),X77)
| X75 = sum(X76,X77) ) ),
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(i_0_21,plain,
! [X107,X108,X109,X110,X111] :
( ~ part_of(X108,X107)
| ~ part_of(X109,X107)
| ~ part_of(X110,X107)
| ~ end_point(X111,X108)
| ~ end_point(X111,X109)
| ~ end_point(X111,X110)
| part_of(X109,X110)
| part_of(X110,X109)
| part_of(X108,X109)
| part_of(X109,X108)
| part_of(X108,X110)
| part_of(X110,X108) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c2])])]) ).
fof(i_0_22,plain,
! [X125,X126,X127,X128,X129] :
( ~ closed(X125)
| ~ meet(X128,X126,X127)
| X125 != sum(X126,X127)
| ~ end_point(X129,X126)
| meet(X129,X126,X127) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c7])])]) ).
fof(i_0_23,plain,
! [X79,X80,X81,X82,X83,X84] :
( ( incident_c(X79,X80)
| ~ end_point(X79,X80) )
& ( ~ part_of(X81,X80)
| ~ part_of(X82,X80)
| ~ incident_c(X79,X81)
| ~ incident_c(X79,X82)
| part_of(X81,X82)
| part_of(X82,X81)
| ~ end_point(X79,X80) )
& ( part_of(esk3_2(X83,X84),X84)
| ~ incident_c(X83,X84)
| end_point(X83,X84) )
& ( part_of(esk4_2(X83,X84),X84)
| ~ incident_c(X83,X84)
| end_point(X83,X84) )
& ( incident_c(X83,esk3_2(X83,X84))
| ~ incident_c(X83,X84)
| end_point(X83,X84) )
& ( incident_c(X83,esk4_2(X83,X84))
| ~ incident_c(X83,X84)
| end_point(X83,X84) )
& ( ~ part_of(esk3_2(X83,X84),esk4_2(X83,X84))
| ~ incident_c(X83,X84)
| end_point(X83,X84) )
& ( ~ part_of(esk4_2(X83,X84),esk3_2(X83,X84))
| ~ incident_c(X83,X84)
| end_point(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)],[end_point_defn])])])])])]) ).
fof(i_0_24,plain,
! [X114,X115] :
( ( meet(X115,esk9_2(X114,X115),esk10_2(X114,X115))
| ~ inner_point(X115,X114) )
& ( X114 = sum(esk9_2(X114,X115),esk10_2(X114,X115))
| ~ inner_point(X115,X114) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c4])])])]) ).
fof(i_0_25,plain,
! [X134,X135] :
( ( ~ incident_c(esk13_2(X134,X135),X134)
| ~ incident_c(esk13_2(X134,X135),X135)
| X134 = X135 )
& ( incident_c(esk13_2(X134,X135),X134)
| incident_c(esk13_2(X134,X135),X135)
| X134 = X135 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c9])])])]) ).
fof(i_0_26,plain,
! [X130,X131,X132] :
( ~ meet(X132,X130,X131)
| esk12_2(X130,X131) = sum(X130,X131) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c8])])])]) ).
fof(i_0_27,plain,
! [X64,X65,X66,X67,X68] :
( ( ~ part_of(X65,X64)
| ~ incident_c(X66,X65)
| incident_c(X66,X64) )
& ( incident_c(esk1_2(X67,X68),X68)
| part_of(X68,X67) )
& ( ~ incident_c(esk1_2(X67,X68),X67)
| part_of(X68,X67) ) ),
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])])])])])]) ).
fof(i_0_28,plain,
! [X118,X119,X120,X121] :
( ~ end_point(X119,X118)
| ~ end_point(X120,X118)
| ~ end_point(X121,X118)
| X119 = X120
| X119 = X121
| X120 = X121 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c5])]) ).
fof(i_0_29,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])])])]) ).
fof(i_0_30,plain,
! [X87,X88] :
( ( incident_c(X87,X88)
| ~ inner_point(X87,X88) )
& ( ~ end_point(X87,X88)
| ~ inner_point(X87,X88) )
& ( ~ incident_c(X87,X88)
| end_point(X87,X88)
| inner_point(X87,X88) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_17])])]) ).
fof(i_0_31,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])])])])]) ).
fof(i_0_32,plain,
! [X105,X106] :
( ~ part_of(X106,X105)
| X106 = X105
| open(X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c1])]) ).
fof(i_0_33,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(i_0_34,plain,
! [X112] : inner_point(esk8_1(X112),X112),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c3])]) ).
fof(i_0_35,negated_conjecture,
( open(esk14_0)
& part_of(esk15_0,esk14_0)
& ~ open(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])])]) ).
cnf(i_0_36,plain,
( meet(X1,X2,X3)
| ~ end_point(esk5_3(X1,X2,X3),X2)
| ~ end_point(esk5_3(X1,X2,X3),X3)
| ~ incident_c(X1,X2)
| ~ incident_c(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_37,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)],[i_0_20]),
[final] ).
cnf(i_0_38,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)],[i_0_20]),
[final] ).
cnf(i_0_39,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)],[i_0_20]),
[final] ).
cnf(i_0_40,plain,
( part_of(X3,X4)
| part_of(X4,X3)
| part_of(X1,X3)
| part_of(X3,X1)
| part_of(X1,X4)
| part_of(X4,X1)
| ~ part_of(X1,X2)
| ~ part_of(X3,X2)
| ~ part_of(X4,X2)
| ~ end_point(X5,X1)
| ~ end_point(X5,X3)
| ~ end_point(X5,X4) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_41,plain,
( incident_c(esk5_3(X1,X2,X3),X2)
| meet(X1,X2,X3)
| ~ incident_c(X1,X2)
| ~ incident_c(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_42,plain,
( incident_c(esk5_3(X1,X2,X3),X3)
| meet(X1,X2,X3)
| ~ incident_c(X1,X2)
| ~ incident_c(X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_43,plain,
( meet(X5,X3,X4)
| ~ closed(X1)
| ~ meet(X2,X3,X4)
| X1 != sum(X3,X4)
| ~ end_point(X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_44,plain,
( end_point(X1,X2)
| ~ incident_c(X1,X2)
| ~ incident_c(X1,X3)
| ~ meet(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_45,plain,
( end_point(X1,X2)
| ~ incident_c(X1,X3)
| ~ incident_c(X1,X2)
| ~ meet(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_46,plain,
( part_of(X1,X3)
| part_of(X3,X1)
| ~ part_of(X1,X2)
| ~ part_of(X3,X2)
| ~ incident_c(X4,X1)
| ~ incident_c(X4,X3)
| ~ end_point(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_47,plain,
( end_point(X1,X2)
| ~ part_of(esk4_2(X1,X2),esk3_2(X1,X2))
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_48,plain,
( end_point(X1,X2)
| ~ part_of(esk3_2(X1,X2),esk4_2(X1,X2))
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_49,plain,
( meet(X1,esk9_2(X2,X1),esk10_2(X2,X1))
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_50,plain,
( X1 = X2
| ~ incident_c(esk13_2(X1,X2),X1)
| ~ incident_c(esk13_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_51,plain,
( esk12_2(X2,X3) = sum(X2,X3)
| ~ meet(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_52,plain,
( incident_c(X1,X2)
| ~ meet(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_53,plain,
( incident_c(X1,X2)
| ~ meet(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_54,plain,
( X1 = sum(esk9_2(X1,X2),esk10_2(X1,X2))
| ~ inner_point(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_55,plain,
( incident_c(esk13_2(X1,X2),X1)
| incident_c(esk13_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_56,plain,
( part_of(X2,X1)
| ~ incident_c(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_57,plain,
( part_of(esk4_2(X1,X2),X2)
| end_point(X1,X2)
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_58,plain,
( part_of(esk3_2(X1,X2),X2)
| end_point(X1,X2)
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_59,plain,
( incident_c(X1,esk4_2(X1,X2))
| end_point(X1,X2)
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_60,plain,
( incident_c(X1,esk3_2(X1,X2))
| end_point(X1,X2)
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_61,plain,
( incident_c(X1,X3)
| incident_c(X1,X4)
| ~ incident_c(X1,X2)
| X2 != sum(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_62,plain,
( X1 = X3
| X1 = X4
| X3 = X4
| ~ end_point(X1,X2)
| ~ end_point(X3,X2)
| ~ end_point(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_63,plain,
( end_point(esk11_2(X1,X2),X1)
| ~ end_point(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_64,plain,
( incident_c(X1,X3)
| ~ incident_c(X1,X2)
| X3 != sum(X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_65,plain,
( incident_c(X1,X3)
| ~ incident_c(X1,X2)
| X3 != sum(X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_66,plain,
( incident_c(X3,X2)
| ~ part_of(X1,X2)
| ~ incident_c(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_67,plain,
( incident_c(esk1_2(X1,X2),X2)
| part_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_68,plain,
( end_point(X1,X2)
| inner_point(X1,X2)
| ~ incident_c(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_69,plain,
( X1 != esk11_2(X2,X1)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_70,plain,
( ~ end_point(X1,X2)
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_71,plain,
( incident_c(X1,X2)
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_72,plain,
( incident_c(X1,X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_73,plain,
( ~ closed(X1)
| ~ end_point(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_74,plain,
( X1 = X2
| open(X1)
| ~ part_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_75,plain,
( end_point(esk7_1(X1),X1)
| ~ open(X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_76,plain,
( open(X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_77,plain,
( end_point(esk6_1(X1),X1)
| closed(X1) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_78,plain,
inner_point(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_79,negated_conjecture,
part_of(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_80,negated_conjecture,
~ open(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_81,negated_conjecture,
open(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_82,axiom,
X1 = X1 ).
cnf(i_0_83,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_84,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_85,axiom,
( X1 != X2
| esk11_2(X1,X3) = esk11_2(X2,X3) ) ).
cnf(i_0_86,axiom,
( X1 != X2
| esk11_2(X3,X1) = esk11_2(X3,X2) ) ).
cnf(i_0_87,axiom,
( X1 != X2
| sum(X1,X3) = sum(X2,X3) ) ).
cnf(i_0_88,axiom,
( X1 != X2
| sum(X3,X1) = sum(X3,X2) ) ).
cnf(i_0_89,axiom,
( X1 != X2
| esk12_2(X1,X3) = esk12_2(X2,X3) ) ).
cnf(i_0_90,axiom,
( X1 != X2
| esk12_2(X3,X1) = esk12_2(X3,X2) ) ).
cnf(i_0_91,axiom,
( X1 != X2
| ~ meet(X1,X3,X4)
| meet(X2,X3,X4) ) ).
cnf(i_0_92,axiom,
( X1 != X2
| ~ meet(X3,X1,X4)
| meet(X3,X2,X4) ) ).
cnf(i_0_93,axiom,
( X1 != X2
| ~ meet(X3,X4,X1)
| meet(X3,X4,X2) ) ).
cnf(i_0_94,axiom,
( X1 != X2
| ~ end_point(X1,X3)
| end_point(X2,X3) ) ).
cnf(i_0_95,axiom,
( X1 != X2
| ~ end_point(X3,X1)
| end_point(X3,X2) ) ).
cnf(i_0_96,axiom,
( X1 != X2
| ~ incident_c(X1,X3)
| incident_c(X2,X3) ) ).
cnf(i_0_97,axiom,
( X1 != X2
| ~ incident_c(X3,X1)
| incident_c(X3,X2) ) ).
cnf(i_0_98,axiom,
( X1 != X2
| ~ part_of(X1,X3)
| part_of(X2,X3) ) ).
cnf(i_0_99,axiom,
( X1 != X2
| ~ part_of(X3,X1)
| part_of(X3,X2) ) ).
cnf(i_0_100,axiom,
( X1 != X2
| ~ closed(X1)
| closed(X2) ) ).
cnf(i_0_101,axiom,
( X1 != X2
| ~ inner_point(X1,X3)
| inner_point(X2,X3) ) ).
cnf(i_0_102,axiom,
( X1 != X2
| ~ inner_point(X3,X1)
| inner_point(X3,X2) ) ).
cnf(i_0_103,axiom,
( X1 != X2
| ~ open(X1)
| open(X2) ) ).
cnf(i_0_82_001,axiom,
X1 = X1 ).
cnf(i_0_83_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_84_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_85_004,axiom,
( X1 != X2
| esk11_2(X1,X3) = esk11_2(X2,X3) ) ).
cnf(i_0_86_005,axiom,
( X1 != X2
| esk11_2(X3,X1) = esk11_2(X3,X2) ) ).
cnf(i_0_87_006,axiom,
( X1 != X2
| sum(X1,X3) = sum(X2,X3) ) ).
cnf(i_0_88_007,axiom,
( X1 != X2
| sum(X3,X1) = sum(X3,X2) ) ).
cnf(i_0_89_008,axiom,
( X1 != X2
| esk12_2(X1,X3) = esk12_2(X2,X3) ) ).
cnf(i_0_90_009,axiom,
( X1 != X2
| esk12_2(X3,X1) = esk12_2(X3,X2) ) ).
cnf(i_0_91_010,axiom,
( X1 != X2
| ~ meet(X1,X3,X4)
| meet(X2,X3,X4) ) ).
cnf(i_0_92_011,axiom,
( X1 != X2
| ~ meet(X3,X1,X4)
| meet(X3,X2,X4) ) ).
cnf(i_0_93_012,axiom,
( X1 != X2
| ~ meet(X3,X4,X1)
| meet(X3,X4,X2) ) ).
cnf(i_0_94_013,axiom,
( X1 != X2
| ~ end_point(X1,X3)
| end_point(X2,X3) ) ).
cnf(i_0_95_014,axiom,
( X1 != X2
| ~ end_point(X3,X1)
| end_point(X3,X2) ) ).
cnf(i_0_96_015,axiom,
( X1 != X2
| ~ incident_c(X1,X3)
| incident_c(X2,X3) ) ).
cnf(i_0_97_016,axiom,
( X1 != X2
| ~ incident_c(X3,X1)
| incident_c(X3,X2) ) ).
cnf(i_0_98_017,axiom,
( X1 != X2
| ~ part_of(X1,X3)
| part_of(X2,X3) ) ).
cnf(i_0_99_018,axiom,
( X1 != X2
| ~ part_of(X3,X1)
| part_of(X3,X2) ) ).
cnf(i_0_100_019,axiom,
( X1 != X2
| ~ closed(X1)
| closed(X2) ) ).
cnf(i_0_101_020,axiom,
( X1 != X2
| ~ inner_point(X1,X3)
| inner_point(X2,X3) ) ).
cnf(i_0_102_021,axiom,
( X1 != X2
| ~ inner_point(X3,X1)
| inner_point(X3,X2) ) ).
cnf(i_0_103_022,axiom,
( X1 != X2
| ~ open(X1)
| open(X2) ) ).
cnf(i_0_104,plain,
( ~ end_point(X1,X2)
| meet(X1,X2,X3)
| ~ meet(X4,X2,X3)
| ~ closed(sum(X2,X3)) ),
inference(equality_inference,[],[43]) ).
cnf(i_0_105,plain,
( incident_c(X1,X2)
| incident_c(X1,X3)
| ~ incident_c(X1,sum(X2,X3)) ),
inference(equality_inference,[],[61]) ).
cnf(i_0_106,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X2) ),
inference(equality_inference,[],[64]) ).
cnf(i_0_107,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X3) ),
inference(equality_inference,[],[65]) ).
cnf(i_0_108,plain,
~ end_point(X1,esk15_0),
inference(scs_inference,[],[i_0_80,i_0_76]) ).
cnf(i_0_109,plain,
( open(X1)
| ~ end_point(X2,X1) ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_110,plain,
incident_c(esk8_1(X1),X1),
inference(scs_inference,[],[i_0_80,i_0_78,i_0_76,i_0_71]) ).
cnf(i_0_111,plain,
( ~ inner_point(X1,X2)
| incident_c(X1,X2) ),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_112,plain,
closed(esk15_0),
inference(scs_inference,[],[i_0_80,i_0_78,i_0_76,i_0_71,i_0_77]) ).
cnf(i_0_113,plain,
( end_point(esk6_1(X1),X1)
| closed(X1) ),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_114,plain,
incident_c(esk8_1(X1),sum(X1,X2)),
inference(scs_inference,[],[i_0_80,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106]) ).
cnf(i_0_115,plain,
( ~ incident_c(X1,X2)
| incident_c(X1,sum(X2,X3)) ),
inference(rename_variables,[],[i_0_106]) ).
cnf(i_0_116,plain,
incident_c(esk8_1(X1),sum(X2,X1)),
inference(scs_inference,[],[i_0_80,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107]) ).
cnf(i_0_117,plain,
( ~ incident_c(X1,X2)
| incident_c(X1,sum(X3,X2)) ),
inference(rename_variables,[],[i_0_107]) ).
cnf(i_0_118,plain,
~ end_point(esk8_1(X1),X1),
inference(scs_inference,[],[i_0_80,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70]) ).
cnf(i_0_119,plain,
( ~ inner_point(X1,X2)
| ~ end_point(X1,X2) ),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_120,plain,
incident_c(esk8_1(esk15_0),esk14_0),
inference(scs_inference,[],[i_0_79,i_0_80,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70,i_0_66]) ).
cnf(i_0_121,plain,
( ~ incident_c(X1,X2)
| incident_c(X1,X3)
| ~ part_of(X2,X3) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_122,plain,
esk15_0 = esk14_0,
inference(scs_inference,[],[i_0_79,i_0_80,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70,i_0_66,i_0_74]) ).
cnf(i_0_123,plain,
( open(X1)
| ~ part_of(X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_124,plain,
esk14_0 != esk15_0,
inference(scs_inference,[],[i_0_79,i_0_80,i_0_81,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70,i_0_66,i_0_74,i_0_103]) ).
cnf(i_0_125,plain,
closed(esk14_0),
inference(scs_inference,[],[i_0_79,i_0_80,i_0_81,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70,i_0_66,i_0_74,i_0_103,i_0_100]) ).
cnf(i_0_126,plain,
~ meet(X1,esk15_0,esk15_0),
inference(scs_inference,[],[i_0_79,i_0_80,i_0_81,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70,i_0_66,i_0_74,i_0_103,i_0_100,i_0_44]) ).
cnf(i_0_127,plain,
( ~ incident_c(X1,X2)
| end_point(X1,X2)
| ~ meet(X3,X2,X4)
| ~ incident_c(X1,X4) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_128,plain,
~ end_point(X1,esk14_0),
inference(scs_inference,[],[i_0_79,i_0_80,i_0_81,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70,i_0_66,i_0_74,i_0_103,i_0_100,i_0_44,i_0_73]) ).
cnf(i_0_129,plain,
( ~ closed(X1)
| ~ end_point(X2,X1) ),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_130,plain,
$false,
inference(scs_inference,[],[i_0_79,i_0_80,i_0_81,i_0_78,i_0_76,i_0_71,i_0_77,i_0_106,i_0_107,i_0_70,i_0_66,i_0_74,i_0_103,i_0_100,i_0_44,i_0_73,i_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO086+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
% 0.14/0.33 % Computer : n006.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:40:31 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.27/1.61 % Version : CSE_E---1.7
% 0.27/1.61 % Problem : theBenchmark.p
% 0.27/1.61 % SZS status Theorem for theBenchmark.p
% 0.27/1.61 % SZS output start CNFRefutation
% See solution above
% 0.38/1.70 % Total time : 1.271s
%------------------------------------------------------------------------------