%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO126+1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n008.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 04:19:23 PM UTC 2026
% Result : Theorem 3.64s 3.10s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 19 unt; 0 def)
% Number of atoms : 156 ( 21 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 168 ( 61 ~; 67 |; 30 &)
% ( 8 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 93 ( 1 sgn 50 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inner_point_defn,axiom,
! [X3,X1] :
( inner_point(X3,X1)
<=> ( incident_c(X3,X1)
& ~ end_point(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).
fof(c3,axiom,
! [X1] :
? [X3] : inner_point(X3,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',c3) ).
fof(o2,axiom,
! [X9] :
? [X1] :
( open(X1)
& ! [X3] :
( incident_o(X3,X9)
<=> incident_c(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o2) ).
fof(start_point_defn,axiom,
! [X3,X9] :
( start_point(X3,X9)
<=> ( incident_o(X3,X9)
& ! [X5] :
( ( X3 != X5
& incident_o(X5,X9) )
=> ordered_by(X9,X3,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',start_point_defn) ).
fof(underlying_curve_defn,axiom,
! [X1,X9] :
( X1 = underlying_curve(X9)
<=> ! [X3] :
( incident_o(X3,X9)
<=> incident_c(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',underlying_curve_defn) ).
fof(theorem_4_11,conjecture,
! [X9] :
? [X3,X5] :
( ordered_by(X9,X3,X5)
& X3 != X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_11) ).
fof(o4,axiom,
! [X9] :
? [X3] : start_point(X3,X9),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o4) ).
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/sandbox/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).
fof(open_defn,axiom,
! [X1] :
( open(X1)
<=> ? [X3] : end_point(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',open_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,
! [X132,X133] :
( ( incident_c(X132,X133)
| ~ inner_point(X132,X133) )
& ( ~ end_point(X132,X133)
| ~ inner_point(X132,X133) )
& ( ~ incident_c(X132,X133)
| end_point(X132,X133)
| inner_point(X132,X133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_11,plain,
! [X157] : inner_point(esk8_1(X157),X157),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c3])]) ).
fof(c_0_12,plain,
! [X211,X213,X214] :
( open(esk17_1(X211))
& ( ~ incident_o(X213,X211)
| incident_c(X213,esk17_1(X211)) )
& ( ~ incident_c(X214,esk17_1(X211))
| incident_o(X214,X211) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[o2])])])])]) ).
cnf(c_0_13,plain,
( incident_c(X1,X2)
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
inner_point(esk8_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X196,X197,X198,X199,X200] :
( ( incident_o(X196,X197)
| ~ start_point(X196,X197) )
& ( X196 = X198
| ~ incident_o(X198,X197)
| ordered_by(X197,X196,X198)
| ~ start_point(X196,X197) )
& ( X199 != esk15_2(X199,X200)
| ~ incident_o(X199,X200)
| start_point(X199,X200) )
& ( incident_o(esk15_2(X199,X200),X200)
| ~ incident_o(X199,X200)
| start_point(X199,X200) )
& ( ~ ordered_by(X200,X199,esk15_2(X199,X200))
| ~ incident_o(X199,X200)
| start_point(X199,X200) ) ),
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)],[start_point_defn])])])])])]) ).
cnf(c_0_16,plain,
( incident_o(X1,X2)
| ~ incident_c(X1,esk17_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
incident_c(esk8_1(X1),X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_18,plain,
! [X240,X241,X242,X243,X244,X245] :
( ( ~ incident_o(X242,X241)
| incident_c(X242,X240)
| X240 != underlying_curve(X241) )
& ( ~ incident_c(X243,X240)
| incident_o(X243,X241)
| X240 != underlying_curve(X241) )
& ( ~ incident_o(esk24_2(X244,X245),X245)
| ~ incident_c(esk24_2(X244,X245),X244)
| X244 = underlying_curve(X245) )
& ( incident_o(esk24_2(X244,X245),X245)
| incident_c(esk24_2(X244,X245),X244)
| X244 = underlying_curve(X245) ) ),
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)],[underlying_curve_defn])])])])])]) ).
fof(c_0_19,negated_conjecture,
~ ! [X9] :
? [X3,X5] :
( ordered_by(X9,X3,X5)
& X3 != X5 ),
inference(assume_negation,[status(cth)],[theorem_4_11]) ).
cnf(c_0_20,plain,
( X1 = X2
| ordered_by(X3,X1,X2)
| ~ incident_o(X2,X3)
| ~ start_point(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
incident_o(esk8_1(esk17_1(X1)),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X228] : start_point(esk20_1(X228),X228),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[o4])]) ).
cnf(c_0_23,plain,
( incident_o(X1,X3)
| ~ incident_c(X1,X2)
| X2 != underlying_curve(X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,negated_conjecture,
! [X248,X249] :
( ~ ordered_by(esk25_0,X248,X249)
| X248 = X249 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_25,plain,
( X1 = esk8_1(esk17_1(X2))
| ordered_by(X2,X1,esk8_1(esk17_1(X2)))
| ~ start_point(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
start_point(esk20_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_27,plain,
! [X124,X125,X126,X127,X128,X129] :
( ( incident_c(X124,X125)
| ~ end_point(X124,X125) )
& ( ~ part_of(X126,X125)
| ~ part_of(X127,X125)
| ~ incident_c(X124,X126)
| ~ incident_c(X124,X127)
| part_of(X126,X127)
| part_of(X127,X126)
| ~ end_point(X124,X125) )
& ( part_of(esk3_2(X128,X129),X129)
| ~ incident_c(X128,X129)
| end_point(X128,X129) )
& ( part_of(esk4_2(X128,X129),X129)
| ~ incident_c(X128,X129)
| end_point(X128,X129) )
& ( incident_c(X128,esk3_2(X128,X129))
| ~ incident_c(X128,X129)
| end_point(X128,X129) )
& ( incident_c(X128,esk4_2(X128,X129))
| ~ incident_c(X128,X129)
| end_point(X128,X129) )
& ( ~ part_of(esk3_2(X128,X129),esk4_2(X128,X129))
| ~ incident_c(X128,X129)
| end_point(X128,X129) )
& ( ~ part_of(esk4_2(X128,X129),esk3_2(X128,X129))
| ~ incident_c(X128,X129)
| end_point(X128,X129) ) ),
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(c_0_28,plain,
! [X146,X148,X149] :
( ( ~ open(X146)
| end_point(esk7_1(X146),X146) )
& ( ~ end_point(X149,X148)
| open(X148) ) ),
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])])])])]) ).
cnf(c_0_29,plain,
( incident_o(X1,X2)
| ~ incident_c(X1,underlying_curve(X2)) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( X1 = X2
| ~ ordered_by(esk25_0,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( esk20_1(X1) = esk8_1(esk17_1(X1))
| ordered_by(X1,esk20_1(X1),esk8_1(esk17_1(X1))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( incident_c(X1,X2)
| ~ end_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( end_point(esk7_1(X1),X1)
| ~ open(X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
incident_o(esk8_1(underlying_curve(X1)),X1),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_35,negated_conjecture,
esk20_1(esk25_0) = esk8_1(esk17_1(esk25_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( incident_c(esk7_1(X1),X1)
| ~ open(X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
open(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_38,plain,
( X1 = esk8_1(underlying_curve(X2))
| ordered_by(X2,X1,esk8_1(underlying_curve(X2)))
| ~ start_point(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
start_point(esk8_1(esk17_1(esk25_0)),esk25_0),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_40,plain,
incident_o(esk7_1(esk17_1(X1)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_36]),c_0_37])]) ).
cnf(c_0_41,negated_conjecture,
esk8_1(esk17_1(esk25_0)) = esk8_1(underlying_curve(esk25_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_30]) ).
cnf(c_0_42,plain,
( ~ end_point(X1,X2)
| ~ inner_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_43,plain,
( X1 = esk7_1(esk17_1(X2))
| ordered_by(X2,X1,esk7_1(esk17_1(X2)))
| ~ start_point(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
start_point(esk8_1(underlying_curve(esk25_0)),esk25_0),
inference(rw,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_45,plain,
~ end_point(esk8_1(X1),X1),
inference(spm,[status(thm)],[c_0_42,c_0_14]) ).
cnf(c_0_46,negated_conjecture,
esk7_1(esk17_1(esk25_0)) = esk8_1(underlying_curve(esk25_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_30]) ).
cnf(c_0_47,negated_conjecture,
~ end_point(esk8_1(underlying_curve(esk25_0)),esk17_1(esk25_0)),
inference(spm,[status(thm)],[c_0_45,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_46]),c_0_37])]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO126+1 : TPTP v9.2.1. Released v2.4.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:42:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.64/3.10 % Version : CSE_E---1.7
% 3.64/3.10 % Problem : theBenchmark.p
% 3.64/3.10 % SZS status Theorem for theBenchmark.p
% 3.64/3.10 % SZS output start CNFRefutation
% See solution above
% 3.64/3.11 % Total time : 2.372s
%------------------------------------------------------------------------------