%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO124+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 : n026.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 04:19:22 PM UTC 2026
% Result : Theorem 1.32s 1.74s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 10 unt; 0 def)
% Number of atoms : 125 ( 14 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 150 ( 54 ~; 57 |; 31 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-5 aty)
% Number of variables : 81 ( 6 sgn 51 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(corollary_4_10_1,conjecture,
! [X9,X3,X5] :
( ( start_point(X3,X9)
& start_point(X5,X9) )
=> X3 = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_4_10_1) ).
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(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/sandbox2/benchmark/Axioms/GEO004+2.ax',start_point_defn) ).
fof(o3,axiom,
! [X3,X5,X7,X9] :
( between_o(X9,X3,X5,X7)
<=> ? [X1] :
( ! [X3] :
( incident_o(X3,X9)
<=> incident_c(X3,X1) )
& between_c(X1,X3,X5,X7) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+2.ax',o3) ).
fof(between_o_defn,axiom,
! [X9,X3,X5,X7] :
( between_o(X9,X3,X5,X7)
<=> ( ( ordered_by(X9,X3,X5)
& ordered_by(X9,X5,X7) )
| ( ordered_by(X9,X7,X5)
& ordered_by(X9,X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+2.ax',between_o_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X9,X3,X5] :
( ( start_point(X3,X9)
& start_point(X5,X9) )
=> X3 = X5 ),
inference(assume_negation,[status(cth)],[corollary_4_10_1]) ).
fof(c_0_6,plain,
! [X182,X183,X184,X185,X187,X188,X189,X190,X191] :
( ( X183 != X185
| ~ between_c(X182,X183,X184,X185) )
& ( part_of(esk14_4(X182,X183,X184,X185),X182)
| ~ between_c(X182,X183,X184,X185) )
& ( end_point(X183,esk14_4(X182,X183,X184,X185))
| ~ between_c(X182,X183,X184,X185) )
& ( end_point(X185,esk14_4(X182,X183,X184,X185))
| ~ between_c(X182,X183,X184,X185) )
& ( inner_point(X184,esk14_4(X182,X183,X184,X185))
| ~ between_c(X182,X183,X184,X185) )
& ( X188 = X190
| ~ part_of(X191,X187)
| ~ end_point(X188,X191)
| ~ end_point(X190,X191)
| ~ inner_point(X189,X191)
| between_c(X187,X188,X189,X190) ) ),
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_7,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])])])])])]) ).
fof(c_0_8,negated_conjecture,
( start_point(esk26_0,esk25_0)
& start_point(esk27_0,esk25_0)
& esk26_0 != esk27_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( X1 != X2
| ~ between_c(X3,X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X215,X216,X217,X218,X220,X221,X222,X223,X224,X225,X226] :
( ( ~ incident_o(X220,X218)
| incident_c(X220,esk18_4(X215,X216,X217,X218))
| ~ between_o(X218,X215,X216,X217) )
& ( ~ incident_c(X221,esk18_4(X215,X216,X217,X218))
| incident_o(X221,X218)
| ~ between_o(X218,X215,X216,X217) )
& ( between_c(esk18_4(X215,X216,X217,X218),X215,X216,X217)
| ~ between_o(X218,X215,X216,X217) )
& ( ~ incident_o(esk19_5(X222,X223,X224,X225,X226),X225)
| ~ incident_c(esk19_5(X222,X223,X224,X225,X226),X226)
| ~ between_c(X226,X222,X223,X224)
| between_o(X225,X222,X223,X224) )
& ( incident_o(esk19_5(X222,X223,X224,X225,X226),X225)
| incident_c(esk19_5(X222,X223,X224,X225,X226),X226)
| ~ between_c(X226,X222,X223,X224)
| between_o(X225,X222,X223,X224) ) ),
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)],[o3])])])])])]) ).
cnf(c_0_11,plain,
( incident_o(X1,X2)
| ~ start_point(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
start_point(esk26_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
start_point(esk27_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
~ between_c(X1,X2,X3,X2),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( between_c(esk18_4(X1,X2,X3,X4),X1,X2,X3)
| ~ between_o(X4,X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,plain,
! [X192,X193,X194,X195] :
( ( ordered_by(X192,X195,X194)
| ordered_by(X192,X193,X194)
| ~ between_o(X192,X193,X194,X195) )
& ( ordered_by(X192,X194,X193)
| ordered_by(X192,X193,X194)
| ~ between_o(X192,X193,X194,X195) )
& ( ordered_by(X192,X195,X194)
| ordered_by(X192,X194,X195)
| ~ between_o(X192,X193,X194,X195) )
& ( ordered_by(X192,X194,X193)
| ordered_by(X192,X194,X195)
| ~ between_o(X192,X193,X194,X195) )
& ( ~ ordered_by(X192,X193,X194)
| ~ ordered_by(X192,X194,X195)
| between_o(X192,X193,X194,X195) )
& ( ~ ordered_by(X192,X195,X194)
| ~ ordered_by(X192,X194,X193)
| between_o(X192,X193,X194,X195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[between_o_defn])])]) ).
cnf(c_0_17,plain,
( X1 = X2
| ordered_by(X3,X1,X2)
| ~ incident_o(X2,X3)
| ~ start_point(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
incident_o(esk26_0,esk25_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
incident_o(esk27_0,esk25_0),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_20,plain,
~ between_o(X1,X2,X3,X2),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( between_o(X1,X4,X3,X2)
| ~ ordered_by(X1,X2,X3)
| ~ ordered_by(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( X1 = esk26_0
| ordered_by(esk25_0,X1,esk26_0)
| ~ start_point(X1,esk25_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
esk26_0 != esk27_0,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( X1 = esk27_0
| ordered_by(esk25_0,X1,esk27_0)
| ~ start_point(X1,esk25_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_25,plain,
( ~ ordered_by(X1,X2,X3)
| ~ ordered_by(X1,X3,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
ordered_by(esk25_0,esk27_0,esk26_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
ordered_by(esk25_0,esk26_0,esk27_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_12]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO124+1 : TPTP v9.2.1. Released v2.4.0.
% 0.12/0.13 % 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
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 17:42:38 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.32/1.74 % Version : CSE_E---1.7
% 1.32/1.74 % Problem : theBenchmark.p
% 1.32/1.74 % SZS status Theorem for theBenchmark.p
% 1.32/1.74 % SZS output start CNFRefutation
% See solution above
% 1.32/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------