%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO083+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 : 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 04:19:15 PM UTC 2026
% Result : Theorem 38.67s 22.69s
% Output : CNFRefutation 38.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 92 ( 10 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 96 ( 33 ~; 43 |; 14 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 75 ( 6 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(corollary_2_6_1,conjecture,
! [X2,X4,X6,X3] :
( ( part_of(X4,X6)
& meet(X3,X2,X4)
& meet(X3,X2,X6) )
=> part_of(sum(X2,X4),sum(X2,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_6_1) ).
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(c_0_3,negated_conjecture,
~ ! [X2,X4,X6,X3] :
( ( part_of(X4,X6)
& meet(X3,X2,X4)
& meet(X3,X2,X6) )
=> part_of(sum(X2,X4),sum(X2,X6)) ),
inference(assume_negation,[status(cth)],[corollary_2_6_1]) ).
fof(c_0_4,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_5,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])])])])])]) ).
fof(c_0_6,negated_conjecture,
( part_of(esk15_0,esk16_0)
& meet(esk17_0,esk14_0,esk15_0)
& meet(esk17_0,esk14_0,esk16_0)
& ~ part_of(sum(esk14_0,esk15_0),sum(esk14_0,esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_7,plain,
( incident_c(X1,X3)
| ~ incident_c(X1,X2)
| X3 != sum(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( incident_c(X3,X2)
| ~ part_of(X1,X2)
| ~ incident_c(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
part_of(esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( part_of(X2,X1)
| ~ incident_c(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X3) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
( incident_c(X1,esk16_0)
| ~ incident_c(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( incident_c(esk1_2(X1,X2),X2)
| part_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,plain,
( part_of(X1,sum(X2,X3))
| ~ incident_c(esk1_2(sum(X2,X3),X1),X3) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( incident_c(esk1_2(X1,esk15_0),esk16_0)
| part_of(esk15_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
part_of(esk15_0,sum(X1,esk16_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( incident_c(X1,X3)
| incident_c(X1,X4)
| ~ incident_c(X1,X2)
| X2 != sum(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,plain,
( incident_c(X1,X3)
| ~ incident_c(X1,X2)
| X3 != sum(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_19,negated_conjecture,
( incident_c(X1,sum(X2,esk16_0))
| ~ incident_c(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_20,plain,
( incident_c(X1,X2)
| incident_c(X1,X3)
| ~ incident_c(X1,sum(X3,X2)) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X2) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( part_of(X1,sum(X2,esk16_0))
| ~ incident_c(esk1_2(sum(X2,esk16_0),X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_23,plain,
( incident_c(esk1_2(X1,sum(X2,X3)),X2)
| incident_c(esk1_2(X1,sum(X2,X3)),X3)
| part_of(sum(X2,X3),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_24,plain,
( part_of(X1,sum(X2,X3))
| ~ incident_c(esk1_2(sum(X2,X3),X1),X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( incident_c(esk1_2(sum(X1,esk16_0),sum(X2,esk15_0)),X2)
| part_of(sum(X2,esk15_0),sum(X1,esk16_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
~ part_of(sum(esk14_0,esk15_0),sum(esk14_0,esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_27,negated_conjecture,
part_of(sum(X1,esk15_0),sum(X1,esk16_0)),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO083+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
% 0.15/0.33 % 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 17:39:58 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 38.67/22.69 % Version : CSE_E---1.7
% 38.67/22.69 % Problem : theBenchmark.p
% 38.67/22.69 % SZS status Theorem for theBenchmark.p
% 38.67/22.69 % SZS output start CNFRefutation
% See solution above
% 38.87/22.82 % Total time : 17.405s
%------------------------------------------------------------------------------