%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO084+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 : n002.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 3.65s 3.06s
% Output : CNFRefutation 3.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 7 unt; 0 def)
% Number of atoms : 111 ( 14 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 109 ( 36 ~; 53 |; 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 : 82 ( 6 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(corollary_2_6_2,conjecture,
! [X2,X4,X6,X3] :
( ( part_of(X2,X6)
& part_of(X4,X6)
& meet(X3,X2,X4) )
=> part_of(sum(X2,X4),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_2) ).
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/sandbox/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/sandbox/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(c_0_3,negated_conjecture,
~ ! [X2,X4,X6,X3] :
( ( part_of(X2,X6)
& part_of(X4,X6)
& meet(X3,X2,X4) )
=> part_of(sum(X2,X4),X6) ),
inference(assume_negation,[status(cth)],[corollary_2_6_2]) ).
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(esk14_0,esk16_0)
& part_of(esk15_0,esk16_0)
& meet(esk17_0,esk14_0,esk15_0)
& ~ part_of(sum(esk14_0,esk15_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(X2,X4) ),
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,negated_conjecture,
part_of(esk14_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( part_of(X2,X1)
| ~ incident_c(esk1_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,plain,
( incident_c(X1,sum(X2,X3))
| ~ incident_c(X1,X2) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_13,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_14,plain,
( incident_c(esk1_2(X1,X2),X2)
| part_of(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( incident_c(X1,esk16_0)
| ~ incident_c(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_10]) ).
cnf(c_0_16,plain,
( part_of(X1,sum(X2,X3))
| ~ incident_c(esk1_2(sum(X2,X3),X1),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( incident_c(esk1_2(X1,esk15_0),esk16_0)
| part_of(esk15_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,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)],[c_0_4]) ).
cnf(c_0_19,negated_conjecture,
( incident_c(esk1_2(X1,esk14_0),esk16_0)
| part_of(esk14_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
part_of(esk15_0,sum(esk16_0,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( sum(X1,X2) = X1
| incident_c(esk2_3(X1,X1,X2),X2)
| incident_c(esk2_3(X1,X1,X2),X1) ),
inference(ef,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
part_of(esk14_0,sum(esk16_0,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( incident_c(X1,sum(esk16_0,X2))
| ~ incident_c(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_20]) ).
cnf(c_0_24,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)],[c_0_4]) ).
cnf(c_0_25,plain,
( sum(X1,X1) = X1
| incident_c(esk2_3(X1,X1,X1),X1) ),
inference(ef,[status(thm)],[c_0_21]) ).
cnf(c_0_26,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_27,negated_conjecture,
( incident_c(X1,sum(esk16_0,X2))
| ~ incident_c(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_8,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( part_of(X1,sum(esk16_0,X2))
| ~ incident_c(esk1_2(sum(esk16_0,X2),X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_29,plain,
sum(X1,X1) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_25]) ).
cnf(c_0_30,plain,
( incident_c(X1,X2)
| incident_c(X1,X3)
| ~ incident_c(X1,sum(X3,X2)) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( part_of(X1,sum(esk16_0,X2))
| ~ incident_c(esk1_2(sum(esk16_0,X2),X1),esk14_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
( part_of(X1,esk16_0)
| ~ incident_c(esk1_2(esk16_0,X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,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_30,c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( part_of(X1,esk16_0)
| ~ incident_c(esk1_2(esk16_0,X1),esk14_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( incident_c(esk1_2(esk16_0,sum(X1,esk15_0)),X1)
| part_of(sum(X1,esk15_0),esk16_0) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
~ part_of(sum(esk14_0,esk15_0),esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO084+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
% 0.16/0.33 % Computer : n002.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 17:41:01 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.65/3.06 % Version : CSE_E---1.7
% 3.65/3.06 % Problem : theBenchmark.p
% 3.65/3.06 % SZS status Theorem for theBenchmark.p
% 3.65/3.06 % SZS output start CNFRefutation
% See solution above
% 3.65/3.07 % Total time : 2.371s
%------------------------------------------------------------------------------