%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO284+1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n001.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 04:20:14 PM UTC 2026
% Result : Theorem 1.66s 1.88s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 16 unt; 0 def)
% Number of atoms : 185 ( 66 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 242 ( 99 ~; 105 |; 36 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 14 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qe(259)',conjecture,
? [X1,X2] :
( ron(vd1127,X2)
& rcenter(vd1123,X2)
& rcircle(X2)
& ron(vd1125,X1)
& ron(vd1123,X1)
& rline(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qe(259)') ).
fof('qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))',axiom,
! [X39,X40] :
( ( X39 != X40
& ? [X41] :
( X40 = X41
& rpoint(X41) )
& ? [X42] :
( X39 = X42
& rpoint(X42) ) )
=> ? [X43] :
( ron(X40,X43)
& rcenter(X39,X43)
& rcircle(X43) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).
fof('and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))',axiom,
( rless(vf(vd1127,vd1129),vf(vd1123,vd1125))
& vd1127 != vd1129
& vd1123 != vd1125
& vd1129 = vd1130
& rpoint(vd1130)
& vd1127 = vd1128
& rpoint(vd1128)
& vd1125 = vd1126
& rpoint(vd1126)
& vd1123 = vd1124
& rpoint(vd1124) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))') ).
fof('holds(258, 1150, 0)',axiom,
vd1123 = vd1129,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(258, 1150, 0)') ).
fof('qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))',axiom,
! [X53,X54] :
( ( X53 != X54
& ? [X55] :
( X54 = X55
& rpoint(X55) )
& ? [X56] :
( X53 = X56
& rpoint(X56) ) )
=> ? [X57] :
( ron(X54,X57)
& ron(X53,X57)
& rline(X57) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))') ).
fof(c_0_5,negated_conjecture,
~ ? [X1,X2] :
( ron(vd1127,X2)
& rcenter(vd1123,X2)
& rcircle(X2)
& ron(vd1125,X1)
& ron(vd1123,X1)
& rline(X1) ),
inference(assume_negation,[status(cth)],['qe(259)']) ).
fof(c_0_6,plain,
! [X1529,X1530,X1531,X1532] :
( ( ron(X1530,esk3_2(X1529,X1530))
| X1529 = X1530
| X1530 != X1531
| ~ rpoint(X1531)
| X1529 != X1532
| ~ rpoint(X1532) )
& ( rcenter(X1529,esk3_2(X1529,X1530))
| X1529 = X1530
| X1530 != X1531
| ~ rpoint(X1531)
| X1529 != X1532
| ~ rpoint(X1532) )
& ( rcircle(esk3_2(X1529,X1530))
| X1529 = X1530
| X1530 != X1531
| ~ rpoint(X1531)
| X1529 != X1532
| ~ rpoint(X1532) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))'])])])])]) ).
cnf(c_0_7,plain,
vd1129 = vd1130,
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_8,plain,
vd1123 = vd1129,
inference(split_conjunct,[status(thm)],['holds(258, 1150, 0)']) ).
fof(c_0_9,negated_conjecture,
! [X1491,X1492] :
( ~ ron(vd1127,X1492)
| ~ rcenter(vd1123,X1492)
| ~ rcircle(X1492)
| ~ ron(vd1125,X1491)
| ~ ron(vd1123,X1491)
| ~ rline(X1491) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
cnf(c_0_10,plain,
( rcenter(X1,esk3_2(X1,X2))
| X1 = X2
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
rpoint(vd1130),
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_12,plain,
vd1130 = vd1123,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ~ ron(vd1127,X1)
| ~ rcenter(vd1123,X1)
| ~ rcircle(X1)
| ~ ron(vd1125,X2)
| ~ ron(vd1123,X2)
| ~ rline(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( X1 = X2
| rcenter(X1,esk3_2(X1,X2))
| ~ rpoint(X1)
| ~ rpoint(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_15,plain,
rpoint(vd1123),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( ron(X1,esk3_2(X2,X1))
| X2 = X1
| X1 != X3
| ~ rpoint(X3)
| X2 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,plain,
rpoint(vd1128),
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_18,plain,
vd1127 = vd1128,
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_19,plain,
vd1127 != vd1129,
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_20,negated_conjecture,
( vd1123 = X1
| ~ rpoint(X1)
| ~ rline(X2)
| ~ rcircle(esk3_2(vd1123,X1))
| ~ ron(vd1127,esk3_2(vd1123,X1))
| ~ ron(vd1123,X2)
| ~ ron(vd1125,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_21,plain,
( X1 = X2
| ron(X1,esk3_2(X2,X1))
| ~ rpoint(X2)
| ~ rpoint(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).
cnf(c_0_22,plain,
rpoint(vd1127),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
vd1127 != vd1123,
inference(rw,[status(thm)],[c_0_19,c_0_8]) ).
cnf(c_0_24,plain,
( rcircle(esk3_2(X1,X2))
| X1 = X2
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_25,plain,
! [X1543,X1544,X1545,X1546] :
( ( ron(X1544,esk5_2(X1543,X1544))
| X1543 = X1544
| X1544 != X1545
| ~ rpoint(X1545)
| X1543 != X1546
| ~ rpoint(X1546) )
& ( ron(X1543,esk5_2(X1543,X1544))
| X1543 = X1544
| X1544 != X1545
| ~ rpoint(X1545)
| X1543 != X1546
| ~ rpoint(X1546) )
& ( rline(esk5_2(X1543,X1544))
| X1543 = X1544
| X1544 != X1545
| ~ rpoint(X1545)
| X1543 != X1546
| ~ rpoint(X1546) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))'])])])])]) ).
cnf(c_0_26,negated_conjecture,
( ~ rline(X1)
| ~ rcircle(esk3_2(vd1123,vd1127))
| ~ ron(vd1123,X1)
| ~ ron(vd1125,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_15])]),c_0_23]) ).
cnf(c_0_27,plain,
( X1 = X2
| rcircle(esk3_2(X1,X2))
| ~ rpoint(X1)
| ~ rpoint(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
cnf(c_0_28,plain,
( rline(esk5_2(X1,X2))
| X1 = X2
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ rline(X1)
| ~ ron(vd1123,X1)
| ~ ron(vd1125,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_15]),c_0_22])]),c_0_23]) ).
cnf(c_0_30,plain,
( X1 = X2
| rline(esk5_2(X1,X2))
| ~ rpoint(X1)
| ~ rpoint(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_28])]) ).
cnf(c_0_31,plain,
( ron(X1,esk5_2(X1,X2))
| X1 = X2
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
rpoint(vd1126),
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_33,plain,
vd1125 = vd1126,
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_34,negated_conjecture,
( X1 = X2
| ~ rpoint(X1)
| ~ rpoint(X2)
| ~ ron(vd1123,esk5_2(X1,X2))
| ~ ron(vd1125,esk5_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( X1 = X2
| ron(X1,esk5_2(X1,X2))
| ~ rpoint(X1)
| ~ rpoint(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_31])]) ).
cnf(c_0_36,plain,
rpoint(vd1125),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,plain,
( ron(X1,esk5_2(X2,X1))
| X2 = X1
| X1 != X3
| ~ rpoint(X3)
| X2 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_38,negated_conjecture,
( vd1125 = X1
| ~ rpoint(X1)
| ~ ron(vd1123,esk5_2(vd1125,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_39,plain,
( X1 = X2
| ron(X1,esk5_2(X2,X1))
| ~ rpoint(X2)
| ~ rpoint(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_37])]) ).
cnf(c_0_40,plain,
vd1123 != vd1125,
inference(split_conjunct,[status(thm)],['and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))']) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_15]),c_0_36])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO284+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n001.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:52:33 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.66/1.88 % Version : CSE_E---1.7
% 1.66/1.88 % Problem : theBenchmark.p
% 1.66/1.88 % SZS status Theorem for theBenchmark.p
% 1.66/1.88 % SZS output start CNFRefutation
% See solution above
% 1.66/1.88 % Total time : 1.424s
%------------------------------------------------------------------------------