%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO278+1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n006.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 04:20:13 PM UTC 2026
% Result : Theorem 3.11s 2.97s
% Output : CNFRefutation 3.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 76 ( 21 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 99 ( 42 ~; 37 |; 17 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))',axiom,
! [X105,X106,X107,X108,X109] :
( ( vf(X107,X105) = vf(X107,X106)
& ron(X106,X109)
& ron(X105,X108)
& rcenter(X107,X109)
& rcenter(X107,X108)
& ? [X110] :
( X106 = X110
& rpoint(X110) )
& ? [X111] :
( X105 = X111
& rpoint(X111) ) )
=> X108 = X109 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))') ).
fof('qu(theu(the(231), 1), imp(the(231)))',conjecture,
! [X1] :
( ( ron(vd1096,X1)
& rcenter(vd1089,X1)
& rcircle(X1) )
=> X1 = vd1102 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(theu(the(231), 1), imp(the(231)))') ).
fof('and(pred(comma_conjunct2(the(231)), 0), and(pred(comma_conjunct1(the(231)), 0), pred(the(231), 0)))',axiom,
( ron(vd1096,vd1102)
& rcenter(vd1089,vd1102)
& rcircle(vd1102) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(comma_conjunct2(the(231)), 0), and(pred(comma_conjunct1(the(231)), 0), pred(the(231), 0)))') ).
fof('pred(229, 0)',axiom,
rpoint(vd1096),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(229, 0)') ).
fof(c_0_4,plain,
! [X1593,X1594,X1595,X1596,X1597,X1598,X1599] :
( vf(X1595,X1593) != vf(X1595,X1594)
| ~ ron(X1594,X1597)
| ~ ron(X1593,X1596)
| ~ rcenter(X1595,X1597)
| ~ rcenter(X1595,X1596)
| X1594 != X1598
| ~ rpoint(X1598)
| X1593 != X1599
| ~ rpoint(X1599)
| X1596 = X1597 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))'])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ( ron(vd1096,X1)
& rcenter(vd1089,X1)
& rcircle(X1) )
=> X1 = vd1102 ),
inference(assume_negation,[status(cth)],['qu(theu(the(231), 1), imp(the(231)))']) ).
cnf(c_0_6,plain,
( X5 = X4
| vf(X1,X2) != vf(X1,X3)
| ~ ron(X3,X4)
| ~ ron(X2,X5)
| ~ rcenter(X1,X4)
| ~ rcenter(X1,X5)
| X3 != X6
| ~ rpoint(X6)
| X2 != X7
| ~ rpoint(X7) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_7,negated_conjecture,
( ron(vd1096,esk1_0)
& rcenter(vd1089,esk1_0)
& rcircle(esk1_0)
& esk1_0 != vd1102 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( X1 = X2
| vf(X3,X4) != vf(X3,X5)
| ~ rpoint(X4)
| ~ rpoint(X5)
| ~ rcenter(X3,X2)
| ~ rcenter(X3,X1)
| ~ ron(X5,X1)
| ~ ron(X4,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6])]) ).
cnf(c_0_9,negated_conjecture,
rcenter(vd1089,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( X1 = esk1_0
| vf(vd1089,X2) != vf(vd1089,X3)
| ~ rpoint(X2)
| ~ rpoint(X3)
| ~ rcenter(vd1089,X1)
| ~ ron(X2,esk1_0)
| ~ ron(X3,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
rcenter(vd1089,vd1102),
inference(split_conjunct,[status(thm)],['and(pred(comma_conjunct2(the(231)), 0), and(pred(comma_conjunct1(the(231)), 0), pred(the(231), 0)))']) ).
cnf(c_0_12,negated_conjecture,
esk1_0 != vd1102,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( vf(vd1089,X1) != vf(vd1089,X2)
| ~ rpoint(X1)
| ~ rpoint(X2)
| ~ ron(X1,esk1_0)
| ~ ron(X2,vd1102) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_14,negated_conjecture,
( ~ rpoint(X1)
| ~ ron(X1,esk1_0)
| ~ ron(X1,vd1102) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_15,negated_conjecture,
ron(vd1096,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
rpoint(vd1096),
inference(split_conjunct,[status(thm)],['pred(229, 0)']) ).
cnf(c_0_17,plain,
ron(vd1096,vd1102),
inference(split_conjunct,[status(thm)],['and(pred(comma_conjunct2(the(231)), 0), and(pred(comma_conjunct1(the(231)), 0), pred(the(231), 0)))']) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO278+1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n006.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 17:51:16 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.11/2.97 % Version : CSE_E---1.7
% 3.11/2.97 % Problem : theBenchmark.p
% 3.11/2.97 % SZS status Theorem for theBenchmark.p
% 3.11/2.97 % SZS output start CNFRefutation
% See solution above
% 3.11/2.97 % Total time : 2.424s
%------------------------------------------------------------------------------