%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO277+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 : n013.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 1.80s 1.88s
% Output : CNFRefutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 54 ( 32 unt; 0 def)
% Number of atoms : 168 ( 79 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 196 ( 82 ~; 78 |; 30 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 26 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))',axiom,
! [X13,X14] :
( ( ? [X15] :
( X14 = X15
& rpoint(X15) )
& ? [X16] :
( X13 = X16
& rpoint(X16) ) )
=> vf(X13,X14) = vf(X14,X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))') ).
fof('qe(s1(plural(224)))',axiom,
? [X8] :
( vd1080 = X8
& rpoint(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(s1(plural(224)))') ).
fof('qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))',axiom,
! [X102,X103,X104,X105] :
( ( ron(X103,X105)
& ron(X103,X104)
& ron(X102,X105)
& ron(X102,X104)
& ? [X106] :
( X105 = X106
& rline(X106) )
& ? [X107] :
( X104 = X107
& rline(X107) )
& X102 != X103
& ? [X108] :
( X103 = X108
& rpoint(X108) )
& ? [X109] :
( X102 = X109
& rpoint(X109) ) )
=> X104 = X105 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))') ).
fof('qu(theu(the(230), 1), imp(the(230)))',conjecture,
! [X1] :
( ( ron(vd1085,X1)
& ron(vd1089,X1)
& rline(X1) )
=> X1 = vd1099 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(theu(the(230), 1), imp(the(230)))') ).
fof('pred(225, 1)',axiom,
rpoint(vd1086),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(225, 1)') ).
fof('pred(225, 4)',axiom,
vd1085 = vd1086,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(225, 4)') ).
fof('holds(226, 1090, 1)',axiom,
vf(vd1089,vd1080) = vf(vd1085,vd1080),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(226, 1090, 1)') ).
fof('pred(226, 0)',axiom,
rpoint(vd1089),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','pred(226, 0)') ).
fof('qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))',axiom,
! [X92,X93] :
( ( ? [X94] :
( X93 = X94
& rpoint(X94) )
& ? [X95] :
( X92 = X95
& rpoint(X95) ) )
=> ( vf(X92,X93) = v0
<=> X92 = X93 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))') ).
fof('holds(226, 1090, 0)',axiom,
vf(vd1089,vd1085) = vf(vd1089,vd1080),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(226, 1090, 0)') ).
fof('and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), pred(the(230), 0)))',axiom,
( ron(vd1085,vd1099)
& ron(vd1089,vd1099)
& rline(vd1099) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), pred(the(230), 0)))') ).
fof('holds(conjunct1(225), 1087, 0)',axiom,
vd1085 != vd1080,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(225), 1087, 0)') ).
fof(c_0_12,plain,
! [X1499,X1500,X1501,X1502] :
( X1500 != X1501
| ~ rpoint(X1501)
| X1499 != X1502
| ~ rpoint(X1502)
| vf(X1499,X1500) = vf(X1500,X1499) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))'])])]) ).
fof(c_0_13,plain,
( vd1080 = esk4_0
& rpoint(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['qe(s1(plural(224)))'])]) ).
fof(c_0_14,plain,
! [X1588,X1589,X1590,X1591,X1592,X1593,X1594,X1595] :
( ~ ron(X1589,X1591)
| ~ ron(X1589,X1590)
| ~ ron(X1588,X1591)
| ~ ron(X1588,X1590)
| X1591 != X1592
| ~ rline(X1592)
| X1590 != X1593
| ~ rline(X1593)
| X1588 = X1589
| X1589 != X1594
| ~ rpoint(X1594)
| X1588 != X1595
| ~ rpoint(X1595)
| X1590 = X1591 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))'])])]) ).
fof(c_0_15,negated_conjecture,
~ ! [X1] :
( ( ron(vd1085,X1)
& ron(vd1089,X1)
& rline(X1) )
=> X1 = vd1099 ),
inference(assume_negation,[status(cth)],['qu(theu(the(230), 1), imp(the(230)))']) ).
cnf(c_0_16,plain,
( vf(X3,X1) = vf(X1,X3)
| X1 != X2
| ~ rpoint(X2)
| X3 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
rpoint(vd1086),
inference(split_conjunct,[status(thm)],['pred(225, 1)']) ).
cnf(c_0_18,plain,
vd1085 = vd1086,
inference(split_conjunct,[status(thm)],['pred(225, 4)']) ).
cnf(c_0_19,plain,
rpoint(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
vd1080 = esk4_0,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( X4 = X1
| X3 = X2
| ~ ron(X1,X2)
| ~ ron(X1,X3)
| ~ ron(X4,X2)
| ~ ron(X4,X3)
| X2 != X5
| ~ rline(X5)
| X3 != X6
| ~ rline(X6)
| X1 != X7
| ~ rpoint(X7)
| X4 != X8
| ~ rpoint(X8) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_22,negated_conjecture,
( ron(vd1085,esk1_0)
& ron(vd1089,esk1_0)
& rline(esk1_0)
& esk1_0 != vd1099 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_23,plain,
vf(vd1089,vd1080) = vf(vd1085,vd1080),
inference(split_conjunct,[status(thm)],['holds(226, 1090, 1)']) ).
cnf(c_0_24,plain,
( vf(X1,X2) = vf(X2,X1)
| ~ rpoint(X2)
| ~ rpoint(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).
cnf(c_0_25,plain,
rpoint(vd1085),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
rpoint(vd1080),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( X1 = X2
| X3 = X4
| ~ rpoint(X4)
| ~ rpoint(X3)
| ~ rline(X2)
| ~ rline(X1)
| ~ ron(X4,X2)
| ~ ron(X4,X1)
| ~ ron(X3,X2)
| ~ ron(X3,X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_28,negated_conjecture,
ron(vd1089,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
rpoint(vd1089),
inference(split_conjunct,[status(thm)],['pred(226, 0)']) ).
cnf(c_0_30,negated_conjecture,
rline(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X1578,X1579,X1580,X1581] :
( ( vf(X1578,X1579) != v0
| X1578 = X1579
| X1579 != X1580
| ~ rpoint(X1580)
| X1578 != X1581
| ~ rpoint(X1581) )
& ( X1578 != X1579
| vf(X1578,X1579) = v0
| X1579 != X1580
| ~ rpoint(X1580)
| X1578 != X1581
| ~ rpoint(X1581) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))'])])])]) ).
cnf(c_0_32,plain,
vf(vd1089,vd1085) = vf(vd1089,vd1080),
inference(split_conjunct,[status(thm)],['holds(226, 1090, 0)']) ).
cnf(c_0_33,plain,
vf(vd1089,vd1080) = vf(vd1080,vd1085),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
cnf(c_0_34,negated_conjecture,
( X1 = esk1_0
| X2 = vd1089
| ~ rpoint(X2)
| ~ rline(X1)
| ~ ron(vd1089,X1)
| ~ ron(X2,esk1_0)
| ~ ron(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]) ).
cnf(c_0_35,plain,
ron(vd1089,vd1099),
inference(split_conjunct,[status(thm)],['and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), pred(the(230), 0)))']) ).
cnf(c_0_36,plain,
rline(vd1099),
inference(split_conjunct,[status(thm)],['and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), pred(the(230), 0)))']) ).
cnf(c_0_37,negated_conjecture,
esk1_0 != vd1099,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_38,plain,
( X1 = X2
| vf(X1,X2) != v0
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
vf(vd1089,vd1085) = vf(vd1080,vd1085),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,plain,
vf(vd1080,vd1085) = vf(vd1080,vd1089),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_33]),c_0_26]),c_0_29])]) ).
cnf(c_0_41,negated_conjecture,
( X1 = vd1089
| ~ rpoint(X1)
| ~ ron(X1,esk1_0)
| ~ ron(X1,vd1099) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
ron(vd1085,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_43,plain,
ron(vd1085,vd1099),
inference(split_conjunct,[status(thm)],['and(pred(s2(plural(the(230))), 0), and(pred(s1(plural(the(230))), 0), pred(the(230), 0)))']) ).
cnf(c_0_44,plain,
( X1 = X2
| vf(X1,X2) != v0
| ~ rpoint(X1)
| ~ rpoint(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_38])]) ).
cnf(c_0_45,plain,
vd1085 != vd1080,
inference(split_conjunct,[status(thm)],['holds(conjunct1(225), 1087, 0)']) ).
cnf(c_0_46,plain,
( vf(X1,X2) = v0
| X1 != X2
| X2 != X3
| ~ rpoint(X3)
| X1 != X4
| ~ rpoint(X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_47,plain,
vf(vd1089,vd1085) = vf(vd1080,vd1089),
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
vd1085 = vd1089,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_25]),c_0_43])]) ).
cnf(c_0_49,plain,
vf(vd1089,vd1080) != v0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_23]),c_0_25]),c_0_26])]),c_0_45]) ).
cnf(c_0_50,plain,
( vf(X1,X1) = v0
| ~ rpoint(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_46])])]) ).
cnf(c_0_51,plain,
vf(vd1089,vd1089) = vf(vd1080,vd1089),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
vf(vd1080,vd1089) != v0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_24]),c_0_26]),c_0_29])]) ).
cnf(c_0_53,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_29])]),c_0_52]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO277+1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n013.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 17:51:11 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.80/1.88 % Version : CSE_E---1.7
% 1.80/1.88 % Problem : theBenchmark.p
% 1.80/1.88 % SZS status Theorem for theBenchmark.p
% 1.80/1.88 % SZS output start CNFRefutation
% See solution above
% 1.80/1.89 % Total time : 1.423s
%------------------------------------------------------------------------------