%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CSR018+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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 : n015.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 04:13:53 PM UTC 2026
% Result : Theorem 1.40s 1.74s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 49 ( 20 unt; 0 def)
% Number of atoms : 339 ( 185 equ)
% Maximal formula atoms : 120 ( 6 avg)
% Number of connectives : 408 ( 118 ~; 208 |; 73 &)
% ( 8 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(initiates_all_defn,axiom,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> ( ( X4 = push
& X2 = forwards
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = backwards
& ~ happens(push,X5) )
| ( X4 = pull
& X2 = spinning
& happens(push,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+2.ax',initiates_all_defn) ).
fof(happens_holds,axiom,
! [X4,X5,X2] :
( ( happens(X4,X5)
& initiates(X4,X2,X5) )
=> holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_holds) ).
fof(happens_all_defn,axiom,
! [X4,X5] :
( happens(X4,X5)
<=> ( ( X4 = push
& X5 = n0 )
| ( X4 = pull
& X5 = n1 )
| ( X4 = pull
& X5 = n2 )
| ( X4 = push
& X5 = n2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+2.ax',happens_all_defn) ).
fof(backwards_2,conjecture,
holdsAt(backwards,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backwards_2) ).
fof(less_or_equal,axiom,
! [X9,X10] :
( less_or_equal(X9,X10)
<=> ( less(X9,X10)
| X9 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_or_equal) ).
fof(symmetry_of_plus,axiom,
! [X9,X10] : plus(X9,X10) = plus(X10,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).
fof(plus1_1,axiom,
plus(n1,n1) = n2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus1_1) ).
fof(less_property,axiom,
! [X9,X10] :
( less(X9,X10)
<=> ( ~ less(X10,X9)
& X10 != X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_property) ).
fof(less2,axiom,
! [X9] :
( less(X9,n2)
<=> less_or_equal(X9,n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less2) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).
fof(push_not_pull,axiom,
push != pull,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+2.ax',push_not_pull) ).
fof(c_0_11,plain,
! [X2,X4,X5] :
( epred1_3(X5,X4,X2)
<=> ( ( X4 = push
& X2 = forwards
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = backwards
& ~ happens(push,X5) )
| ( X4 = pull
& X2 = spinning
& happens(push,X5) ) ) ),
introduced(definition) ).
fof(c_0_12,plain,
! [X4,X2,X5] :
( initiates(X4,X2,X5)
<=> epred1_3(X5,X4,X2) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[initiates_all_defn]),c_0_11]) ).
fof(c_0_13,plain,
! [X126,X127,X128] :
( ~ happens(X126,X127)
| ~ initiates(X126,X128,X127)
| holdsAt(X128,plus(X127,n1)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[happens_holds])]) ).
fof(c_0_14,plain,
! [X138,X139,X140] :
( ( ~ initiates(X138,X139,X140)
| epred1_3(X140,X138,X139) )
& ( ~ epred1_3(X140,X138,X139)
| initiates(X138,X139,X140) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_15,plain,
! [X167,X168,X169] :
( ( X168 = pull
| X168 = pull
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| X168 = pull
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| X168 = pull
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| X167 = backwards
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| X167 = backwards
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| X167 = backwards
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| ~ happens(push,X169)
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| ~ happens(push,X169)
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| ~ happens(push,X169)
| X168 = push
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| X168 = pull
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| X168 = pull
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| X168 = pull
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| X167 = backwards
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| X167 = backwards
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| X167 = backwards
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| ~ happens(push,X169)
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| ~ happens(push,X169)
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| ~ happens(push,X169)
| X167 = forwards
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| X168 = pull
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| X168 = pull
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| X168 = pull
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| X167 = backwards
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| X167 = backwards
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| X167 = backwards
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( X168 = pull
| ~ happens(push,X169)
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( X167 = spinning
| ~ happens(push,X169)
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( happens(push,X169)
| ~ happens(push,X169)
| ~ happens(pull,X169)
| ~ epred1_3(X169,X168,X167) )
& ( X168 != push
| X167 != forwards
| happens(pull,X169)
| epred1_3(X169,X168,X167) )
& ( X168 != pull
| X167 != backwards
| happens(push,X169)
| epred1_3(X169,X168,X167) )
& ( X168 != pull
| X167 != spinning
| ~ happens(push,X169)
| epred1_3(X169,X168,X167) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_16,plain,
( holdsAt(X3,plus(X2,n1))
| ~ happens(X1,X2)
| ~ initiates(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( initiates(X2,X3,X1)
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( happens(push,X3)
| epred1_3(X3,X1,X2)
| X1 != pull
| X2 != backwards ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X147,X148] :
( ( X147 = push
| X147 = pull
| X147 = pull
| X147 = push
| ~ happens(X147,X148) )
& ( X148 = n2
| X147 = pull
| X147 = pull
| X147 = push
| ~ happens(X147,X148) )
& ( X147 = push
| X148 = n2
| X147 = pull
| X147 = push
| ~ happens(X147,X148) )
& ( X148 = n2
| X148 = n2
| X147 = pull
| X147 = push
| ~ happens(X147,X148) )
& ( X147 = push
| X147 = pull
| X148 = n1
| X147 = push
| ~ happens(X147,X148) )
& ( X148 = n2
| X147 = pull
| X148 = n1
| X147 = push
| ~ happens(X147,X148) )
& ( X147 = push
| X148 = n2
| X148 = n1
| X147 = push
| ~ happens(X147,X148) )
& ( X148 = n2
| X148 = n2
| X148 = n1
| X147 = push
| ~ happens(X147,X148) )
& ( X147 = push
| X147 = pull
| X147 = pull
| X148 = n0
| ~ happens(X147,X148) )
& ( X148 = n2
| X147 = pull
| X147 = pull
| X148 = n0
| ~ happens(X147,X148) )
& ( X147 = push
| X148 = n2
| X147 = pull
| X148 = n0
| ~ happens(X147,X148) )
& ( X148 = n2
| X148 = n2
| X147 = pull
| X148 = n0
| ~ happens(X147,X148) )
& ( X147 = push
| X147 = pull
| X148 = n1
| X148 = n0
| ~ happens(X147,X148) )
& ( X148 = n2
| X147 = pull
| X148 = n1
| X148 = n0
| ~ happens(X147,X148) )
& ( X147 = push
| X148 = n2
| X148 = n1
| X148 = n0
| ~ happens(X147,X148) )
& ( X148 = n2
| X148 = n2
| X148 = n1
| X148 = n0
| ~ happens(X147,X148) )
& ( X147 != push
| X148 != n0
| happens(X147,X148) )
& ( X147 != pull
| X148 != n1
| happens(X147,X148) )
& ( X147 != pull
| X148 != n2
| happens(X147,X148) )
& ( X147 != push
| X148 != n2
| happens(X147,X148) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[happens_all_defn])])]) ).
cnf(c_0_20,plain,
( holdsAt(X1,plus(X2,n1))
| ~ epred1_3(X2,X3,X1)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
( epred1_3(X1,pull,backwards)
| happens(push,X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_18])]) ).
cnf(c_0_22,plain,
( happens(X1,X2)
| X1 != pull
| X2 != n1 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_23,negated_conjecture,
~ holdsAt(backwards,n2),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[backwards_2])]) ).
fof(c_0_24,plain,
! [X151,X152] :
( ( ~ less_or_equal(X151,X152)
| less(X151,X152)
| X151 = X152 )
& ( ~ less(X151,X152)
| less_or_equal(X151,X152) )
& ( X151 != X152
| less_or_equal(X151,X152) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less_or_equal])])]) ).
fof(c_0_25,plain,
! [X149,X150] : plus(X149,X150) = plus(X150,X149),
inference(variable_rename,[status(thm)],[symmetry_of_plus]) ).
cnf(c_0_26,plain,
( X1 = n2
| X1 = n2
| X2 = pull
| X1 = n0
| ~ happens(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( holdsAt(backwards,plus(X1,n1))
| happens(push,X1)
| ~ happens(pull,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
plus(n1,n1) = n2,
inference(split_conjunct,[status(thm)],[plus1_1]) ).
cnf(c_0_29,plain,
happens(pull,n1),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_30,negated_conjecture,
~ holdsAt(backwards,n2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X9,X10] :
( less(X9,X10)
<=> ( ~ less(X10,X9)
& X10 != X9 ) ),
inference(fof_simplification,[status(thm)],[less_property]) ).
fof(c_0_32,plain,
! [X155] :
( ( ~ less(X155,n2)
| less_or_equal(X155,n1) )
& ( ~ less_or_equal(X155,n1)
| less(X155,n2) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less2])]) ).
cnf(c_0_33,plain,
( less_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
plus(n0,n1) = n1,
inference(split_conjunct,[status(thm)],[plus0_1]) ).
cnf(c_0_35,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,plain,
( X2 = pull
| X1 = n0
| X1 = n2
| ~ happens(X2,X1) ),
inference(cn,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
happens(push,n1),
inference(sr,[status(thm)],[inference(cn,[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_38,plain,
push != pull,
inference(split_conjunct,[status(thm)],[push_not_pull]) ).
fof(c_0_39,plain,
! [X163,X164] :
( ( ~ less(X164,X163)
| ~ less(X163,X164) )
& ( X164 != X163
| ~ less(X163,X164) )
& ( less(X164,X163)
| X164 = X163
| less(X163,X164) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])]) ).
cnf(c_0_40,plain,
( less(X1,n2)
| ~ less_or_equal(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
less_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,plain,
( n2 = n1
| n0 = n1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_44,plain,
( X1 != X2
| ~ less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_45,plain,
less(n1,n2),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,plain,
n2 = n1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_28])]) ).
cnf(c_0_47,plain,
~ less(X1,X1),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_48,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR018+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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
% 0.15/0.33 % Computer : n015.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 16:27:02 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.40/1.74 % Version : CSE_E---1.7
% 1.40/1.74 % Problem : theBenchmark.p
% 1.40/1.74 % SZS status Theorem for theBenchmark.p
% 1.40/1.74 % SZS output start CNFRefutation
% See solution above
% 1.40/1.75 % Total time : 1.370s
%------------------------------------------------------------------------------