%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CSR017+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 : n031.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 04:13:52 PM UTC 2026
% Result : Theorem 1.31s 1.72s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 20 unt; 0 def)
% Number of atoms : 423 ( 207 equ)
% Maximal formula atoms : 149 ( 7 avg)
% Number of connectives : 508 ( 142 ~; 253 |; 100 &)
% ( 11 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(happens_terminates_not_holds,axiom,
! [X4,X5,X2] :
( ( happens(X4,X5)
& terminates(X4,X2,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+0.ax',happens_terminates_not_holds) ).
fof(symmetry_of_plus,axiom,
! [X9,X10] : plus(X9,X10) = plus(X10,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_plus) ).
fof(plus0_1,axiom,
plus(n0,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus0_1) ).
fof(terminates_all_defn,axiom,
! [X4,X2,X5] :
( terminates(X4,X2,X5)
<=> ( ( X4 = push
& X2 = backwards
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = forwards
& ~ happens(push,X5) )
| ( X4 = pull
& X2 = forwards
& happens(push,X5) )
| ( X4 = pull
& X2 = backwards
& happens(push,X5) )
| ( X4 = push
& X2 = spinning
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = spinning
& ~ happens(push,X5) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+2.ax',terminates_all_defn) ).
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(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(not_spinning_1,conjecture,
~ holdsAt(spinning,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_spinning_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(less1,axiom,
! [X9] :
( less(X9,n1)
<=> less_or_equal(X9,n0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less1) ).
fof(push_not_pull,axiom,
push != pull,
file('/export/starexec/sandbox/benchmark/Axioms/CSR001+2.ax',push_not_pull) ).
fof(c_0_11,plain,
! [X4,X5,X2] :
( ( happens(X4,X5)
& terminates(X4,X2,X5) )
=> ~ holdsAt(X2,plus(X5,n1)) ),
inference(fof_simplification,[status(thm)],[happens_terminates_not_holds]) ).
fof(c_0_12,plain,
! [X129,X130,X131] :
( ~ happens(X129,X130)
| ~ terminates(X129,X131,X130)
| ~ holdsAt(X131,plus(X130,n1)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_13,plain,
! [X149,X150] : plus(X149,X150) = plus(X150,X149),
inference(variable_rename,[status(thm)],[symmetry_of_plus]) ).
fof(c_0_14,plain,
! [X2,X4,X5] :
( epred3_3(X5,X4,X2)
<=> ( ( X4 = push
& X2 = backwards
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = forwards
& ~ happens(push,X5) )
| ( X4 = pull
& X2 = forwards
& happens(push,X5) )
| ( X4 = pull
& X2 = backwards
& happens(push,X5) )
| ( X4 = push
& X2 = spinning
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = spinning
& ~ happens(push,X5) ) ) ),
introduced(definition) ).
fof(c_0_15,plain,
! [X2,X4,X5] :
( epred2_3(X5,X4,X2)
<=> ( ( X4 = push
& X2 = backwards
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = forwards
& ~ happens(push,X5) )
| ( X4 = pull
& X2 = forwards
& happens(push,X5) ) ) ),
introduced(definition) ).
cnf(c_0_16,plain,
( ~ happens(X1,X2)
| ~ terminates(X1,X3,X2)
| ~ holdsAt(X3,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
plus(n0,n1) = n1,
inference(split_conjunct,[status(thm)],[plus0_1]) ).
fof(c_0_19,plain,
! [X4,X2,X5] :
( terminates(X4,X2,X5)
<=> epred3_3(X5,X4,X2) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[terminates_all_defn]),c_0_14]) ).
fof(c_0_20,plain,
! [X2,X4,X5] :
( epred3_3(X5,X4,X2)
<=> ( epred2_3(X5,X4,X2)
| ( X4 = pull
& X2 = backwards
& happens(push,X5) )
| ( X4 = push
& X2 = spinning
& ~ happens(pull,X5) )
| ( X4 = pull
& X2 = spinning
& ~ happens(push,X5) ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( ~ holdsAt(X1,plus(n1,X2))
| ~ terminates(X3,X1,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
plus(n1,n0) = n1,
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
fof(c_0_23,plain,
! [X141,X142,X143] :
( ( ~ terminates(X141,X142,X143)
| epred3_3(X143,X141,X142) )
& ( ~ epred3_3(X143,X141,X142)
| terminates(X141,X142,X143) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])]) ).
fof(c_0_24,plain,
! [X173,X174,X175] :
( ( X174 = pull
| X174 = push
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| X174 = push
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| X174 = push
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| X173 = spinning
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| X173 = spinning
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| X173 = spinning
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| ~ happens(pull,X175)
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| ~ happens(pull,X175)
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| ~ happens(pull,X175)
| X174 = pull
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| X174 = push
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| X174 = push
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| X174 = push
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| X173 = spinning
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| X173 = spinning
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| X173 = spinning
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| ~ happens(pull,X175)
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| ~ happens(pull,X175)
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| ~ happens(pull,X175)
| X173 = backwards
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| X174 = push
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| X174 = push
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| X174 = push
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| X173 = spinning
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| X173 = spinning
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| X173 = spinning
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X174 = pull
| ~ happens(pull,X175)
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( X173 = spinning
| ~ happens(pull,X175)
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ happens(push,X175)
| ~ happens(pull,X175)
| happens(push,X175)
| epred2_3(X175,X174,X173)
| ~ epred3_3(X175,X174,X173) )
& ( ~ epred2_3(X175,X174,X173)
| epred3_3(X175,X174,X173) )
& ( X174 != pull
| X173 != backwards
| ~ happens(push,X175)
| epred3_3(X175,X174,X173) )
& ( X174 != push
| X173 != spinning
| happens(pull,X175)
| epred3_3(X175,X174,X173) )
& ( X174 != pull
| X173 != spinning
| happens(push,X175)
| epred3_3(X175,X174,X173) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])]) ).
fof(c_0_25,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])])]) ).
fof(c_0_26,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])])]) ).
cnf(c_0_27,plain,
( ~ holdsAt(X1,n1)
| ~ terminates(X2,X1,n0)
| ~ happens(X2,n0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( terminates(X2,X3,X1)
| ~ epred3_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( happens(pull,X3)
| epred3_3(X3,X1,X2)
| X1 != push
| X2 != spinning ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_30,negated_conjecture,
holdsAt(spinning,n1),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[not_spinning_1])]) ).
cnf(c_0_31,plain,
( happens(X1,X2)
| X1 != push
| X2 != n0 ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X9,X10] :
( less(X9,X10)
<=> ( ~ less(X10,X9)
& X10 != X9 ) ),
inference(fof_simplification,[status(thm)],[less_property]) ).
fof(c_0_33,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_34,plain,
( less_or_equal(X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_35,plain,
! [X154] :
( ( ~ less(X154,n1)
| less_or_equal(X154,n0) )
& ( ~ less_or_equal(X154,n0)
| less(X154,n1) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[less1])]) ).
cnf(c_0_36,plain,
( X1 = push
| X2 = n2
| X2 = n1
| X1 = push
| ~ happens(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,plain,
( ~ epred3_3(n0,X1,X2)
| ~ holdsAt(X2,n1)
| ~ happens(X1,n0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_38,plain,
( epred3_3(X1,push,spinning)
| happens(pull,X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_29])]) ).
cnf(c_0_39,negated_conjecture,
holdsAt(spinning,n1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
happens(push,n0),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_31])]) ).
fof(c_0_41,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_32])])]) ).
cnf(c_0_42,plain,
( less(X1,n2)
| ~ less_or_equal(X1,n1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
less_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
( less(X1,n1)
| ~ less_or_equal(X1,n0) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,plain,
( X2 = n1
| X2 = n2
| X1 = push
| ~ happens(X1,X2) ),
inference(cn,[status(thm)],[c_0_36]) ).
cnf(c_0_46,plain,
happens(pull,n0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_47,plain,
push != pull,
inference(split_conjunct,[status(thm)],[push_not_pull]) ).
cnf(c_0_48,plain,
( ~ less(X1,X2)
| ~ less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
less(n1,n2),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
less(n0,n1),
inference(spm,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_51,plain,
( n0 = n2
| n0 = n1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_52,plain,
~ less(n2,n1),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( X1 != X2
| ~ less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
n0 = n1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_55,plain,
~ less(X1,X1),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_56,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : CSR017+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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
% 0.15/0.32 % Computer : n031.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 16:28:53 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.31/1.72 % Version : CSE_E---1.7
% 1.31/1.72 % Problem : theBenchmark.p
% 1.31/1.72 % SZS status Theorem for theBenchmark.p
% 1.31/1.72 % SZS output start CNFRefutation
% See solution above
% 1.31/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------