%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : CSR021+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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 : n007.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 1.32s 1.72s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 361 ( 187 equ)
% Maximal formula atoms : 149 ( 11 avg)
% Number of connectives : 447 ( 118 ~; 229 |; 92 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 9 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 38 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',symmetry_of_plus) ).
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/sandbox2/benchmark/Axioms/CSR001+2.ax',terminates_all_defn) ).
fof(plus1_2,axiom,
plus(n1,n2) = n3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1_2) ).
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/sandbox2/benchmark/Axioms/CSR001+2.ax',happens_all_defn) ).
fof(not_backwards_3,conjecture,
~ holdsAt(backwards,n3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_backwards_3) ).
fof(c_0_6,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_7,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_6])]) ).
fof(c_0_8,plain,
! [X149,X150] : plus(X149,X150) = plus(X150,X149),
inference(variable_rename,[status(thm)],[symmetry_of_plus]) ).
fof(c_0_9,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_10,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_11,plain,
( ~ happens(X1,X2)
| ~ terminates(X1,X3,X2)
| ~ holdsAt(X3,plus(X2,n1)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
plus(X1,X2) = plus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,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_9]) ).
fof(c_0_14,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_9,c_0_10]) ).
cnf(c_0_15,plain,
( ~ holdsAt(X1,plus(n1,X2))
| ~ terminates(X3,X1,X2)
| ~ happens(X3,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
plus(n1,n2) = n3,
inference(split_conjunct,[status(thm)],[plus1_2]) ).
fof(c_0_17,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_13])]) ).
fof(c_0_18,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_14])])]) ).
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,n3)
| ~ terminates(X2,X1,n2)
| ~ happens(X2,n2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( terminates(X2,X3,X1)
| ~ epred3_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( epred3_3(X3,X1,X2)
| X1 != pull
| X2 != backwards
| ~ happens(push,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,negated_conjecture,
holdsAt(backwards,n3),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[not_backwards_3])]) ).
cnf(c_0_24,plain,
( happens(X1,X2)
| X1 != pull
| X2 != n2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
( happens(X1,X2)
| X1 != push
| X2 != n2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( ~ epred3_3(n2,X1,X2)
| ~ holdsAt(X2,n3)
| ~ happens(X1,n2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( epred3_3(X1,pull,backwards)
| ~ happens(push,X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_28,negated_conjecture,
holdsAt(backwards,n3),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
happens(pull,n2),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
cnf(c_0_30,plain,
happens(push,n2),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_25])]) ).
cnf(c_0_31,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR021+1 : TPTP v9.2.1. Bugfixed v3.1.0.
% 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
% 0.13/0.32 % Computer : n007.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 16:25:54 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.32/1.72 % Version : CSE_E---1.7
% 1.32/1.72 % Problem : theBenchmark.p
% 1.32/1.72 % SZS status Theorem for theBenchmark.p
% 1.32/1.72 % SZS output start CNFRefutation
% See solution above
% 1.32/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------