TSTP Solution File: HAL006+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : HAL006+1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n020.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 : 600s
% DateTime : Sat Jul 16 12:45:12 EDT 2022
% Result : Theorem 0.24s 1.42s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 6 unt; 0 def)
% Number of atoms : 104 ( 26 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 121 ( 50 ~; 44 |; 19 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 30 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subtract_distribution,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ! [X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> apply(X1,subtract(X2,X5,X6)) = subtract(X3,apply(X1,X5),apply(X1,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_distribution) ).
fof(lemma12,conjecture,
! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lemma12) ).
fof(g_morphism,axiom,
morphism(g,b,e),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',g_morphism) ).
fof(lemma8,axiom,
! [X19] :
( element(X19,e)
=> ? [X21,X22,X23] :
( element(X21,b)
& element(X22,e)
& subtract(e,apply(g,X21),X19) = X22
& element(X23,a)
& apply(gamma,apply(f,X23)) = X22
& apply(g,apply(alpha,X23)) = X22 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',lemma8) ).
fof(subtract_cancellation,axiom,
! [X2,X5,X6] :
( ( element(X5,X2)
& element(X6,X2) )
=> subtract(X2,X5,subtract(X2,X5,X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',subtract_cancellation) ).
fof(morphism,axiom,
! [X1,X2,X3] :
( morphism(X1,X2,X3)
=> ( ! [X4] :
( element(X4,X2)
=> element(apply(X1,X4),X3) )
& apply(X1,zero(X2)) = zero(X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/HAL001+0.ax',morphism) ).
fof(alpha_morphism,axiom,
morphism(alpha,a,b),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in',alpha_morphism) ).
fof(c_0_7,plain,
! [X7,X8,X9,X10,X11] :
( ~ morphism(X7,X8,X9)
| ~ element(X10,X8)
| ~ element(X11,X8)
| apply(X7,subtract(X8,X10,X11)) = subtract(X9,apply(X7,X10),apply(X7,X11)) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_distribution])])])])]) ).
fof(c_0_8,negated_conjecture,
~ ! [X19] :
( element(X19,e)
=> ? [X21,X24] :
( element(X21,b)
& element(X24,b)
& apply(g,subtract(b,X21,X24)) = X19 ) ),
inference(assume_negation,[status(cth)],[lemma12]) ).
cnf(c_0_9,plain,
( apply(X1,subtract(X2,X3,X4)) = subtract(X5,apply(X1,X3),apply(X1,X4))
| ~ element(X4,X2)
| ~ element(X3,X2)
| ~ morphism(X1,X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
morphism(g,b,e),
inference(split_conjunct,[status(thm)],[g_morphism]) ).
fof(c_0_11,plain,
! [X24] :
( ( element(esk4_1(X24),b)
| ~ element(X24,e) )
& ( element(esk5_1(X24),e)
| ~ element(X24,e) )
& ( subtract(e,apply(g,esk4_1(X24)),X24) = esk5_1(X24)
| ~ element(X24,e) )
& ( element(esk6_1(X24),a)
| ~ element(X24,e) )
& ( apply(gamma,apply(f,esk6_1(X24))) = esk5_1(X24)
| ~ element(X24,e) )
& ( apply(g,apply(alpha,esk6_1(X24))) = esk5_1(X24)
| ~ element(X24,e) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lemma8])])])])])]) ).
fof(c_0_12,negated_conjecture,
! [X26,X27] :
( element(esk1_0,e)
& ( ~ element(X26,b)
| ~ element(X27,b)
| apply(g,subtract(b,X26,X27)) != esk1_0 ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).
cnf(c_0_13,plain,
( subtract(e,apply(g,X1),apply(g,X2)) = apply(g,subtract(b,X1,X2))
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( apply(g,apply(alpha,esk6_1(X1))) = esk5_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X7,X8,X9] :
( ~ element(X8,X7)
| ~ element(X9,X7)
| subtract(X7,X8,subtract(X7,X8,X9)) = X9 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subtract_cancellation])]) ).
fof(c_0_16,plain,
! [X5,X6,X7,X8] :
( ( ~ element(X8,X6)
| element(apply(X5,X8),X7)
| ~ morphism(X5,X6,X7) )
& ( apply(X5,zero(X6)) = zero(X7)
| ~ morphism(X5,X6,X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[morphism])])])])])]) ).
cnf(c_0_17,negated_conjecture,
( apply(g,subtract(b,X1,X2)) != esk1_0
| ~ element(X2,b)
| ~ element(X1,b) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( subtract(e,apply(g,X1),esk5_1(X2)) = apply(g,subtract(b,X1,apply(alpha,esk6_1(X2))))
| ~ element(apply(alpha,esk6_1(X2)),b)
| ~ element(X1,b)
| ~ element(X2,e) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( subtract(X1,X2,subtract(X1,X2,X3)) = X3
| ~ element(X3,X1)
| ~ element(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( subtract(e,apply(g,esk4_1(X1)),X1) = esk5_1(X1)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( element(apply(X1,X4),X3)
| ~ morphism(X1,X2,X3)
| ~ element(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( subtract(e,apply(g,X1),esk5_1(X2)) != esk1_0
| ~ element(apply(alpha,esk6_1(X2)),b)
| ~ element(X1,b)
| ~ element(X2,e) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( subtract(e,apply(g,esk4_1(X1)),esk5_1(X1)) = X1
| ~ element(apply(g,esk4_1(X1)),e)
| ~ element(X1,e) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( element(apply(g,X1),e)
| ~ element(X1,b) ),
inference(spm,[status(thm)],[c_0_21,c_0_10]) ).
cnf(c_0_25,plain,
( element(esk4_1(X1),b)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,plain,
morphism(alpha,a,b),
inference(split_conjunct,[status(thm)],[alpha_morphism]) ).
cnf(c_0_27,negated_conjecture,
( X1 != esk1_0
| ~ element(apply(alpha,esk6_1(X1)),b)
| ~ element(X1,e) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
( element(apply(alpha,X1),b)
| ~ element(X1,a) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_29,plain,
( element(esk6_1(X1),a)
| ~ element(X1,e) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( X1 != esk1_0
| ~ element(X1,e) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,negated_conjecture,
element(esk1_0,e),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_30,c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HAL006+1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 7 21:05:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.24/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.24/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.24/1.42 # Preprocessing time : 0.019 s
% 0.24/1.42
% 0.24/1.42 # Proof found!
% 0.24/1.42 # SZS status Theorem
% 0.24/1.42 # SZS output start CNFRefutation
% See solution above
% 0.24/1.42 # Proof object total steps : 33
% 0.24/1.42 # Proof object clause steps : 20
% 0.24/1.42 # Proof object formula steps : 13
% 0.24/1.42 # Proof object conjectures : 9
% 0.24/1.42 # Proof object clause conjectures : 6
% 0.24/1.42 # Proof object formula conjectures : 3
% 0.24/1.42 # Proof object initial clauses used : 11
% 0.24/1.42 # Proof object initial formulas used : 7
% 0.24/1.42 # Proof object generating inferences : 9
% 0.24/1.42 # Proof object simplifying inferences : 3
% 0.24/1.42 # Training examples: 0 positive, 0 negative
% 0.24/1.42 # Parsed axioms : 33
% 0.24/1.42 # Removed by relevancy pruning/SinE : 5
% 0.24/1.42 # Initial clauses : 52
% 0.24/1.42 # Removed in clause preprocessing : 0
% 0.24/1.42 # Initial clauses in saturation : 52
% 0.24/1.42 # Processed clauses : 553
% 0.24/1.42 # ...of these trivial : 8
% 0.24/1.42 # ...subsumed : 263
% 0.24/1.42 # ...remaining for further processing : 282
% 0.24/1.42 # Other redundant clauses eliminated : 2
% 0.24/1.42 # Clauses deleted for lack of memory : 0
% 0.24/1.42 # Backward-subsumed : 13
% 0.24/1.42 # Backward-rewritten : 10
% 0.24/1.42 # Generated clauses : 2290
% 0.24/1.42 # ...of the previous two non-trivial : 2131
% 0.24/1.42 # Contextual simplify-reflections : 239
% 0.24/1.42 # Paramodulations : 2285
% 0.24/1.42 # Factorizations : 0
% 0.24/1.42 # Equation resolutions : 5
% 0.24/1.42 # Current number of processed clauses : 259
% 0.24/1.42 # Positive orientable unit clauses : 25
% 0.24/1.42 # Positive unorientable unit clauses: 0
% 0.24/1.42 # Negative unit clauses : 2
% 0.24/1.42 # Non-unit-clauses : 232
% 0.24/1.42 # Current number of unprocessed clauses: 1527
% 0.24/1.42 # ...number of literals in the above : 10165
% 0.24/1.42 # Current number of archived formulas : 0
% 0.24/1.42 # Current number of archived clauses : 23
% 0.24/1.42 # Clause-clause subsumption calls (NU) : 10890
% 0.24/1.42 # Rec. Clause-clause subsumption calls : 4105
% 0.24/1.42 # Non-unit clause-clause subsumptions : 499
% 0.24/1.42 # Unit Clause-clause subsumption calls : 58
% 0.24/1.42 # Rewrite failures with RHS unbound : 0
% 0.24/1.42 # BW rewrite match attempts : 10
% 0.24/1.42 # BW rewrite match successes : 8
% 0.24/1.42 # Condensation attempts : 0
% 0.24/1.42 # Condensation successes : 0
% 0.24/1.42 # Termbank termtop insertions : 72131
% 0.24/1.42
% 0.24/1.42 # -------------------------------------------------
% 0.24/1.42 # User time : 0.128 s
% 0.24/1.42 # System time : 0.004 s
% 0.24/1.42 # Total time : 0.132 s
% 0.24/1.42 # Maximum resident set size: 5496 pages
% 0.24/23.46 eprover: CPU time limit exceeded, terminating
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.47 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48 eprover: No such file or directory
% 0.24/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.48 eprover: No such file or directory
% 0.24/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49 eprover: No such file or directory
% 0.24/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49 eprover: No such file or directory
% 0.24/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.49 eprover: No such file or directory
% 0.24/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50 eprover: No such file or directory
% 0.24/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50 eprover: No such file or directory
% 0.24/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.24/23.50 eprover: No such file or directory
%------------------------------------------------------------------------------