TSTP Solution File: GRP167-2 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : GRP167-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 17:39:04 EDT 2023

% Result   : Unsatisfiable 0.22s 0.59s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of clauses     :   61 (  61 unt;   0 nHn;   5 RR)
%            Number of literals    :   61 (  60 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-2 aty)
%            Number of variables   :   96 (   8 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(associativity,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',associativity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X1),X1) = identity,
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',left_inverse) ).

cnf(left_identity,axiom,
    multiply(identity,X1) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',left_identity) ).

cnf(lat4_2,axiom,
    inverse(inverse(X1)) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',lat4_2) ).

cnf(lat4_5,axiom,
    negative_part(X1) = greatest_lower_bound(X1,identity),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',lat4_5) ).

cnf(symmetry_of_glb,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',symmetry_of_glb) ).

cnf(associativity_of_glb,axiom,
    greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',associativity_of_glb) ).

cnf(monotony_glb2,axiom,
    multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',monotony_glb2) ).

cnf(monotony_lub1,axiom,
    multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',monotony_lub1) ).

cnf(lat4_4,axiom,
    positive_part(X1) = least_upper_bound(X1,identity),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',lat4_4) ).

cnf(symmetry_of_lub,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',symmetry_of_lub) ).

cnf(glb_absorbtion,axiom,
    greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',glb_absorbtion) ).

cnf(associativity_of_lub,axiom,
    least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',associativity_of_lub) ).

cnf(lub_absorbtion,axiom,
    least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',lub_absorbtion) ).

cnf(lat4_3,axiom,
    inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',lat4_3) ).

cnf(lat4_1,axiom,
    inverse(identity) = identity,
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',lat4_1) ).

cnf(prove_lat4,negated_conjecture,
    a != multiply(positive_part(a),negative_part(a)),
    file('/export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p',prove_lat4) ).

cnf(c_0_17,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_18,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_19,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_20,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

cnf(c_0_21,axiom,
    inverse(inverse(X1)) = X1,
    lat4_2 ).

cnf(c_0_22,axiom,
    negative_part(X1) = greatest_lower_bound(X1,identity),
    lat4_5 ).

cnf(c_0_23,axiom,
    greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
    symmetry_of_glb ).

cnf(c_0_24,axiom,
    greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
    associativity_of_glb ).

cnf(c_0_25,axiom,
    multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
    monotony_glb2 ).

cnf(c_0_26,axiom,
    multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
    monotony_lub1 ).

cnf(c_0_27,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_18]),c_0_21]) ).

cnf(c_0_28,axiom,
    positive_part(X1) = least_upper_bound(X1,identity),
    lat4_4 ).

cnf(c_0_29,axiom,
    least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
    symmetry_of_lub ).

cnf(c_0_30,axiom,
    greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
    glb_absorbtion ).

cnf(c_0_31,plain,
    greatest_lower_bound(identity,X1) = negative_part(X1),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_32,axiom,
    least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
    associativity_of_lub ).

cnf(c_0_33,axiom,
    least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
    lub_absorbtion ).

cnf(c_0_34,plain,
    negative_part(greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,negative_part(X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_22]) ).

cnf(c_0_35,plain,
    greatest_lower_bound(X1,multiply(X2,X1)) = multiply(negative_part(X2),X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_22]),c_0_23]) ).

cnf(c_0_36,plain,
    least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,positive_part(X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]) ).

cnf(c_0_37,plain,
    negative_part(least_upper_bound(identity,X1)) = identity,
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_38,plain,
    positive_part(least_upper_bound(X1,X2)) = least_upper_bound(X1,positive_part(X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_28]) ).

cnf(c_0_39,plain,
    least_upper_bound(identity,negative_part(X1)) = identity,
    inference(spm,[status(thm)],[c_0_33,c_0_31]) ).

cnf(c_0_40,plain,
    least_upper_bound(identity,X1) = positive_part(X1),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_41,axiom,
    inverse(multiply(X1,X2)) = multiply(inverse(X2),inverse(X1)),
    lat4_3 ).

cnf(c_0_42,plain,
    greatest_lower_bound(X1,negative_part(multiply(X2,X1))) = negative_part(multiply(negative_part(X2),X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_43,plain,
    multiply(inverse(X1),positive_part(X1)) = positive_part(inverse(X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_18]),c_0_28]) ).

cnf(c_0_44,plain,
    negative_part(positive_part(X1)) = identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_29]),c_0_28]) ).

cnf(c_0_45,plain,
    least_upper_bound(X1,positive_part(multiply(X1,X2))) = positive_part(multiply(X1,positive_part(X2))),
    inference(spm,[status(thm)],[c_0_38,c_0_36]) ).

cnf(c_0_46,plain,
    multiply(negative_part(inverse(X1)),X1) = negative_part(X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_18]),c_0_22]) ).

cnf(c_0_47,plain,
    positive_part(negative_part(X1)) = identity,
    inference(rw,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_48,plain,
    inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
    inference(spm,[status(thm)],[c_0_41,c_0_21]) ).

cnf(c_0_49,plain,
    least_upper_bound(X1,negative_part(X1)) = X1,
    inference(spm,[status(thm)],[c_0_33,c_0_22]) ).

cnf(c_0_50,plain,
    negative_part(multiply(negative_part(inverse(X1)),positive_part(X1))) = identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_22]),c_0_44]) ).

cnf(c_0_51,plain,
    positive_part(multiply(negative_part(inverse(X1)),positive_part(X1))) = identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_28]),c_0_47]) ).

cnf(c_0_52,plain,
    multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_41]),c_0_21]) ).

cnf(c_0_53,plain,
    multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
    inference(spm,[status(thm)],[c_0_48,c_0_20]) ).

cnf(c_0_54,plain,
    multiply(negative_part(inverse(X1)),positive_part(X1)) = identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_28]),c_0_51]) ).

cnf(c_0_55,axiom,
    inverse(identity) = identity,
    lat4_1 ).

cnf(c_0_56,plain,
    multiply(positive_part(X1),inverse(positive_part(inverse(X1)))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_43]),c_0_21]) ).

cnf(c_0_57,plain,
    inverse(positive_part(X1)) = negative_part(inverse(X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_19]) ).

cnf(c_0_58,negated_conjecture,
    a != multiply(positive_part(a),negative_part(a)),
    prove_lat4 ).

cnf(c_0_59,plain,
    multiply(positive_part(X1),negative_part(X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_21]) ).

cnf(c_0_60,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : GRP167-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14  % Command    : run_E %s %d THM
% 0.15/0.35  % Computer : n006.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 2400
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Oct  3 02:07:10 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.22/0.49  Running first-order theorem proving
% 0.22/0.49  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.IvlYGM2jzq/E---3.1_22607.p
% 0.22/0.59  # Version: 3.1pre001
% 0.22/0.59  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.59  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.22/0.59  # Starting sh5l with 300s (1) cores
% 0.22/0.59  # new_bool_1 with pid 22727 completed with status 0
% 0.22/0.59  # Result found by new_bool_1
% 0.22/0.59  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.59  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.22/0.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.59  # Search class: FUUPM-FFSF21-SFFFFFNN
% 0.22/0.59  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.59  # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.22/0.59  # U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 22732 completed with status 0
% 0.22/0.59  # Result found by U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.59  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.59  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.59  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.59  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.59  # Starting new_bool_1 with 300s (1) cores
% 0.22/0.59  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.59  # Search class: FUUPM-FFSF21-SFFFFFNN
% 0.22/0.59  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.59  # Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 0.22/0.59  # Preprocessing time       : 0.001 s
% 0.22/0.59  # Presaturation interreduction done
% 0.22/0.59  
% 0.22/0.59  # Proof found!
% 0.22/0.59  # SZS status Unsatisfiable
% 0.22/0.59  # SZS output start CNFRefutation
% See solution above
% 0.22/0.59  # Parsed axioms                        : 23
% 0.22/0.59  # Removed by relevancy pruning/SinE    : 0
% 0.22/0.59  # Initial clauses                      : 23
% 0.22/0.59  # Removed in clause preprocessing      : 0
% 0.22/0.59  # Initial clauses in saturation        : 23
% 0.22/0.59  # Processed clauses                    : 582
% 0.22/0.59  # ...of these trivial                  : 232
% 0.22/0.59  # ...subsumed                          : 97
% 0.22/0.59  # ...remaining for further processing  : 253
% 0.22/0.59  # Other redundant clauses eliminated   : 0
% 0.22/0.59  # Clauses deleted for lack of memory   : 0
% 0.22/0.59  # Backward-subsumed                    : 0
% 0.22/0.59  # Backward-rewritten                   : 48
% 0.22/0.59  # Generated clauses                    : 11581
% 0.22/0.59  # ...of the previous two non-redundant : 4805
% 0.22/0.59  # ...aggressively subsumed             : 0
% 0.22/0.59  # Contextual simplify-reflections      : 0
% 0.22/0.59  # Paramodulations                      : 11581
% 0.22/0.59  # Factorizations                       : 0
% 0.22/0.59  # NegExts                              : 0
% 0.22/0.59  # Equation resolutions                 : 0
% 0.22/0.59  # Total rewrite steps                  : 22060
% 0.22/0.59  # Propositional unsat checks           : 0
% 0.22/0.59  #    Propositional check models        : 0
% 0.22/0.59  #    Propositional check unsatisfiable : 0
% 0.22/0.59  #    Propositional clauses             : 0
% 0.22/0.59  #    Propositional clauses after purity: 0
% 0.22/0.59  #    Propositional unsat core size     : 0
% 0.22/0.59  #    Propositional preprocessing time  : 0.000
% 0.22/0.59  #    Propositional encoding time       : 0.000
% 0.22/0.59  #    Propositional solver time         : 0.000
% 0.22/0.59  #    Success case prop preproc time    : 0.000
% 0.22/0.59  #    Success case prop encoding time   : 0.000
% 0.22/0.59  #    Success case prop solver time     : 0.000
% 0.22/0.59  # Current number of processed clauses  : 182
% 0.22/0.59  #    Positive orientable unit clauses  : 178
% 0.22/0.59  #    Positive unorientable unit clauses: 4
% 0.22/0.59  #    Negative unit clauses             : 0
% 0.22/0.59  #    Non-unit-clauses                  : 0
% 0.22/0.59  # Current number of unprocessed clauses: 4229
% 0.22/0.59  # ...number of literals in the above   : 4229
% 0.22/0.59  # Current number of archived formulas  : 0
% 0.22/0.59  # Current number of archived clauses   : 71
% 0.22/0.59  # Clause-clause subsumption calls (NU) : 0
% 0.22/0.59  # Rec. Clause-clause subsumption calls : 0
% 0.22/0.59  # Non-unit clause-clause subsumptions  : 0
% 0.22/0.59  # Unit Clause-clause subsumption calls : 11
% 0.22/0.59  # Rewrite failures with RHS unbound    : 0
% 0.22/0.59  # BW rewrite match attempts            : 245
% 0.22/0.59  # BW rewrite match successes           : 128
% 0.22/0.59  # Condensation attempts                : 0
% 0.22/0.59  # Condensation successes               : 0
% 0.22/0.59  # Termbank termtop insertions          : 95402
% 0.22/0.59  
% 0.22/0.59  # -------------------------------------------------
% 0.22/0.59  # User time                : 0.074 s
% 0.22/0.59  # System time              : 0.010 s
% 0.22/0.59  # Total time               : 0.085 s
% 0.22/0.59  # Maximum resident set size: 1624 pages
% 0.22/0.59  
% 0.22/0.59  # -------------------------------------------------
% 0.22/0.59  # User time                : 0.077 s
% 0.22/0.59  # System time              : 0.012 s
% 0.22/0.59  # Total time               : 0.088 s
% 0.22/0.59  # Maximum resident set size: 1676 pages
% 0.22/0.59  % E---3.1 exiting
% 0.22/0.59  % E---3.1 exiting
%------------------------------------------------------------------------------