TSTP Solution File: RNG026-7 by E-SAT---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1.00
% Problem  : RNG026-7 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n011.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 21 02:36:42 EDT 2024

% Result   : Unsatisfiable 0.23s 0.56s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of clauses     :   42 (  42 unt;   0 nHn;   9 RR)
%            Number of literals    :   42 (  41 equ;   8 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :   14 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-3 aty)
%            Number of variables   :   72 (   2 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_teichmuller_identity,negated_conjecture,
    add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_teichmuller_identity) ).

cnf(associativity_for_addition,axiom,
    add(X1,add(X2,X3)) = add(add(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associativity_for_addition) ).

cnf(right_additive_inverse,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_inverse) ).

cnf(left_additive_identity,axiom,
    add(additive_identity,X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',left_additive_identity) ).

cnf(associator,axiom,
    associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',associator) ).

cnf(additive_inverse_additive_inverse,axiom,
    additive_inverse(additive_inverse(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',additive_inverse_additive_inverse) ).

cnf(commutativity_for_addition,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',commutativity_for_addition) ).

cnf(inverse_product2,axiom,
    multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product2) ).

cnf(distribute1,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute1) ).

cnf(distribute2,axiom,
    multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',distribute2) ).

cnf(right_multiplicative_zero,axiom,
    multiply(X1,additive_identity) = additive_identity,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_multiplicative_zero) ).

cnf(right_additive_identity,axiom,
    add(X1,additive_identity) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/RNG003-0.ax',right_additive_identity) ).

cnf(c_0_12,negated_conjecture,
    add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
    inference(fof_simplification,[status(thm)],[prove_teichmuller_identity]) ).

cnf(c_0_13,axiom,
    add(X1,add(X2,X3)) = add(add(X1,X2),X3),
    associativity_for_addition ).

cnf(c_0_14,axiom,
    add(X1,additive_inverse(X1)) = additive_identity,
    right_additive_inverse ).

cnf(c_0_15,axiom,
    add(additive_identity,X1) = X1,
    left_additive_identity ).

cnf(c_0_16,negated_conjecture,
    add(add(associator(multiply(a,b),c,d),associator(a,b,multiply(c,d))),additive_inverse(add(add(associator(a,multiply(b,c),d),multiply(a,associator(b,c,d))),multiply(associator(a,b,c),d)))) != additive_identity,
    c_0_12 ).

cnf(c_0_17,axiom,
    associator(X1,X2,X3) = add(multiply(multiply(X1,X2),X3),additive_inverse(multiply(X1,multiply(X2,X3)))),
    associator ).

cnf(c_0_18,plain,
    add(X1,add(additive_inverse(X1),X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).

cnf(c_0_19,axiom,
    additive_inverse(additive_inverse(X1)) = X1,
    additive_inverse_additive_inverse ).

cnf(c_0_20,negated_conjecture,
    add(add(add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d)))),add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d)))))),additive_inverse(add(add(add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))),multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d)))))),multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d)))) != additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).

cnf(c_0_21,axiom,
    add(X1,X2) = add(X2,X1),
    commutativity_for_addition ).

cnf(c_0_22,plain,
    add(additive_inverse(X1),add(X1,X2)) = X2,
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,negated_conjecture,
    add(add(add(multiply(multiply(a,b),multiply(c,d)),additive_inverse(multiply(a,multiply(b,multiply(c,d))))),add(multiply(multiply(multiply(a,b),c),d),additive_inverse(multiply(multiply(a,b),multiply(c,d))))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),additive_inverse(multiply(a,multiply(b,c)))),d),add(multiply(a,add(multiply(multiply(b,c),d),additive_inverse(multiply(b,multiply(c,d))))),add(multiply(multiply(a,multiply(b,c)),d),additive_inverse(multiply(a,multiply(multiply(b,c),d)))))))) != additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_21]),c_0_21]) ).

cnf(c_0_24,axiom,
    multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
    inverse_product2 ).

cnf(c_0_25,plain,
    add(additive_inverse(X1),add(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_22,c_0_21]) ).

cnf(c_0_26,plain,
    add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
    inference(spm,[status(thm)],[c_0_21,c_0_13]) ).

cnf(c_0_27,negated_conjecture,
    add(multiply(multiply(a,b),multiply(c,d)),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),add(multiply(a,add(multiply(multiply(b,c),d),multiply(b,multiply(c,additive_inverse(d))))),add(multiply(multiply(a,multiply(b,c)),d),multiply(a,multiply(multiply(b,c),additive_inverse(d))))))))))) != additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_13]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_13]),c_0_13]) ).

cnf(c_0_28,axiom,
    multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
    distribute1 ).

cnf(c_0_29,axiom,
    multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
    distribute2 ).

cnf(c_0_30,plain,
    add(X1,add(X2,additive_inverse(X1))) = X2,
    inference(spm,[status(thm)],[c_0_18,c_0_21]) ).

cnf(c_0_31,plain,
    add(X1,additive_inverse(add(X2,X1))) = additive_inverse(X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_21]) ).

cnf(c_0_32,plain,
    add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
    inference(spm,[status(thm)],[c_0_26,c_0_21]) ).

cnf(c_0_33,negated_conjecture,
    add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(a,multiply(b,multiply(c,additive_inverse(d)))),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),additive_inverse(add(multiply(multiply(a,multiply(b,c)),d),add(multiply(add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c)))),d),multiply(a,add(multiply(multiply(b,c),d),add(multiply(b,multiply(c,additive_inverse(d))),multiply(multiply(b,c),additive_inverse(d)))))))))))) != additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_26]),c_0_26]),c_0_21]),c_0_26]),c_0_28]),c_0_13]),c_0_26]),c_0_21]),c_0_13]),c_0_21]),c_0_26]),c_0_21]) ).

cnf(c_0_34,plain,
    add(multiply(X1,X2),add(multiply(X3,X2),X4)) = add(multiply(add(X1,X3),X2),X4),
    inference(spm,[status(thm)],[c_0_13,c_0_29]) ).

cnf(c_0_35,plain,
    add(multiply(X1,X2),add(X3,multiply(X1,additive_inverse(X2)))) = X3,
    inference(spm,[status(thm)],[c_0_30,c_0_24]) ).

cnf(c_0_36,plain,
    add(X1,add(X2,additive_inverse(add(X3,X1)))) = add(X2,additive_inverse(X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_31]),c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    add(multiply(multiply(a,b),multiply(c,d)),add(multiply(multiply(multiply(a,b),c),d),add(multiply(multiply(a,b),multiply(c,additive_inverse(d))),multiply(add(multiply(a,multiply(b,c)),add(multiply(multiply(a,b),c),multiply(a,multiply(b,additive_inverse(c))))),additive_inverse(d))))) != additive_identity,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_36]),c_0_24]) ).

cnf(c_0_38,plain,
    add(multiply(X1,X2),add(X3,multiply(X1,X4))) = add(X3,multiply(X1,add(X4,X2))),
    inference(spm,[status(thm)],[c_0_26,c_0_28]) ).

cnf(c_0_39,axiom,
    multiply(X1,additive_identity) = additive_identity,
    right_multiplicative_zero ).

cnf(c_0_40,axiom,
    add(X1,additive_identity) = X1,
    right_additive_identity ).

cnf(c_0_41,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_28]),c_0_21]),c_0_14]),c_0_39]),c_0_39]),c_0_40]),c_0_38]),c_0_21]),c_0_14]),c_0_39]),c_0_40]),c_0_28]),c_0_28]),c_0_14]),c_0_39]),c_0_39])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem    : RNG026-7 : TPTP v8.2.0. Released v1.0.0.
% 0.13/0.16  % Command    : run_E %s %d THM
% 0.16/0.38  % Computer : n011.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Sat May 18 12:02:38 EDT 2024
% 0.16/0.38  % CPUTime    : 
% 0.23/0.50  Running first-order model finding
% 0.23/0.50  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.56  # Version: 3.1.0
% 0.23/0.56  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56  # Starting new_bool_3 with 300s (1) cores
% 0.23/0.56  # Starting new_bool_1 with 300s (1) cores
% 0.23/0.56  # Starting sh5l with 300s (1) cores
% 0.23/0.56  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 10722 completed with status 0
% 0.23/0.56  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.56  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56  # No SInE strategy applied
% 0.23/0.56  # Search class: FUUPM-FFMF21-DFFFFFNN
% 0.23/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.56  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 811s (1) cores
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.56  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 0.23/0.56  # Starting new_bool_3 with 136s (1) cores
% 0.23/0.56  # Starting new_bool_1 with 136s (1) cores
% 0.23/0.56  # H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 10727 completed with status 0
% 0.23/0.56  # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 0.23/0.56  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56  # No SInE strategy applied
% 0.23/0.56  # Search class: FUUPM-FFMF21-DFFFFFNN
% 0.23/0.56  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.56  # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 811s (1) cores
% 0.23/0.56  # Preprocessing time       : 0.001 s
% 0.23/0.56  # Presaturation interreduction done
% 0.23/0.56  
% 0.23/0.56  # Proof found!
% 0.23/0.56  # SZS status Unsatisfiable
% 0.23/0.56  # SZS output start CNFRefutation
% See solution above
% 0.23/0.56  # Parsed axioms                        : 23
% 0.23/0.56  # Removed by relevancy pruning/SinE    : 0
% 0.23/0.56  # Initial clauses                      : 23
% 0.23/0.56  # Removed in clause preprocessing      : 2
% 0.23/0.56  # Initial clauses in saturation        : 21
% 0.23/0.56  # Processed clauses                    : 573
% 0.23/0.56  # ...of these trivial                  : 212
% 0.23/0.56  # ...subsumed                          : 254
% 0.23/0.56  # ...remaining for further processing  : 106
% 0.23/0.56  # Other redundant clauses eliminated   : 0
% 0.23/0.56  # Clauses deleted for lack of memory   : 0
% 0.23/0.56  # Backward-subsumed                    : 0
% 0.23/0.56  # Backward-rewritten                   : 11
% 0.23/0.56  # Generated clauses                    : 4268
% 0.23/0.56  # ...of the previous two non-redundant : 3102
% 0.23/0.56  # ...aggressively subsumed             : 0
% 0.23/0.56  # Contextual simplify-reflections      : 0
% 0.23/0.56  # Paramodulations                      : 4268
% 0.23/0.56  # Factorizations                       : 0
% 0.23/0.56  # NegExts                              : 0
% 0.23/0.56  # Equation resolutions                 : 0
% 0.23/0.56  # Disequality decompositions           : 0
% 0.23/0.56  # Total rewrite steps                  : 8652
% 0.23/0.56  # ...of those cached                   : 6316
% 0.23/0.56  # Propositional unsat checks           : 0
% 0.23/0.56  #    Propositional check models        : 0
% 0.23/0.56  #    Propositional check unsatisfiable : 0
% 0.23/0.56  #    Propositional clauses             : 0
% 0.23/0.56  #    Propositional clauses after purity: 0
% 0.23/0.56  #    Propositional unsat core size     : 0
% 0.23/0.56  #    Propositional preprocessing time  : 0.000
% 0.23/0.56  #    Propositional encoding time       : 0.000
% 0.23/0.56  #    Propositional solver time         : 0.000
% 0.23/0.56  #    Success case prop preproc time    : 0.000
% 0.23/0.56  #    Success case prop encoding time   : 0.000
% 0.23/0.56  #    Success case prop solver time     : 0.000
% 0.23/0.56  # Current number of processed clauses  : 78
% 0.23/0.56  #    Positive orientable unit clauses  : 69
% 0.23/0.56  #    Positive unorientable unit clauses: 6
% 0.23/0.56  #    Negative unit clauses             : 3
% 0.23/0.56  #    Non-unit-clauses                  : 0
% 0.23/0.56  # Current number of unprocessed clauses: 2495
% 0.23/0.56  # ...number of literals in the above   : 2495
% 0.23/0.56  # Current number of archived formulas  : 0
% 0.23/0.56  # Current number of archived clauses   : 30
% 0.23/0.56  # Clause-clause subsumption calls (NU) : 0
% 0.23/0.56  # Rec. Clause-clause subsumption calls : 0
% 0.23/0.56  # Non-unit clause-clause subsumptions  : 0
% 0.23/0.56  # Unit Clause-clause subsumption calls : 40
% 0.23/0.56  # Rewrite failures with RHS unbound    : 0
% 0.23/0.56  # BW rewrite match attempts            : 231
% 0.23/0.56  # BW rewrite match successes           : 118
% 0.23/0.56  # Condensation attempts                : 0
% 0.23/0.56  # Condensation successes               : 0
% 0.23/0.56  # Termbank termtop insertions          : 54298
% 0.23/0.56  # Search garbage collected termcells   : 2
% 0.23/0.56  
% 0.23/0.56  # -------------------------------------------------
% 0.23/0.56  # User time                : 0.038 s
% 0.23/0.56  # System time              : 0.007 s
% 0.23/0.56  # Total time               : 0.045 s
% 0.23/0.56  # Maximum resident set size: 1664 pages
% 0.23/0.56  
% 0.23/0.56  # -------------------------------------------------
% 0.23/0.56  # User time                : 0.212 s
% 0.23/0.56  # System time              : 0.014 s
% 0.23/0.56  # Total time               : 0.226 s
% 0.23/0.56  # Maximum resident set size: 1708 pages
% 0.23/0.56  % E---3.1 exiting
%------------------------------------------------------------------------------