%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:06:53 PM UTC 2026
% Result : Unsatisfiable 0.32s 0.83s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 4 RR)
% Number of literals : 30 ( 29 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 80 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) = multiply(X1,X2,multiply(X3,X4,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(ternary_multiply_1,axiom,
multiply(X1,X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_1) ).
cnf(ternary_multiply_2,axiom,
multiply(X1,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ternary_multiply_2) ).
cnf(extra_lemma,axiom,
multiply(X1,X2,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extra_lemma) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(prove_equation,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_6,axiom,
multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) = multiply(X1,X2,multiply(X3,X4,X5)),
associativity ).
cnf(c_0_7,axiom,
multiply(X1,X2,X2) = X2,
ternary_multiply_1 ).
cnf(c_0_8,axiom,
multiply(X1,X1,X2) = X1,
ternary_multiply_2 ).
cnf(c_0_9,plain,
multiply(multiply(X1,X2,X3),X4,X2) = multiply(X1,X2,multiply(X3,X4,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,axiom,
multiply(X1,X2,X1) = X1,
extra_lemma ).
cnf(c_0_11,plain,
multiply(X1,X2,multiply(X3,multiply(X1,X2,X3),X4)) = multiply(X1,X2,X3),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_12,plain,
multiply(X1,X2,multiply(X1,X3,X2)) = multiply(X1,X3,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(X1,X2,multiply(X3,X1,X4)) = multiply(X3,X1,multiply(X1,X2,X4)),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_14,plain,
multiply(X1,X2,multiply(X3,X4,multiply(X1,X2,X3))) = multiply(X1,X2,X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
multiply(X1,X2,multiply(X3,X1,X2)) = multiply(X3,X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_16,plain,
multiply(multiply(X1,X2,X3),X4,X1) = multiply(X1,X2,multiply(X3,X4,X1)),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_17,plain,
multiply(X1,multiply(X2,X3,X1),X2) = multiply(X2,X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_11]),c_0_7]) ).
cnf(c_0_18,plain,
multiply(X1,X2,multiply(X3,X4,multiply(X1,X2,X4))) = multiply(X1,X2,X4),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_19,plain,
multiply(X1,multiply(X2,X3,X1),multiply(X2,X4,X1)) = multiply(multiply(X2,X3,X1),X4,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
multiply(inverse(X1),X1,X2) = X2,
left_inverse ).
cnf(c_0_21,plain,
multiply(X1,multiply(X2,X3,X1),X3) = multiply(X2,X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_11]),c_0_7]) ).
cnf(c_0_22,plain,
multiply(multiply(inverse(X1),X2,X3),X1,X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_10]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(X2,X1,X3),X3) = multiply(X2,X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
multiply(a,inverse(a),b) != b,
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_25,plain,
multiply(multiply(X1,inverse(X2),X3),X2,X3) = X3,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
multiply(multiply(X1,X2,X3),X1,X3) = multiply(X1,X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_8]),c_0_17]) ).
cnf(c_0_27,negated_conjecture,
multiply(a,inverse(a),b) != b,
c_0_24 ).
cnf(c_0_28,plain,
multiply(X1,inverse(X1),X2) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO002-2 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.09 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 % Computer : n014.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Mon Sep 21 13:45:49 UTC 2026
% 0.22/0.50 % CPUTime :
% 0.22/0.50 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.59 Running first-order theorem proving
% 0.26/0.59 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/benchmark/theBenchmark.p
% 0.32/0.83 % Version: 3.5.1
% 0.32/0.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.32/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.32/0.83 % Starting new_bool_3 with 300s (1) cores
% 0.32/0.83 % Starting new_bool_1 with 300s (1) cores
% 0.32/0.83 % Starting sh5l with 300s (1) cores
% 0.32/0.83 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 22641 completed with status 0
% 0.32/0.83 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.32/0.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.32/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.32/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.83 % No SInE strategy applied
% 0.32/0.83 % Search class: FUUPM-FFSF32-SFFFFFNN
% 0.32/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.83 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.32/0.83 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.32/0.83 % Starting new_bool_3 with 136s (1) cores
% 0.32/0.83 % Starting new_bool_1 with 136s (1) cores
% 0.32/0.83 % new_bool_1 with pid 22650 completed with status 0
% 0.32/0.83 % Result found by new_bool_1
% 0.32/0.83 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.32/0.83 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.32/0.83 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.32/0.83 % No SInE strategy applied
% 0.32/0.83 % Search class: FUUPM-FFSF32-SFFFFFNN
% 0.32/0.83 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.32/0.83 % Starting SubtermCWHack with 136s (1) cores
% 0.32/0.83 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.32/0.83 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.32/0.83 % Starting new_bool_3 with 136s (1) cores
% 0.32/0.83 % Starting new_bool_1 with 136s (1) cores
% 0.32/0.83 % Preprocessing time : 0.002 s
% 0.32/0.83 % Presaturation interreduction done
% 0.32/0.83
% 0.32/0.83 % Proof found!
% 0.32/0.83 % SZS status Unsatisfiable
% 0.32/0.83 % SZS output start CNFRefutation
% See solution above
% 0.32/0.83 % Parsed axioms : 6
% 0.32/0.83 % Removed by relevancy pruning/SinE : 0
% 0.32/0.83 % Initial clauses : 6
% 0.32/0.83 % Removed in clause preprocessing : 0
% 0.32/0.83 % Initial clauses in saturation : 6
% 0.32/0.83 % Processed clauses : 128
% 0.32/0.83 % ...of these trivial : 48
% 0.32/0.83 % ...subsumed : 6
% 0.32/0.83 % ...remaining for further processing : 74
% 0.32/0.83 % Other redundant clauses eliminated : 0
% 0.32/0.83 % Clauses deleted for lack of memory : 0
% 0.32/0.83 % Backward-subsumed : 0
% 0.32/0.83 % Backward-rewritten : 5
% 0.32/0.83 % Generated clauses : 7431
% 0.32/0.83 % ...of the previous two non-redundant : 3907
% 0.32/0.83 % ...aggressively subsumed : 0
% 0.32/0.83 % Contextual simplify-reflections : 0
% 0.32/0.83 % Paramodulations : 7431
% 0.32/0.83 % Factorizations : 0
% 0.32/0.83 % NegExts : 0
% 0.32/0.83 % Equation resolutions : 0
% 0.32/0.83 % Disequality decompositions : 0
% 0.32/0.83 % Total rewrite steps : 7002
% 0.32/0.83 % ...of those cached : 4642
% 0.32/0.83 % Propositional unsat checks : 0
% 0.32/0.83 % Propositional check models : 0
% 0.32/0.83 % Propositional check unsatisfiable : 0
% 0.32/0.83 % Propositional clauses : 0
% 0.32/0.83 % Propositional clauses after purity: 0
% 0.32/0.83 % Propositional unsat core size : 0
% 0.32/0.83 % Propositional preprocessing time : 0.000
% 0.32/0.83 % Propositional encoding time : 0.000
% 0.32/0.83 % Propositional solver time : 0.000
% 0.32/0.83 % Success case prop preproc time : 0.000
% 0.32/0.83 % Success case prop encoding time : 0.000
% 0.32/0.83 % Success case prop solver time : 0.000
% 0.32/0.83 % Current number of processed clauses : 63
% 0.32/0.83 % Positive orientable unit clauses : 61
% 0.32/0.83 % Positive unorientable unit clauses: 2
% 0.32/0.83 % Negative unit clauses : 0
% 0.32/0.83 % Non-unit-clauses : 0
% 0.32/0.83 % Current number of unprocessed clauses: 3788
% 0.32/0.83 % ...number of literals in the above : 3788
% 0.32/0.83 % Current number of archived formulas : 0
% 0.32/0.83 % Current number of archived clauses : 11
% 0.32/0.83 % Clause-clause subsumption calls (NU) : 0
% 0.32/0.83 % Rec. Clause-clause subsumption calls : 0
% 0.32/0.83 % Non-unit clause-clause subsumptions : 0
% 0.32/0.83 % Unit Clause-clause subsumption calls : 20
% 0.32/0.83 % Rewrite failures with RHS unbound : 0
% 0.32/0.83 % BW rewrite match attempts : 1567
% 0.32/0.83 % BW rewrite match successes : 10
% 0.32/0.83 % Condensation attempts : 0
% 0.32/0.83 % Condensation successes : 0
% 0.32/0.83 % Termbank termtop insertions : 57408
% 0.32/0.83 % Search garbage collected termcells : 2
% 0.32/0.83
% 0.32/0.83 % -------------------------------------------------
% 0.32/0.83 % User time : 0.146 s
% 0.32/0.83 % System time : 0.009 s
% 0.32/0.83 % Total time : 0.154 s
% 0.32/0.83 % Maximum resident set size: 3628 pages
% 0.32/0.83
% 0.32/0.83 % -------------------------------------------------
% 0.32/0.83 % User time : 0.689 s
% 0.32/0.83 % System time : 0.038 s
% 0.32/0.83 % Total time : 0.727 s
% 0.32/0.83 % Maximum resident set size: 4608 pages
% 0.32/0.83 % E exiting
%------------------------------------------------------------------------------