%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 0.48s 0.49s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 4 RR)
% Number of literals : 29 ( 28 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 : 78 ( 10 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/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(ternary_multiply_1,axiom,
multiply(X1,X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_1) ).
cnf(ternary_multiply_2,axiom,
multiply(X1,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ternary_multiply_2) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(prove_equation,negated_conjecture,
multiply(a,inverse(a),b) != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
cnf(c_0_5,axiom,
multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5)) = multiply(X1,X2,multiply(X3,X4,X5)),
associativity ).
cnf(c_0_6,axiom,
multiply(X1,X2,X2) = X2,
ternary_multiply_1 ).
cnf(c_0_7,axiom,
multiply(X1,X1,X2) = X1,
ternary_multiply_2 ).
cnf(c_0_8,plain,
multiply(multiply(X1,X2,X3),X4,X2) = multiply(X1,X2,multiply(X3,X4,X2)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,plain,
multiply(X1,X2,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_7]),c_0_7]) ).
cnf(c_0_10,plain,
multiply(X1,X2,multiply(X3,multiply(X1,X2,X3),X4)) = multiply(X1,X2,X3),
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_11,plain,
multiply(X1,X2,multiply(X1,X3,X2)) = multiply(X1,X3,X2),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
multiply(X1,X2,multiply(X3,X1,X4)) = multiply(X3,X1,multiply(X1,X2,X4)),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_13,plain,
multiply(X1,X2,multiply(X3,X4,multiply(X1,X2,X3))) = multiply(X1,X2,X3),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
multiply(X1,X2,multiply(X3,X1,X2)) = multiply(X3,X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_6]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,X2,X3),X4,X1) = multiply(X1,X2,multiply(X3,X4,X1)),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_16,plain,
multiply(X1,multiply(X2,X3,X1),X2) = multiply(X2,X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_10]),c_0_6]) ).
cnf(c_0_17,plain,
multiply(X1,X2,multiply(X3,X4,multiply(X1,X2,X4))) = multiply(X1,X2,X4),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(X2,X3,X1),multiply(X2,X4,X1)) = multiply(multiply(X2,X3,X1),X4,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
multiply(inverse(X1),X1,X2) = X2,
left_inverse ).
cnf(c_0_20,plain,
multiply(X1,multiply(X2,X3,X1),X3) = multiply(X2,X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_6]) ).
cnf(c_0_21,plain,
multiply(multiply(inverse(X1),X2,X3),X1,X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_9]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(X2,X1,X3),X3) = multiply(X2,X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
multiply(a,inverse(a),b) != b,
inference(fof_simplification,[status(thm)],[prove_equation]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,inverse(X2),X3),X2,X3) = X3,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
multiply(multiply(X1,X2,X3),X1,X3) = multiply(X1,X2,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_7]),c_0_16]) ).
cnf(c_0_26,negated_conjecture,
multiply(a,inverse(a),b) != b,
c_0_23 ).
cnf(c_0_27,plain,
multiply(X1,inverse(X1),X2) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:41:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.48/0.49 % Version: 3.5.1
% 0.48/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.48/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.48/0.49 % Starting new_bool_3 with 300s (1) cores
% 0.48/0.49 % Starting new_bool_1 with 300s (1) cores
% 0.48/0.49 % Starting sh5l with 300s (1) cores
% 0.48/0.49 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2463094 completed with status 0
% 0.48/0.49 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.48/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.48/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.48/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.48/0.49 % No SInE strategy applied
% 0.48/0.49 % Search class: FUUPM-FFSF32-SFFFFFNN
% 0.48/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.48/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.48/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.48/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.48/0.49 % Starting new_bool_3 with 136s (1) cores
% 0.48/0.49 % Starting new_bool_1 with 136s (1) cores
% 0.48/0.49 % new_bool_3 with pid 2463103 completed with status 0
% 0.48/0.49 % Result found by new_bool_3
% 0.48/0.49 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.48/0.49 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.48/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.48/0.49 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.48/0.49 % No SInE strategy applied
% 0.48/0.49 % Search class: FUUPM-FFSF32-SFFFFFNN
% 0.48/0.49 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.48/0.49 % Starting SubtermCWHack with 136s (1) cores
% 0.48/0.49 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.48/0.49 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.48/0.49 % Starting new_bool_3 with 136s (1) cores
% 0.48/0.49 % Preprocessing time : 0.001 s
% 0.48/0.49 % Presaturation interreduction done
% 0.48/0.49
% 0.48/0.49 % Proof found!
% 0.48/0.49 % SZS status Unsatisfiable
% 0.48/0.49 % SZS output start CNFRefutation
% See solution above
% 0.48/0.49 % Parsed axioms : 5
% 0.48/0.49 % Removed by relevancy pruning/SinE : 0
% 0.48/0.49 % Initial clauses : 5
% 0.48/0.49 % Removed in clause preprocessing : 0
% 0.48/0.49 % Initial clauses in saturation : 5
% 0.48/0.49 % Processed clauses : 128
% 0.48/0.49 % ...of these trivial : 49
% 0.48/0.49 % ...subsumed : 6
% 0.48/0.49 % ...remaining for further processing : 73
% 0.48/0.49 % Other redundant clauses eliminated : 0
% 0.48/0.49 % Clauses deleted for lack of memory : 0
% 0.48/0.49 % Backward-subsumed : 0
% 0.48/0.49 % Backward-rewritten : 5
% 0.48/0.49 % Generated clauses : 7431
% 0.48/0.49 % ...of the previous two non-redundant : 3909
% 0.48/0.49 % ...aggressively subsumed : 0
% 0.48/0.49 % Contextual simplify-reflections : 0
% 0.48/0.49 % Paramodulations : 7431
% 0.48/0.49 % Factorizations : 0
% 0.48/0.49 % NegExts : 0
% 0.48/0.49 % Equation resolutions : 0
% 0.48/0.49 % Disequality decompositions : 0
% 0.48/0.49 % Total rewrite steps : 7001
% 0.48/0.49 % ...of those cached : 4641
% 0.48/0.49 % Propositional unsat checks : 0
% 0.48/0.49 % Propositional check models : 0
% 0.48/0.49 % Propositional check unsatisfiable : 0
% 0.48/0.49 % Propositional clauses : 0
% 0.48/0.49 % Propositional clauses after purity: 0
% 0.48/0.49 % Propositional unsat core size : 0
% 0.48/0.49 % Propositional preprocessing time : 0.000
% 0.48/0.49 % Propositional encoding time : 0.000
% 0.48/0.49 % Propositional solver time : 0.000
% 0.48/0.49 % Success case prop preproc time : 0.000
% 0.48/0.50 % Success case prop encoding time : 0.000
% 0.48/0.50 % Success case prop solver time : 0.000
% 0.48/0.50 % Current number of processed clauses : 63
% 0.48/0.50 % Positive orientable unit clauses : 61
% 0.48/0.50 % Positive unorientable unit clauses: 2
% 0.48/0.50 % Negative unit clauses : 0
% 0.48/0.50 % Non-unit-clauses : 0
% 0.48/0.50 % Current number of unprocessed clauses: 3788
% 0.48/0.50 % ...number of literals in the above : 3788
% 0.48/0.50 % Current number of archived formulas : 0
% 0.48/0.50 % Current number of archived clauses : 10
% 0.48/0.50 % Clause-clause subsumption calls (NU) : 0
% 0.48/0.50 % Rec. Clause-clause subsumption calls : 0
% 0.48/0.50 % Non-unit clause-clause subsumptions : 0
% 0.48/0.50 % Unit Clause-clause subsumption calls : 20
% 0.48/0.50 % Rewrite failures with RHS unbound : 0
% 0.48/0.50 % BW rewrite match attempts : 1569
% 0.48/0.50 % BW rewrite match successes : 10
% 0.48/0.50 % Condensation attempts : 0
% 0.48/0.50 % Condensation successes : 0
% 0.48/0.50 % Termbank termtop insertions : 57402
% 0.48/0.50 % Search garbage collected termcells : 2
% 0.48/0.50
% 0.48/0.50 % -------------------------------------------------
% 0.48/0.50 % User time : 0.046 s
% 0.48/0.50 % System time : 0.004 s
% 0.48/0.50 % Total time : 0.050 s
% 0.48/0.50 % Maximum resident set size: 3628 pages
% 0.48/0.50
% 0.48/0.50 % -------------------------------------------------
% 0.48/0.50 % User time : 0.243 s
% 0.48/0.50 % System time : 0.024 s
% 0.48/0.50 % Total time : 0.267 s
% 0.48/0.50 % Maximum resident set size: 4864 pages
% 0.48/0.50 % E exiting
%------------------------------------------------------------------------------