%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO009-2 : 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 : n013.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 12:06:56 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(additive_id2,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
cnf(distributivity1,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(prove_operation,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_operation) ).
cnf(c_0_10,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2 ).
cnf(c_0_11,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_12,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_13,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_14,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_15,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4 ).
cnf(c_0_16,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).
cnf(c_0_17,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_18,axiom,
add(additive_identity,X1) = X1,
additive_id2 ).
cnf(c_0_19,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_16]),c_0_12]),c_0_17]) ).
cnf(c_0_20,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_21,plain,
multiply(additive_identity,X1) = additive_identity,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
distributivity1 ).
cnf(c_0_23,plain,
multiply(X1,additive_identity) = additive_identity,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
multiply(a,add(a,b)) != a,
inference(fof_simplification,[status(thm)],[prove_operation]) ).
cnf(c_0_25,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_23]),c_0_18]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
multiply(a,add(a,b)) != a,
c_0_24 ).
cnf(c_0_27,plain,
multiply(X1,add(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
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 : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n013.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 13:47:07 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.46 % Version: 3.5.1
% 0.12/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.46 % Starting sh5l with 300s (1) cores
% 0.12/0.46 % sh5l with pid 915774 completed with status 0
% 0.12/0.46 % Result found by sh5l
% 0.12/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.46 % Starting sh5l with 300s (1) cores
% 0.12/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.46 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.12/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.46 % SubtermCWHack with pid 915777 completed with status 0
% 0.12/0.46 % Result found by SubtermCWHack
% 0.12/0.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.46 % Starting sh5l with 300s (1) cores
% 0.12/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.12/0.46 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.12/0.46 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.12/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.12/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.12/0.46 % Preprocessing time : 0.001 s
% 0.12/0.46
% 0.12/0.46 % Proof found!
% 0.12/0.46 % SZS status Unsatisfiable
% 0.12/0.46 % SZS output start CNFRefutation
% See solution above
% 0.12/0.46 % Parsed axioms : 15
% 0.12/0.46 % Removed by relevancy pruning/SinE : 0
% 0.12/0.46 % Initial clauses : 15
% 0.12/0.46 % Removed in clause preprocessing : 0
% 0.12/0.46 % Initial clauses in saturation : 15
% 0.12/0.46 % Processed clauses : 39
% 0.12/0.46 % ...of these trivial : 10
% 0.12/0.46 % ...subsumed : 0
% 0.12/0.46 % ...remaining for further processing : 29
% 0.12/0.46 % Other redundant clauses eliminated : 0
% 0.12/0.46 % Clauses deleted for lack of memory : 0
% 0.12/0.46 % Backward-subsumed : 0
% 0.12/0.46 % Backward-rewritten : 3
% 0.12/0.46 % Generated clauses : 205
% 0.12/0.46 % ...of the previous two non-redundant : 98
% 0.12/0.46 % ...aggressively subsumed : 0
% 0.12/0.46 % Contextual simplify-reflections : 0
% 0.12/0.46 % Paramodulations : 205
% 0.12/0.46 % Factorizations : 0
% 0.12/0.46 % NegExts : 0
% 0.12/0.46 % Equation resolutions : 0
% 0.12/0.46 % Disequality decompositions : 0
% 0.12/0.46 % Total rewrite steps : 178
% 0.12/0.46 % ...of those cached : 113
% 0.12/0.46 % Propositional unsat checks : 0
% 0.12/0.46 % Propositional check models : 0
% 0.12/0.46 % Propositional check unsatisfiable : 0
% 0.12/0.46 % Propositional clauses : 0
% 0.12/0.46 % Propositional clauses after purity: 0
% 0.12/0.46 % Propositional unsat core size : 0
% 0.12/0.46 % Propositional preprocessing time : 0.000
% 0.12/0.46 % Propositional encoding time : 0.000
% 0.12/0.46 % Propositional solver time : 0.000
% 0.12/0.46 % Success case prop preproc time : 0.000
% 0.12/0.46 % Success case prop encoding time : 0.000
% 0.12/0.46 % Success case prop solver time : 0.000
% 0.12/0.46 % Current number of processed clauses : 26
% 0.12/0.46 % Positive orientable unit clauses : 24
% 0.12/0.46 % Positive unorientable unit clauses: 2
% 0.12/0.46 % Negative unit clauses : 0
% 0.12/0.46 % Non-unit-clauses : 0
% 0.12/0.46 % Current number of unprocessed clauses: 74
% 0.12/0.46 % ...number of literals in the above : 74
% 0.12/0.46 % Current number of archived formulas : 0
% 0.12/0.46 % Current number of archived clauses : 3
% 0.12/0.46 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.46 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.46 % Non-unit clause-clause subsumptions : 0
% 0.12/0.46 % Unit Clause-clause subsumption calls : 0
% 0.12/0.46 % Rewrite failures with RHS unbound : 0
% 0.12/0.46 % BW rewrite match attempts : 61
% 0.12/0.46 % BW rewrite match successes : 17
% 0.12/0.46 % Condensation attempts : 0
% 0.12/0.46 % Condensation successes : 0
% 0.12/0.46 % Termbank termtop insertions : 1328
% 0.12/0.46 % Search garbage collected termcells : 2
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.005 s
% 0.12/0.46 % System time : 0.001 s
% 0.12/0.46 % Total time : 0.006 s
% 0.12/0.46 % Maximum resident set size: 3640 pages
% 0.12/0.46
% 0.12/0.46 % -------------------------------------------------
% 0.12/0.46 % User time : 0.008 s
% 0.12/0.46 % System time : 0.004 s
% 0.12/0.46 % Total time : 0.012 s
% 0.12/0.46 % Maximum resident set size: 4608 pages
% 0.12/0.46 % E exiting
%------------------------------------------------------------------------------