%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 4 RR)
% Number of literals : 27 ( 26 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 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 : 39 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
cnf(distributivity2,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
cnf(prove_operation,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_operation) ).
cnf(c_0_9,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity1 ).
cnf(c_0_10,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_11,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_12,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_13,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity2 ).
cnf(c_0_14,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_15,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_16,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_17,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_10]) ).
cnf(c_0_20,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_21,negated_conjecture,
multiply(a,add(a,b)) != a,
inference(fof_simplification,[status(thm)],[prove_operation]) ).
cnf(c_0_22,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_10]),c_0_11]) ).
cnf(c_0_23,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_13,c_0_11]),c_0_19]),c_0_11]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
multiply(a,add(a,b)) != a,
c_0_21 ).
cnf(c_0_25,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_22]),c_0_23]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.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 13:52:59 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % sh5l with pid 3287752 completed with status 0
% 0.10/0.43 % Result found by sh5l
% 0.10/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.43 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % SubtermCWHack with pid 3287754 completed with status 0
% 0.10/0.43 % Result found by SubtermCWHack
% 0.10/0.43 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.10/0.43 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.10/0.43 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 s
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Unsatisfiable
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.43 % Parsed axioms : 9
% 0.10/0.43 % Removed by relevancy pruning/SinE : 0
% 0.10/0.43 % Initial clauses : 9
% 0.10/0.43 % Removed in clause preprocessing : 0
% 0.10/0.43 % Initial clauses in saturation : 9
% 0.10/0.43 % Processed clauses : 36
% 0.10/0.43 % ...of these trivial : 9
% 0.10/0.43 % ...subsumed : 1
% 0.10/0.43 % ...remaining for further processing : 26
% 0.10/0.43 % Other redundant clauses eliminated : 0
% 0.10/0.43 % Clauses deleted for lack of memory : 0
% 0.10/0.43 % Backward-subsumed : 0
% 0.10/0.43 % Backward-rewritten : 1
% 0.10/0.43 % Generated clauses : 156
% 0.10/0.43 % ...of the previous two non-redundant : 68
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 0
% 0.10/0.43 % Paramodulations : 156
% 0.10/0.43 % Factorizations : 0
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 0
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 141
% 0.10/0.43 % ...of those cached : 91
% 0.10/0.43 % Propositional unsat checks : 0
% 0.10/0.43 % Propositional check models : 0
% 0.10/0.43 % Propositional check unsatisfiable : 0
% 0.10/0.43 % Propositional clauses : 0
% 0.10/0.43 % Propositional clauses after purity: 0
% 0.10/0.43 % Propositional unsat core size : 0
% 0.10/0.43 % Propositional preprocessing time : 0.000
% 0.10/0.43 % Propositional encoding time : 0.000
% 0.10/0.43 % Propositional solver time : 0.000
% 0.10/0.43 % Success case prop preproc time : 0.000
% 0.10/0.43 % Success case prop encoding time : 0.000
% 0.10/0.43 % Success case prop solver time : 0.000
% 0.10/0.43 % Current number of processed clauses : 25
% 0.10/0.43 % Positive orientable unit clauses : 23
% 0.10/0.43 % Positive unorientable unit clauses: 2
% 0.10/0.43 % Negative unit clauses : 0
% 0.10/0.43 % Non-unit-clauses : 0
% 0.10/0.43 % Current number of unprocessed clauses: 41
% 0.10/0.43 % ...number of literals in the above : 41
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 1
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.10/0.43 % Non-unit clause-clause subsumptions : 0
% 0.10/0.43 % Unit Clause-clause subsumption calls : 0
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 46
% 0.10/0.43 % BW rewrite match successes : 9
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 991
% 0.10/0.43 % Search garbage collected termcells : 2
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.003 s
% 0.10/0.43 % System time : 0.002 s
% 0.10/0.43 % Total time : 0.005 s
% 0.10/0.43 % Maximum resident set size: 3636 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.005 s
% 0.10/0.43 % System time : 0.007 s
% 0.10/0.43 % Total time : 0.011 s
% 0.10/0.43 % Maximum resident set size: 4864 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------