%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:22:46 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.61s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of clauses : 42 ( 17 unt; 6 nHn; 42 RR)
% Number of literals : 89 ( 0 equ; 47 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(existence_of_inverse_multiplication,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_3) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(associativity_multiplication_2,axiom,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_2) ).
cnf(product_2,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_2) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(not_product_4,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_4) ).
cnf(c_0_10,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_multiplication]) ).
cnf(c_0_11,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_3]) ).
cnf(c_0_12,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_13,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_10 ).
cnf(c_0_14,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_15,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_11 ).
cnf(c_0_16,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_1]) ).
cnf(c_0_17,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_12 ).
cnf(c_0_18,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_16 ).
cnf(c_0_20,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_inverse(a),X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_23,hypothesis,
( ~ product(X1,a,a)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_24,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_22 ).
cnf(c_0_25,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[associativity_multiplication_2]) ).
cnf(c_0_26,hypothesis,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_14])]) ).
cnf(c_0_27,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
product_2 ).
cnf(c_0_28,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_25 ).
cnf(c_0_29,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
product(a,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_31,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_multiplicative_inverse]) ).
cnf(c_0_32,hypothesis,
( ~ product(X3,multiplicative_identity,X1)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_33,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_34,negated_conjecture,
( ~ product(X1,a,multiplicative_identity)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_31 ).
cnf(c_0_36,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
inference(fof_simplification,[status(thm)],[not_product_4]) ).
cnf(c_0_37,hypothesis,
( ~ defined(X2)
| ~ product(X2,multiplicative_identity,X1)
| product(X1,multiplicative_identity,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,hypothesis,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_39,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_14]),c_0_15]) ).
cnf(c_0_40,negated_conjecture,
~ product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(a)),
c_0_36 ).
cnf(c_0_41,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD031-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.53 % Computer : n018.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Mon Sep 21 15:41:16 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.58 Running first-order theorem proving
% 0.14/0.58 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
% 0.14/0.61 % Version: 3.5.1
% 0.14/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.61 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.61 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.61 % Starting sh5l with 300s (1) cores
% 0.14/0.61 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2242595 completed with status 0
% 0.14/0.61 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.61 % No SInE strategy applied
% 0.14/0.61 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.14/0.61 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.14/0.61 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.61 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.61 % G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 2242608 completed with status 0
% 0.14/0.61 % Result found by G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.61 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.61 % No SInE strategy applied
% 0.14/0.61 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.14/0.61 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.61 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.61 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.14/0.61 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.61 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.14/0.61 % Preprocessing time : 0.002 s
% 0.14/0.61 % Presaturation interreduction done
% 0.14/0.61
% 0.14/0.61 % Proof found!
% 0.14/0.61 % SZS status Unsatisfiable
% 0.14/0.61 % SZS output start CNFRefutation
% See solution above
% 0.14/0.61 % Parsed axioms : 30
% 0.14/0.61 % Removed by relevancy pruning/SinE : 0
% 0.14/0.61 % Initial clauses : 30
% 0.14/0.61 % Removed in clause preprocessing : 0
% 0.14/0.61 % Initial clauses in saturation : 30
% 0.14/0.61 % Processed clauses : 131
% 0.14/0.61 % ...of these trivial : 1
% 0.14/0.61 % ...subsumed : 17
% 0.14/0.61 % ...remaining for further processing : 113
% 0.14/0.61 % Other redundant clauses eliminated : 0
% 0.14/0.61 % Clauses deleted for lack of memory : 0
% 0.14/0.61 % Backward-subsumed : 0
% 0.14/0.61 % Backward-rewritten : 0
% 0.14/0.61 % Generated clauses : 242
% 0.14/0.61 % ...of the previous two non-redundant : 209
% 0.14/0.61 % ...aggressively subsumed : 0
% 0.14/0.61 % Contextual simplify-reflections : 0
% 0.14/0.61 % Paramodulations : 242
% 0.14/0.61 % Factorizations : 0
% 0.14/0.61 % NegExts : 0
% 0.14/0.61 % Equation resolutions : 0
% 0.14/0.61 % Disequality decompositions : 0
% 0.14/0.61 % Total rewrite steps : 33
% 0.14/0.61 % ...of those cached : 23
% 0.14/0.61 % Propositional unsat checks : 0
% 0.14/0.61 % Propositional check models : 0
% 0.14/0.61 % Propositional check unsatisfiable : 0
% 0.14/0.61 % Propositional clauses : 0
% 0.14/0.61 % Propositional clauses after purity: 0
% 0.14/0.61 % Propositional unsat core size : 0
% 0.14/0.61 % Propositional preprocessing time : 0.000
% 0.14/0.61 % Propositional encoding time : 0.000
% 0.14/0.61 % Propositional solver time : 0.000
% 0.14/0.61 % Success case prop preproc time : 0.000
% 0.14/0.61 % Success case prop encoding time : 0.000
% 0.14/0.61 % Success case prop solver time : 0.000
% 0.14/0.61 % Current number of processed clauses : 83
% 0.14/0.61 % Positive orientable unit clauses : 14
% 0.14/0.61 % Positive unorientable unit clauses: 0
% 0.14/0.61 % Negative unit clauses : 3
% 0.14/0.61 % Non-unit-clauses : 66
% 0.14/0.61 % Current number of unprocessed clauses: 135
% 0.14/0.61 % ...number of literals in the above : 505
% 0.14/0.61 % Current number of archived formulas : 0
% 0.14/0.61 % Current number of archived clauses : 30
% 0.14/0.61 % Clause-clause subsumption calls (NU) : 351
% 0.14/0.61 % Rec. Clause-clause subsumption calls : 277
% 0.14/0.61 % Non-unit clause-clause subsumptions : 17
% 0.14/0.61 % Unit Clause-clause subsumption calls : 35
% 0.14/0.61 % Rewrite failures with RHS unbound : 0
% 0.14/0.61 % BW rewrite match attempts : 2
% 0.14/0.61 % BW rewrite match successes : 0
% 0.14/0.61 % Condensation attempts : 0
% 0.14/0.61 % Condensation successes : 0
% 0.14/0.61 % Termbank termtop insertions : 4454
% 0.14/0.61 % Search garbage collected termcells : 118
% 0.14/0.61
% 0.14/0.61 % -------------------------------------------------
% 0.14/0.61 % User time : 0.010 s
% 0.14/0.61 % System time : 0.005 s
% 0.14/0.61 % Total time : 0.015 s
% 0.14/0.61 % Maximum resident set size: 3660 pages
% 0.14/0.61
% 0.14/0.61 % -------------------------------------------------
% 0.14/0.61 % User time : 0.054 s
% 0.14/0.61 % System time : 0.019 s
% 0.14/0.61 % Total time : 0.073 s
% 0.14/0.61 % Maximum resident set size: 4608 pages
% 0.14/0.61 % E exiting
%------------------------------------------------------------------------------