%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:22:38 PM UTC 2026
% Result : Unsatisfiable 4.73s 1.31s
% Output : CNFRefutation 4.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 14 unt; 6 nHn; 35 RR)
% Number of literals : 74 ( 0 equ; 39 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 3 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/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_3,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_3) ).
cnf(associativity_multiplication_1,axiom,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(totality_of_multiplication,axiom,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',totality_of_multiplication) ).
cnf(not_product_4,negated_conjecture,
~ product(a,X1,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
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(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_13,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_14,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_15,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_10 ).
cnf(c_0_16,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_17,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_11 ).
cnf(c_0_18,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_12 ).
cnf(c_0_19,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_13 ).
cnf(c_0_20,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_14 ).
cnf(c_0_21,hypothesis,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_22,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_23,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,hypothesis,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
inference(fof_simplification,[status(thm)],[totality_of_multiplication]) ).
cnf(c_0_26,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_22 ).
cnf(c_0_27,negated_conjecture,
~ product(a,X1,b),
inference(fof_simplification,[status(thm)],[not_product_4]) ).
cnf(c_0_28,hypothesis,
( ~ defined(X2)
| ~ product(multiplicative_inverse(a),X2,X1)
| product(a,X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ defined(X2)
| ~ defined(X1)
| product(X1,X2,multiply(X1,X2)) ),
c_0_25 ).
cnf(c_0_30,hypothesis,
defined(multiplicative_inverse(a)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_16]),c_0_17]) ).
cnf(c_0_31,negated_conjecture,
~ product(a,X1,b),
c_0_27 ).
cnf(c_0_32,hypothesis,
( ~ defined(X1)
| product(a,multiply(multiplicative_inverse(a),X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : FLD009-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.47 % Computer : n026.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 15:39:37 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.55 Running first-order theorem proving
% 0.21/0.55 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
% 4.73/1.31 % Version: 3.5.1
% 4.73/1.31 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.73/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.73/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.73/1.31 % Starting new_bool_3 with 300s (1) cores
% 4.73/1.31 % Starting new_bool_1 with 300s (1) cores
% 4.73/1.31 % Starting sh5l with 300s (1) cores
% 4.73/1.31 % new_bool_1 with pid 2631752 completed with status 9
% 4.73/1.31 % new_bool_3 with pid 2631751 completed with status 9
% 4.73/1.31 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2631750 completed with status 0
% 4.73/1.31 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 4.73/1.31 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.73/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.73/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.73/1.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.73/1.31 % No SInE strategy applied
% 4.73/1.31 % Search class: FGUNF-FFMS21-SFFFFFNN
% 4.73/1.31 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 4.73/1.31 % Starting SubtermCWHack with 136s (1) cores
% 4.73/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.73/1.31 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 4.73/1.31 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.73/1.31 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.73/1.31 % U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 2631759 completed with status 0
% 4.73/1.31 % Result found by U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 4.73/1.31 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.73/1.31 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.73/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.73/1.31 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.73/1.31 % No SInE strategy applied
% 4.73/1.31 % Search class: FGUNF-FFMS21-SFFFFFNN
% 4.73/1.31 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 4.73/1.31 % Starting SubtermCWHack with 136s (1) cores
% 4.73/1.31 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.73/1.31 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 4.73/1.31 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.73/1.31 % Preprocessing time : 0.003 s
% 4.73/1.31 % Presaturation interreduction done
% 4.73/1.31
% 4.73/1.31 % Proof found!
% 4.73/1.31 % SZS status Unsatisfiable
% 4.73/1.31 % SZS output start CNFRefutation
% See solution above
% 4.73/1.31 % Parsed axioms : 30
% 4.73/1.31 % Removed by relevancy pruning/SinE : 0
% 4.73/1.31 % Initial clauses : 30
% 4.73/1.31 % Removed in clause preprocessing : 0
% 4.73/1.31 % Initial clauses in saturation : 30
% 4.73/1.31 % Processed clauses : 2863
% 4.73/1.31 % ...of these trivial : 29
% 4.73/1.31 % ...subsumed : 1240
% 4.73/1.31 % ...remaining for further processing : 1594
% 4.73/1.31 % Other redundant clauses eliminated : 0
% 4.73/1.31 % Clauses deleted for lack of memory : 0
% 4.73/1.31 % Backward-subsumed : 27
% 4.73/1.31 % Backward-rewritten : 1
% 4.73/1.31 % Generated clauses : 17061
% 4.73/1.31 % ...of the previous two non-redundant : 15804
% 4.73/1.31 % ...aggressively subsumed : 0
% 4.73/1.31 % Contextual simplify-reflections : 1
% 4.73/1.31 % Paramodulations : 17061
% 4.73/1.31 % Factorizations : 0
% 4.73/1.31 % NegExts : 0
% 4.73/1.31 % Equation resolutions : 0
% 4.73/1.31 % Disequality decompositions : 0
% 4.73/1.31 % Total rewrite steps : 3982
% 4.73/1.31 % ...of those cached : 3910
% 4.73/1.31 % Propositional unsat checks : 0
% 4.73/1.31 % Propositional check models : 0
% 4.73/1.31 % Propositional check unsatisfiable : 0
% 4.73/1.31 % Propositional clauses : 0
% 4.73/1.31 % Propositional clauses after purity: 0
% 4.73/1.31 % Propositional unsat core size : 0
% 4.73/1.31 % Propositional preprocessing time : 0.000
% 4.73/1.31 % Propositional encoding time : 0.000
% 4.73/1.31 % Propositional solver time : 0.000
% 4.73/1.31 % Success case prop preproc time : 0.000
% 4.73/1.31 % Success case prop encoding time : 0.000
% 4.73/1.31 % Success case prop solver time : 0.000
% 4.73/1.31 % Current number of processed clauses : 1536
% 4.73/1.31 % Positive orientable unit clauses : 72
% 4.73/1.31 % Positive unorientable unit clauses: 0
% 4.73/1.31 % Negative unit clauses : 4
% 4.73/1.31 % Non-unit-clauses : 1460
% 4.73/1.31 % Current number of unprocessed clauses: 12983
% 4.73/1.31 % ...number of literals in the above : 51983
% 4.73/1.31 % Current number of archived formulas : 0
% 4.73/1.31 % Current number of archived clauses : 58
% 4.73/1.31 % Clause-clause subsumption calls (NU) : 143121
% 4.73/1.31 % Rec. Clause-clause subsumption calls : 87473
% 4.73/1.31 % Non-unit clause-clause subsumptions : 1254
% 4.73/1.31 % Unit Clause-clause subsumption calls : 1702
% 4.73/1.31 % Rewrite failures with RHS unbound : 0
% 4.73/1.31 % BW rewrite match attempts : 22
% 4.73/1.31 % BW rewrite match successes : 12
% 4.73/1.31 % Condensation attempts : 0
% 4.73/1.31 % Condensation successes : 0
% 4.73/1.31 % Termbank termtop insertions : 288902
% 4.73/1.31 % Search garbage collected termcells : 118
% 4.73/1.31
% 4.73/1.31 % -------------------------------------------------
% 4.73/1.31 % User time : 0.677 s
% 4.73/1.31 % System time : 0.030 s
% 4.73/1.31 % Total time : 0.706 s
% 4.73/1.31 % Maximum resident set size: 3608 pages
% 4.73/1.31
% 4.73/1.31 % -------------------------------------------------
% 4.73/1.31 % User time : 3.533 s
% 4.73/1.31 % System time : 0.203 s
% 4.73/1.31 % Total time : 3.736 s
% 4.73/1.31 % Maximum resident set size: 4608 pages
% 4.73/1.31 % E exiting
%------------------------------------------------------------------------------