%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD001-3 : 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 : 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 12:22:36 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.52s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 15 unt; 3 nHn; 49 RR)
% Number of literals : 116 ( 0 equ; 67 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 85 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(compatibility_of_order_relation_and_addition,axiom,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',compatibility_of_order_relation_and_addition) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(totality_of_order_relation,axiom,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',totality_of_order_relation) ).
cnf(sum_3,hypothesis,
sum(additive_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
cnf(transitivity_of_order_relation,axiom,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',transitivity_of_order_relation) ).
cnf(well_definedness_of_additive_identity,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_additive_identity) ).
cnf(distributivity_2,axiom,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',distributivity_2) ).
cnf(antisymmetry_of_order_relation,axiom,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',antisymmetry_of_order_relation) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
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(not_product_4,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_4) ).
cnf(c_0_12,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[compatibility_of_order_relation_and_addition]) ).
cnf(c_0_13,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_14,plain,
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ less_or_equal(X3,X4)
| less_or_equal(X1,X2) ),
c_0_12 ).
cnf(c_0_15,plain,
( ~ defined(X1)
| sum(additive_identity,X1,X1) ),
c_0_13 ).
cnf(c_0_16,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[totality_of_order_relation]) ).
cnf(c_0_17,plain,
( ~ sum(X3,X2,X1)
| ~ defined(X2)
| ~ less_or_equal(X3,additive_identity)
| less_or_equal(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,hypothesis,
sum(additive_identity,a,b),
sum_3 ).
cnf(c_0_19,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_20,plain,
( ~ defined(X2)
| ~ defined(X1)
| less_or_equal(X2,X1)
| less_or_equal(X1,X2) ),
c_0_16 ).
cnf(c_0_21,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_order_relation]) ).
cnf(c_0_22,hypothesis,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(b,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_23,plain,
( ~ defined(X1)
| less_or_equal(X1,X1) ),
inference(ef,[status(thm)],[c_0_20]) ).
cnf(c_0_24,axiom,
defined(additive_identity),
well_definedness_of_additive_identity ).
cnf(c_0_25,hypothesis,
( ~ sum(X2,a,X1)
| ~ less_or_equal(X2,additive_identity)
| less_or_equal(X1,b) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_26,plain,
( ~ less_or_equal(X3,X2)
| ~ less_or_equal(X1,X3)
| less_or_equal(X1,X2) ),
c_0_21 ).
cnf(c_0_27,hypothesis,
less_or_equal(b,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_28,hypothesis,
( ~ less_or_equal(additive_identity,additive_identity)
| less_or_equal(a,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_15]),c_0_19])]) ).
cnf(c_0_29,plain,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[distributivity_2]) ).
cnf(c_0_30,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
inference(fof_simplification,[status(thm)],[antisymmetry_of_order_relation]) ).
cnf(c_0_31,hypothesis,
( ~ less_or_equal(X1,b)
| less_or_equal(X1,a) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,hypothesis,
less_or_equal(a,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_24])]) ).
cnf(c_0_33,plain,
( ~ sum(X6,X7,X3)
| ~ product(X5,X2,X7)
| ~ product(X4,X2,X6)
| ~ sum(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_29 ).
cnf(c_0_34,plain,
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X1,X2)
| sum(additive_identity,X1,X2) ),
c_0_30 ).
cnf(c_0_35,hypothesis,
less_or_equal(a,a),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_37,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_38,hypothesis,
( ~ sum(X4,X3,X1)
| ~ product(X4,X2,additive_identity)
| ~ product(X3,X2,a)
| product(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_39,hypothesis,
sum(additive_identity,a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_35])]) ).
cnf(c_0_40,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_36 ).
cnf(c_0_41,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_37 ).
cnf(c_0_42,hypothesis,
( ~ product(additive_identity,X1,additive_identity)
| ~ product(a,X1,a)
| product(a,X1,b) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,hypothesis,
( ~ product(additive_identity,multiplicative_identity,additive_identity)
| product(a,multiplicative_identity,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_19])]) ).
cnf(c_0_45,negated_conjecture,
~ product(multiplicative_identity,a,b),
inference(fof_simplification,[status(thm)],[not_product_4]) ).
cnf(c_0_46,hypothesis,
product(a,multiplicative_identity,b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_43]),c_0_24])]) ).
cnf(c_0_47,negated_conjecture,
~ product(multiplicative_identity,a,b),
c_0_45 ).
cnf(c_0_48,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_46]),c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD001-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n013.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 15:35:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.52 % Version: 3.5.1
% 0.10/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.52 % Starting sh5l with 300s (1) cores
% 0.10/0.52 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1098019 completed with status 0
% 0.10/0.52 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.10/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.52 % No SInE strategy applied
% 0.10/0.52 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.10/0.52 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.52 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.10/0.52 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.52 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.10/0.52 % G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 1098027 completed with status 0
% 0.10/0.52 % Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 0.10/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.10/0.52 % No SInE strategy applied
% 0.10/0.52 % Search class: FGUNF-FFMS21-SFFFFFNN
% 0.10/0.52 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.10/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.10/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.10/0.52 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 0.10/0.52 % Preprocessing time : 0.001 s
% 0.10/0.52 % Presaturation interreduction done
% 0.10/0.52
% 0.10/0.52 % Proof found!
% 0.10/0.52 % SZS status Unsatisfiable
% 0.10/0.52 % SZS output start CNFRefutation
% See solution above
% 0.10/0.52 % Parsed axioms : 30
% 0.10/0.52 % Removed by relevancy pruning/SinE : 0
% 0.10/0.52 % Initial clauses : 30
% 0.10/0.52 % Removed in clause preprocessing : 0
% 0.10/0.52 % Initial clauses in saturation : 30
% 0.10/0.52 % Processed clauses : 785
% 0.10/0.52 % ...of these trivial : 93
% 0.10/0.52 % ...subsumed : 195
% 0.10/0.52 % ...remaining for further processing : 497
% 0.10/0.52 % Other redundant clauses eliminated : 0
% 0.10/0.52 % Clauses deleted for lack of memory : 0
% 0.10/0.52 % Backward-subsumed : 12
% 0.10/0.52 % Backward-rewritten : 18
% 0.10/0.52 % Generated clauses : 4506
% 0.10/0.52 % ...of the previous two non-redundant : 3648
% 0.10/0.52 % ...aggressively subsumed : 0
% 0.10/0.52 % Contextual simplify-reflections : 1
% 0.10/0.52 % Paramodulations : 4494
% 0.10/0.52 % Factorizations : 12
% 0.10/0.52 % NegExts : 0
% 0.10/0.52 % Equation resolutions : 0
% 0.10/0.52 % Disequality decompositions : 0
% 0.10/0.52 % Total rewrite steps : 2611
% 0.10/0.52 % ...of those cached : 2501
% 0.10/0.52 % Propositional unsat checks : 0
% 0.10/0.52 % Propositional check models : 0
% 0.10/0.52 % Propositional check unsatisfiable : 0
% 0.10/0.52 % Propositional clauses : 0
% 0.10/0.52 % Propositional clauses after purity: 0
% 0.10/0.52 % Propositional unsat core size : 0
% 0.10/0.52 % Propositional preprocessing time : 0.000
% 0.10/0.52 % Propositional encoding time : 0.000
% 0.10/0.52 % Propositional solver time : 0.000
% 0.10/0.52 % Success case prop preproc time : 0.000
% 0.10/0.52 % Success case prop encoding time : 0.000
% 0.10/0.52 % Success case prop solver time : 0.000
% 0.10/0.52 % Current number of processed clauses : 437
% 0.10/0.52 % Positive orientable unit clauses : 124
% 0.10/0.52 % Positive unorientable unit clauses: 0
% 0.10/0.52 % Negative unit clauses : 2
% 0.10/0.52 % Non-unit-clauses : 311
% 0.10/0.52 % Current number of unprocessed clauses: 2918
% 0.10/0.52 % ...number of literals in the above : 9936
% 0.10/0.52 % Current number of archived formulas : 0
% 0.10/0.52 % Current number of archived clauses : 60
% 0.10/0.52 % Clause-clause subsumption calls (NU) : 7437
% 0.10/0.52 % Rec. Clause-clause subsumption calls : 5857
% 0.10/0.52 % Non-unit clause-clause subsumptions : 207
% 0.10/0.52 % Unit Clause-clause subsumption calls : 249
% 0.10/0.52 % Rewrite failures with RHS unbound : 0
% 0.10/0.52 % BW rewrite match attempts : 101
% 0.10/0.52 % BW rewrite match successes : 15
% 0.10/0.52 % Condensation attempts : 0
% 0.10/0.52 % Condensation successes : 0
% 0.10/0.52 % Termbank termtop insertions : 68063
% 0.10/0.52 % Search garbage collected termcells : 116
% 0.10/0.52
% 0.10/0.52 % -------------------------------------------------
% 0.10/0.52 % User time : 0.074 s
% 0.10/0.52 % System time : 0.007 s
% 0.10/0.52 % Total time : 0.081 s
% 0.10/0.52 % Maximum resident set size: 3404 pages
% 0.10/0.52
% 0.10/0.52 % -------------------------------------------------
% 0.10/0.52 % User time : 0.348 s
% 0.10/0.52 % System time : 0.024 s
% 0.10/0.52 % Total time : 0.372 s
% 0.10/0.52 % Maximum resident set size: 4608 pages
% 0.10/0.52 % E exiting
%------------------------------------------------------------------------------