%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD049-4 : 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 : n009.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 12:22:51 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.47s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 60 ( 31 unt; 8 nHn; 60 RR)
% Number of literals : 108 ( 0 equ; 49 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(product_10,negated_conjecture,
product(c,multiplicative_inverse(d),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_10) ).
cnf(not_sum_8,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_8) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_is_defined) ).
cnf(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(d_is_defined,hypothesis,
defined(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_is_defined) ).
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(product_9,negated_conjecture,
product(a,multiplicative_inverse(b),s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_9) ).
cnf(not_sum_7,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_7) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_defined) ).
cnf(product_11,negated_conjecture,
product(a,d,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_11) ).
cnf(not_product_12,negated_conjecture,
~ product(b,c,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_12) ).
cnf(c_0_15,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_16,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_17,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_18,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_15 ).
cnf(c_0_19,negated_conjecture,
product(c,multiplicative_inverse(d),s),
product_10 ).
cnf(c_0_20,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_16 ).
cnf(c_0_21,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_17 ).
cnf(c_0_22,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_8]) ).
cnf(c_0_23,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_24,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_25,negated_conjecture,
( ~ product(X1,X3,c)
| ~ product(X3,multiplicative_inverse(d),X2)
| product(X1,X2,s) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_identity,multiplicative_inverse(X1),multiplicative_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
defined(d),
d_is_defined ).
cnf(c_0_28,negated_conjecture,
~ sum(additive_identity,d,additive_identity),
c_0_22 ).
cnf(c_0_29,hypothesis,
product(multiplicative_identity,c,c),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_30,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_24 ).
cnf(c_0_31,negated_conjecture,
( ~ product(X1,multiplicative_identity,c)
| product(X1,multiplicative_inverse(d),s) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_32,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_33,negated_conjecture,
product(a,multiplicative_inverse(b),s),
product_9 ).
cnf(c_0_34,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_7]) ).
cnf(c_0_35,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,c,X2)
| product(X1,X2,c) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( ~ product(X1,multiplicative_identity,c)
| product(multiplicative_inverse(d),X1,s) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,hypothesis,
product(c,multiplicative_identity,c),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_38,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_32 ).
cnf(c_0_39,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_40,negated_conjecture,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_inverse(b),X2)
| product(X1,X2,s) ),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_41,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_42,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
c_0_34 ).
cnf(c_0_43,negated_conjecture,
( ~ product(X1,multiplicative_inverse(d),multiplicative_identity)
| product(X1,s,c) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]) ).
cnf(c_0_44,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(X1,multiplicative_inverse(X1),multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_45,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( ~ product(X1,multiplicative_identity,a)
| product(X1,multiplicative_inverse(b),s) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_26]),c_0_41])]),c_0_42]) ).
cnf(c_0_47,negated_conjecture,
product(a,d,k),
product_11 ).
cnf(c_0_48,negated_conjecture,
product(d,s,c),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_27])]),c_0_28]) ).
cnf(c_0_49,hypothesis,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,a,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
( ~ product(X1,multiplicative_identity,a)
| product(multiplicative_inverse(b),X1,s) ),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_51,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( ~ product(X1,X3,a)
| ~ product(X3,d,X2)
| product(X1,X2,k) ),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
product(s,d,c),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( ~ product(X1,multiplicative_inverse(b),multiplicative_identity)
| product(X1,s,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_55,negated_conjecture,
~ product(b,c,k),
inference(fof_simplification,[status(thm)],[not_product_12]) ).
cnf(c_0_56,negated_conjecture,
( ~ product(X1,s,a)
| product(X1,c,k) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
product(b,s,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_44]),c_0_41])]),c_0_42]) ).
cnf(c_0_58,negated_conjecture,
~ product(b,c,k),
c_0_55 ).
cnf(c_0_59,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD049-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 15:41:58 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.47 % Version: 3.5.1
% 0.11/0.47 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.11/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.47 % Starting sh5l with 300s (1) cores
% 0.11/0.47 % new_bool_1 with pid 2122559 completed with status 0
% 0.11/0.47 % Result found by new_bool_1
% 0.11/0.47 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.11/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.47 % Search class: FGUNF-FFSM11-SFFFFFNN
% 0.11/0.47 % partial match(1): FGUNF-FFSF11-SFFFFFNN
% 0.11/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.47 % SubtermCWHack with pid 2122564 completed with status 0
% 0.11/0.47 % Result found by SubtermCWHack
% 0.11/0.47 % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.11/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.11/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.11/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.11/0.47 % Search class: FGUNF-FFSM11-SFFFFFNN
% 0.11/0.47 % partial match(1): FGUNF-FFSF11-SFFFFFNN
% 0.11/0.47 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.11/0.47 % Starting SubtermCWHack with 31s (1) cores
% 0.11/0.47 % Preprocessing time : 0.002 s
% 0.11/0.47
% 0.11/0.47 % Proof found!
% 0.11/0.47 % SZS status Unsatisfiable
% 0.11/0.47 % SZS output start CNFRefutation
% See solution above
% 0.11/0.47 % Parsed axioms : 38
% 0.11/0.47 % Removed by relevancy pruning/SinE : 11
% 0.11/0.47 % Initial clauses : 27
% 0.11/0.47 % Removed in clause preprocessing : 0
% 0.11/0.47 % Initial clauses in saturation : 27
% 0.11/0.47 % Processed clauses : 185
% 0.11/0.47 % ...of these trivial : 0
% 0.11/0.47 % ...subsumed : 32
% 0.11/0.47 % ...remaining for further processing : 153
% 0.11/0.47 % Other redundant clauses eliminated : 0
% 0.11/0.47 % Clauses deleted for lack of memory : 0
% 0.11/0.47 % Backward-subsumed : 0
% 0.11/0.47 % Backward-rewritten : 0
% 0.11/0.47 % Generated clauses : 589
% 0.11/0.47 % ...of the previous two non-redundant : 479
% 0.11/0.47 % ...aggressively subsumed : 0
% 0.11/0.47 % Contextual simplify-reflections : 0
% 0.11/0.47 % Paramodulations : 589
% 0.11/0.47 % Factorizations : 0
% 0.11/0.47 % NegExts : 0
% 0.11/0.47 % Equation resolutions : 0
% 0.11/0.47 % Disequality decompositions : 0
% 0.11/0.47 % Total rewrite steps : 122
% 0.11/0.47 % ...of those cached : 93
% 0.11/0.47 % Propositional unsat checks : 0
% 0.11/0.47 % Propositional check models : 0
% 0.11/0.47 % Propositional check unsatisfiable : 0
% 0.11/0.47 % Propositional clauses : 0
% 0.11/0.47 % Propositional clauses after purity: 0
% 0.11/0.47 % Propositional unsat core size : 0
% 0.11/0.47 % Propositional preprocessing time : 0.000
% 0.11/0.47 % Propositional encoding time : 0.000
% 0.11/0.47 % Propositional solver time : 0.000
% 0.11/0.47 % Success case prop preproc time : 0.000
% 0.11/0.47 % Success case prop encoding time : 0.000
% 0.11/0.47 % Success case prop solver time : 0.000
% 0.11/0.47 % Current number of processed clauses : 153
% 0.11/0.47 % Positive orientable unit clauses : 35
% 0.11/0.47 % Positive unorientable unit clauses: 0
% 0.11/0.47 % Negative unit clauses : 4
% 0.11/0.47 % Non-unit-clauses : 114
% 0.11/0.47 % Current number of unprocessed clauses: 316
% 0.11/0.47 % ...number of literals in the above : 1159
% 0.11/0.47 % Current number of archived formulas : 0
% 0.11/0.47 % Current number of archived clauses : 0
% 0.11/0.47 % Clause-clause subsumption calls (NU) : 1980
% 0.11/0.47 % Rec. Clause-clause subsumption calls : 1593
% 0.11/0.47 % Non-unit clause-clause subsumptions : 32
% 0.11/0.47 % Unit Clause-clause subsumption calls : 16
% 0.11/0.47 % Rewrite failures with RHS unbound : 0
% 0.11/0.47 % BW rewrite match attempts : 1
% 0.11/0.47 % BW rewrite match successes : 0
% 0.11/0.47 % Condensation attempts : 0
% 0.11/0.47 % Condensation successes : 0
% 0.11/0.47 % Termbank termtop insertions : 8364
% 0.11/0.47 % Search garbage collected termcells : 144
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.027 s
% 0.11/0.47 % System time : 0.005 s
% 0.11/0.47 % Total time : 0.032 s
% 0.11/0.47 % Maximum resident set size: 3612 pages
% 0.11/0.47
% 0.11/0.47 % -------------------------------------------------
% 0.11/0.47 % User time : 0.028 s
% 0.11/0.47 % System time : 0.009 s
% 0.11/0.47 % Total time : 0.038 s
% 0.11/0.47 % Maximum resident set size: 4864 pages
% 0.11/0.47 % E exiting
%------------------------------------------------------------------------------