%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD031-3 : 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 : n007.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 12:22:45 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.59s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of clauses : 36 ( 17 unt; 3 nHn; 36 RR)
% Number of literals : 67 ( 0 equ; 34 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 : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(product_2,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_2) ).
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(not_product_4,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_4) ).
cnf(c_0_8,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_9,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_10,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_8 ).
cnf(c_0_11,hypothesis,
defined(a),
a_is_defined ).
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,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_9 ).
cnf(c_0_14,hypothesis,
product(multiplicative_identity,a,a),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_12 ).
cnf(c_0_16,hypothesis,
product(a,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
product(multiplicative_identity,a,multiplicative_identity),
product_2 ).
cnf(c_0_18,hypothesis,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,X2,a) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
product(a,multiplicative_identity,multiplicative_identity),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( ~ product(X1,a,a)
| product(X1,multiplicative_identity,a) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,negated_conjecture,
( ~ product(X1,X3,a)
| ~ product(X3,multiplicative_identity,X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_19]) ).
cnf(c_0_22,hypothesis,
product(multiplicative_identity,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_23,negated_conjecture,
( ~ product(X1,multiplicative_identity,a)
| product(X1,a,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
( ~ product(X1,multiplicative_identity,a)
| product(a,X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_13,c_0_23]) ).
cnf(c_0_25,negated_conjecture,
( ~ product(X1,X3,multiplicative_identity)
| ~ product(X3,a,X2)
| product(X1,X2,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_26,hypothesis,
product(a,a,multiplicative_identity),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_27,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_28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_3]) ).
cnf(c_0_29,hypothesis,
( ~ product(X1,a,multiplicative_identity)
| product(X1,multiplicative_identity,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_27 ).
cnf(c_0_31,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
c_0_28 ).
cnf(c_0_32,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
inference(fof_simplification,[status(thm)],[not_product_4]) ).
cnf(c_0_33,hypothesis,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_11])]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
c_0_32 ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_33]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD031-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.52 % Computer : n007.cluster.edu
% 0.08/0.52 % Model : x86_64 x86_64
% 0.08/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.52 % Memory : 8046.5625MB
% 0.08/0.52 % OS : Linux 6.8.0-71-generic
% 0.08/0.52 % CPULimit : 300
% 0.08/0.52 % WCLimit : 300
% 0.08/0.52 % DateTime : Mon Sep 21 15:37:06 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.53 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.57 Running first-order theorem proving
% 0.16/0.57 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
% 0.16/0.59 % Version: 3.5.1
% 0.16/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.16/0.59 % Starting sh5l with 300s (1) cores
% 0.16/0.59 % new_bool_3 with pid 1442798 completed with status 0
% 0.16/0.59 % Result found by new_bool_3
% 0.16/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.59 % Search class: FGUNF-FFSS11-SFFFFFNN
% 0.16/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.59 % SubtermCWHack with pid 1442803 completed with status 0
% 0.16/0.59 % Result found by SubtermCWHack
% 0.16/0.59 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.16/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/0.59 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.16/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.16/0.59 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.16/0.59 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.16/0.59 % Search class: FGUNF-FFSS11-SFFFFFNN
% 0.16/0.59 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.16/0.59 % Starting SubtermCWHack with 31s (1) cores
% 0.16/0.59 % Preprocessing time : 0.001 s
% 0.16/0.59
% 0.16/0.59 % Proof found!
% 0.16/0.59 % SZS status Unsatisfiable
% 0.16/0.59 % SZS output start CNFRefutation
% See solution above
% 0.16/0.59 % Parsed axioms : 30
% 0.16/0.59 % Removed by relevancy pruning/SinE : 11
% 0.16/0.59 % Initial clauses : 19
% 0.16/0.59 % Removed in clause preprocessing : 0
% 0.16/0.59 % Initial clauses in saturation : 19
% 0.16/0.59 % Processed clauses : 87
% 0.16/0.59 % ...of these trivial : 0
% 0.16/0.59 % ...subsumed : 9
% 0.16/0.59 % ...remaining for further processing : 78
% 0.16/0.59 % Other redundant clauses eliminated : 0
% 0.16/0.59 % Clauses deleted for lack of memory : 0
% 0.16/0.59 % Backward-subsumed : 0
% 0.16/0.59 % Backward-rewritten : 0
% 0.16/0.59 % Generated clauses : 192
% 0.16/0.59 % ...of the previous two non-redundant : 131
% 0.16/0.59 % ...aggressively subsumed : 0
% 0.16/0.59 % Contextual simplify-reflections : 0
% 0.16/0.59 % Paramodulations : 192
% 0.16/0.59 % Factorizations : 0
% 0.16/0.59 % NegExts : 0
% 0.16/0.59 % Equation resolutions : 0
% 0.16/0.59 % Disequality decompositions : 0
% 0.16/0.59 % Total rewrite steps : 44
% 0.16/0.59 % ...of those cached : 28
% 0.16/0.59 % Propositional unsat checks : 0
% 0.16/0.59 % Propositional check models : 0
% 0.16/0.59 % Propositional check unsatisfiable : 0
% 0.16/0.59 % Propositional clauses : 0
% 0.16/0.59 % Propositional clauses after purity: 0
% 0.16/0.59 % Propositional unsat core size : 0
% 0.16/0.59 % Propositional preprocessing time : 0.000
% 0.16/0.59 % Propositional encoding time : 0.000
% 0.16/0.59 % Propositional solver time : 0.000
% 0.16/0.59 % Success case prop preproc time : 0.000
% 0.16/0.59 % Success case prop encoding time : 0.000
% 0.16/0.59 % Success case prop solver time : 0.000
% 0.16/0.59 % Current number of processed clauses : 78
% 0.16/0.59 % Positive orientable unit clauses : 19
% 0.16/0.59 % Positive unorientable unit clauses: 0
% 0.16/0.59 % Negative unit clauses : 3
% 0.16/0.59 % Non-unit-clauses : 56
% 0.16/0.59 % Current number of unprocessed clauses: 63
% 0.16/0.59 % ...number of literals in the above : 248
% 0.16/0.59 % Current number of archived formulas : 0
% 0.16/0.59 % Current number of archived clauses : 0
% 0.16/0.59 % Clause-clause subsumption calls (NU) : 257
% 0.16/0.59 % Rec. Clause-clause subsumption calls : 257
% 0.16/0.59 % Non-unit clause-clause subsumptions : 9
% 0.16/0.59 % Unit Clause-clause subsumption calls : 0
% 0.16/0.59 % Rewrite failures with RHS unbound : 0
% 0.16/0.59 % BW rewrite match attempts : 6
% 0.16/0.59 % BW rewrite match successes : 0
% 0.16/0.59 % Condensation attempts : 0
% 0.16/0.59 % Condensation successes : 0
% 0.16/0.59 % Termbank termtop insertions : 3183
% 0.16/0.59 % Search garbage collected termcells : 142
% 0.16/0.59
% 0.16/0.59 % -------------------------------------------------
% 0.16/0.59 % User time : 0.005 s
% 0.16/0.59 % System time : 0.001 s
% 0.16/0.59 % Total time : 0.007 s
% 0.16/0.59 % Maximum resident set size: 3660 pages
% 0.16/0.59
% 0.16/0.59 % -------------------------------------------------
% 0.16/0.59 % User time : 0.006 s
% 0.16/0.59 % System time : 0.008 s
% 0.16/0.59 % Total time : 0.013 s
% 0.16/0.59 % Maximum resident set size: 4608 pages
% 0.16/0.59 % E exiting
%------------------------------------------------------------------------------