%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : FLD036-3 : 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 : n012.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 12:22:47 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.47s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 53 ( 24 unt; 6 nHn; 53 RR)
% Number of literals : 106 ( 0 equ; 53 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 : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 74 ( 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/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(commutativity_multiplication,axiom,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD002-0.ax',commutativity_multiplication) ).
cnf(product_6,negated_conjecture,
product(b,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_6) ).
cnf(b_is_defined,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_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/sandbox2/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(not_sum_8,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_8) ).
cnf(c_is_defined,hypothesis,
defined(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
cnf(product_5,negated_conjecture,
product(a,c,u),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_5) ).
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(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(not_product_7,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_7) ).
cnf(c_0_13,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_14,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_multiplication]) ).
cnf(c_0_15,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_multiplication]) ).
cnf(c_0_16,plain,
( ~ product(X5,X6,X3)
| ~ product(X4,X6,X2)
| ~ product(X1,X4,X5)
| product(X1,X2,X3) ),
c_0_13 ).
cnf(c_0_17,plain,
( ~ defined(X1)
| product(multiplicative_identity,X1,X1) ),
c_0_14 ).
cnf(c_0_18,plain,
( ~ product(X2,X1,X3)
| product(X1,X2,X3) ),
c_0_15 ).
cnf(c_0_19,negated_conjecture,
product(b,c,u),
product_6 ).
cnf(c_0_20,plain,
( ~ defined(X3)
| ~ product(X4,X3,X2)
| ~ product(X1,X4,multiplicative_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
product(c,b,u),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,hypothesis,
defined(b),
b_is_defined ).
cnf(c_0_23,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_24,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
inference(fof_simplification,[status(thm)],[not_sum_8]) ).
cnf(c_0_25,negated_conjecture,
( ~ product(X1,c,multiplicative_identity)
| product(X1,u,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
c_0_23 ).
cnf(c_0_27,hypothesis,
defined(c),
c_is_defined ).
cnf(c_0_28,negated_conjecture,
~ sum(additive_identity,c,additive_identity),
c_0_24 ).
cnf(c_0_29,negated_conjecture,
product(a,c,u),
product_5 ).
cnf(c_0_30,negated_conjecture,
product(multiplicative_inverse(c),u,b),
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_31,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_32,negated_conjecture,
product(c,a,u),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_33,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_34,negated_conjecture,
( ~ product(X3,u,X2)
| ~ product(X1,X3,multiplicative_inverse(c))
| product(X1,X2,b) ),
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_35,plain,
( ~ product(X4,X6,X3)
| ~ product(X5,X2,X6)
| ~ product(X4,X5,X1)
| product(X1,X2,X3) ),
c_0_31 ).
cnf(c_0_36,negated_conjecture,
( ~ product(X1,c,multiplicative_identity)
| product(X1,u,a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_32]),c_0_33])]) ).
cnf(c_0_37,negated_conjecture,
( ~ product(X1,multiplicative_inverse(c),multiplicative_inverse(c))
| product(X1,b,b) ),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_38,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_39,negated_conjecture,
( ~ product(X3,c,X1)
| ~ product(X3,u,X2)
| product(X1,b,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_21]) ).
cnf(c_0_40,negated_conjecture,
product(multiplicative_inverse(c),u,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_41,plain,
( ~ defined(X1)
| product(X1,multiplicative_identity,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_42,negated_conjecture,
( ~ defined(multiplicative_inverse(c))
| product(multiplicative_identity,b,b) ),
inference(spm,[status(thm)],[c_0_37,c_0_17]) ).
cnf(c_0_43,plain,
( ~ defined(X1)
| sum(additive_identity,X1,additive_identity)
| defined(multiplicative_inverse(X1)) ),
c_0_38 ).
cnf(c_0_44,negated_conjecture,
( ~ product(multiplicative_inverse(c),c,X1)
| product(X1,b,a) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( ~ defined(X3)
| ~ product(X1,X4,X3)
| ~ product(X4,multiplicative_identity,X2)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
product(multiplicative_identity,b,b),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_27])]),c_0_28]) ).
cnf(c_0_47,negated_conjecture,
product(multiplicative_identity,b,a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_48,negated_conjecture,
~ product(multiplicative_identity,a,b),
inference(fof_simplification,[status(thm)],[not_product_7]) ).
cnf(c_0_49,negated_conjecture,
( ~ product(b,multiplicative_identity,X1)
| product(multiplicative_identity,X1,b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_22])]) ).
cnf(c_0_50,negated_conjecture,
product(b,multiplicative_identity,a),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
~ product(multiplicative_identity,a,b),
c_0_48 ).
cnf(c_0_52,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD036-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 15:39:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.47 % Version: 3.5.1
% 0.12/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.47 % Starting sh5l with 300s (1) cores
% 0.12/0.47 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2674646 completed with status 0
% 0.12/0.47 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.47 % No SInE strategy applied
% 0.12/0.47 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.12/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.47 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.12/0.47 % Starting new_bool_3 with 269s (1) cores
% 0.12/0.47 % Starting G-E--_107_B00_00_F1_PI_AE_Q4_CS_SP_PS_S08BN with 136s (1) cores
% 0.12/0.47 % new_bool_3 with pid 2674654 completed with status 0
% 0.12/0.47 % Result found by new_bool_3
% 0.12/0.47 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.47 % No SInE strategy applied
% 0.12/0.47 % Search class: FGUNF-FFMM21-SFFFFFNN
% 0.12/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.47 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.47 % Starting H----_102_C18_F1_PI_AE_CS_SP_PS_S2S with 296s (1) cores
% 0.12/0.47 % Starting new_bool_3 with 269s (1) cores
% 0.12/0.47 % Preprocessing time : 0.001 s
% 0.12/0.47 % Presaturation interreduction done
% 0.12/0.47
% 0.12/0.47 % Proof found!
% 0.12/0.47 % SZS status Unsatisfiable
% 0.12/0.47 % SZS output start CNFRefutation
% See solution above
% 0.12/0.47 % Parsed axioms : 34
% 0.12/0.47 % Removed by relevancy pruning/SinE : 0
% 0.12/0.47 % Initial clauses : 34
% 0.12/0.47 % Removed in clause preprocessing : 0
% 0.12/0.47 % Initial clauses in saturation : 34
% 0.12/0.47 % Processed clauses : 407
% 0.12/0.47 % ...of these trivial : 21
% 0.12/0.47 % ...subsumed : 69
% 0.12/0.47 % ...remaining for further processing : 317
% 0.12/0.47 % Other redundant clauses eliminated : 0
% 0.12/0.47 % Clauses deleted for lack of memory : 0
% 0.12/0.47 % Backward-subsumed : 0
% 0.12/0.47 % Backward-rewritten : 15
% 0.12/0.47 % Generated clauses : 1646
% 0.12/0.47 % ...of the previous two non-redundant : 1267
% 0.12/0.47 % ...aggressively subsumed : 0
% 0.12/0.47 % Contextual simplify-reflections : 0
% 0.12/0.47 % Paramodulations : 1644
% 0.12/0.47 % Factorizations : 2
% 0.12/0.47 % NegExts : 0
% 0.12/0.47 % Equation resolutions : 0
% 0.12/0.47 % Disequality decompositions : 0
% 0.12/0.47 % Total rewrite steps : 981
% 0.12/0.47 % ...of those cached : 911
% 0.12/0.47 % Propositional unsat checks : 0
% 0.12/0.47 % Propositional check models : 0
% 0.12/0.47 % Propositional check unsatisfiable : 0
% 0.12/0.47 % Propositional clauses : 0
% 0.12/0.47 % Propositional clauses after purity: 0
% 0.12/0.47 % Propositional unsat core size : 0
% 0.12/0.47 % Propositional preprocessing time : 0.000
% 0.12/0.47 % Propositional encoding time : 0.000
% 0.12/0.47 % Propositional solver time : 0.000
% 0.12/0.47 % Success case prop preproc time : 0.000
% 0.12/0.47 % Success case prop encoding time : 0.000
% 0.12/0.47 % Success case prop solver time : 0.000
% 0.12/0.47 % Current number of processed clauses : 268
% 0.12/0.47 % Positive orientable unit clauses : 76
% 0.12/0.47 % Positive unorientable unit clauses: 0
% 0.12/0.47 % Negative unit clauses : 3
% 0.12/0.47 % Non-unit-clauses : 189
% 0.12/0.47 % Current number of unprocessed clauses: 920
% 0.12/0.47 % ...number of literals in the above : 2871
% 0.12/0.47 % Current number of archived formulas : 0
% 0.12/0.47 % Current number of archived clauses : 49
% 0.12/0.47 % Clause-clause subsumption calls (NU) : 2210
% 0.12/0.47 % Rec. Clause-clause subsumption calls : 1765
% 0.12/0.47 % Non-unit clause-clause subsumptions : 69
% 0.12/0.47 % Unit Clause-clause subsumption calls : 78
% 0.12/0.47 % Rewrite failures with RHS unbound : 0
% 0.12/0.47 % BW rewrite match attempts : 48
% 0.12/0.47 % BW rewrite match successes : 13
% 0.12/0.47 % Condensation attempts : 0
% 0.12/0.47 % Condensation successes : 0
% 0.12/0.47 % Termbank termtop insertions : 23882
% 0.12/0.47 % Search garbage collected termcells : 118
% 0.12/0.47
% 0.12/0.47 % -------------------------------------------------
% 0.12/0.47 % User time : 0.032 s
% 0.12/0.47 % System time : 0.004 s
% 0.12/0.47 % Total time : 0.036 s
% 0.12/0.47 % Maximum resident set size: 3660 pages
% 0.12/0.47
% 0.12/0.47 % -------------------------------------------------
% 0.12/0.47 % User time : 0.152 s
% 0.12/0.47 % System time : 0.024 s
% 0.12/0.47 % Total time : 0.176 s
% 0.12/0.47 % Maximum resident set size: 4864 pages
% 0.12/0.47 % E exiting
%------------------------------------------------------------------------------