%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : FLD007-1 : 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 : n003.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 12:23:05 PM UTC 2026
% Result : Unsatisfiable 59.88s 9.21s
% Output : CNFRefutation 59.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 54 ( 6 unt; 0 nHn; 54 RR)
% Number of literals : 141 ( 0 equ; 90 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_equality,axiom,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',transitivity_of_equality) ).
cnf(existence_of_identity_addition,axiom,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_identity_addition) ).
cnf(compatibility_of_equality_and_addition,axiom,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_addition) ).
cnf(existence_of_inverse_addition,axiom,
( ~ defined(X1)
| equalish(add(X1,additive_inverse(X1)),additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',existence_of_inverse_addition) ).
cnf(associativity_addition,axiom,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',associativity_addition) ).
cnf(well_definedness_of_additive_inverse,axiom,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_additive_inverse) ).
cnf(commutativity_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',commutativity_addition) ).
cnf(well_definedness_of_addition,axiom,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',well_definedness_of_addition) ).
cnf(symmetry_of_equality,axiom,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
cnf(additive_inverse_not_equal_to_a_2,negated_conjecture,
~ equalish(additive_inverse(additive_inverse(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse_not_equal_to_a_2) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(c_0_11,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[transitivity_of_equality]) ).
cnf(c_0_12,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
inference(fof_simplification,[status(thm)],[existence_of_identity_addition]) ).
cnf(c_0_13,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
inference(fof_simplification,[status(thm)],[compatibility_of_equality_and_addition]) ).
cnf(c_0_14,plain,
( ~ defined(X1)
| equalish(add(X1,additive_inverse(X1)),additive_identity) ),
inference(fof_simplification,[status(thm)],[existence_of_inverse_addition]) ).
cnf(c_0_15,plain,
( ~ equalish(X3,X2)
| ~ equalish(X1,X3)
| equalish(X1,X2) ),
c_0_11 ).
cnf(c_0_16,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),X1) ),
c_0_12 ).
cnf(c_0_17,plain,
( ~ equalish(X1,X3)
| ~ defined(X2)
| equalish(add(X1,X2),add(X3,X2)) ),
c_0_13 ).
cnf(c_0_18,plain,
( ~ defined(X1)
| equalish(add(X1,additive_inverse(X1)),additive_identity) ),
c_0_14 ).
cnf(c_0_19,plain,
( ~ equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( ~ defined(X1)
| ~ defined(X2)
| equalish(add(add(X1,additive_inverse(X1)),X2),add(additive_identity,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( ~ defined(X1)
| ~ defined(X2)
| equalish(add(add(X1,additive_inverse(X1)),X2),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)) ),
inference(fof_simplification,[status(thm)],[associativity_addition]) ).
cnf(c_0_23,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_additive_inverse]) ).
cnf(c_0_24,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
inference(fof_simplification,[status(thm)],[commutativity_addition]) ).
cnf(c_0_25,plain,
( ~ equalish(X1,add(add(X3,additive_inverse(X3)),X2))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_26,plain,
( ~ defined(X3)
| ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,add(X2,X3)),add(add(X1,X2),X3)) ),
c_0_22 ).
cnf(c_0_27,plain,
( ~ defined(X1)
| defined(additive_inverse(X1)) ),
c_0_23 ).
cnf(c_0_28,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(X1,X2),add(X2,X1)) ),
c_0_24 ).
cnf(c_0_29,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
inference(fof_simplification,[status(thm)],[well_definedness_of_addition]) ).
cnf(c_0_30,plain,
( ~ defined(X1)
| ~ defined(X2)
| equalish(add(X1,add(additive_inverse(X1),X2)),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_31,plain,
( ~ equalish(X1,add(X3,X2))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,add(X2,X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_32,plain,
( ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3)
| equalish(add(add(X1,X2),X3),add(add(X2,X1),X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_28]) ).
cnf(c_0_33,plain,
( ~ defined(X2)
| ~ defined(X1)
| defined(add(X1,X2)) ),
c_0_29 ).
cnf(c_0_34,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
inference(fof_simplification,[status(thm)],[symmetry_of_equality]) ).
cnf(c_0_35,plain,
( ~ equalish(X1,add(X2,additive_inverse(X2)))
| ~ defined(X2)
| equalish(X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_36,plain,
( ~ equalish(X1,add(X3,add(additive_inverse(X3),X2)))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_30]) ).
cnf(c_0_37,plain,
( ~ defined(X1)
| ~ defined(X2)
| ~ defined(X3)
| equalish(add(add(X1,X2),X3),add(X3,add(X2,X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_38,plain,
( ~ equalish(X2,X1)
| equalish(X1,X2) ),
c_0_34 ).
cnf(c_0_39,plain,
( ~ defined(X1)
| equalish(add(additive_inverse(X1),X1),additive_identity) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_27]) ).
cnf(c_0_40,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(add(X1,additive_inverse(X2)),X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_27]) ).
cnf(c_0_41,plain,
( ~ defined(X1)
| equalish(additive_identity,add(additive_inverse(X1),X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
( ~ equalish(X1,add(add(X2,additive_inverse(X3)),X3))
| ~ defined(X3)
| ~ defined(X2)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_40]) ).
cnf(c_0_43,plain,
( ~ defined(X2)
| ~ defined(X1)
| equalish(add(additive_identity,X1),add(add(additive_inverse(X2),X2),X1)) ),
inference(spm,[status(thm)],[c_0_17,c_0_41]) ).
cnf(c_0_44,plain,
( ~ defined(X1)
| ~ defined(additive_inverse(additive_inverse(X1)))
| equalish(add(additive_identity,X1),additive_inverse(additive_inverse(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_27]) ).
cnf(c_0_45,plain,
( ~ defined(X1)
| equalish(add(additive_identity,X1),additive_inverse(additive_inverse(X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_27]),c_0_27]) ).
cnf(c_0_46,plain,
( ~ equalish(X1,add(additive_identity,X2))
| ~ defined(X2)
| equalish(X1,additive_inverse(additive_inverse(X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_45]) ).
cnf(c_0_47,plain,
( ~ defined(X1)
| equalish(X1,add(additive_identity,X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_48,negated_conjecture,
~ equalish(additive_inverse(additive_inverse(a)),a),
inference(fof_simplification,[status(thm)],[additive_inverse_not_equal_to_a_2]) ).
cnf(c_0_49,plain,
( ~ defined(X1)
| equalish(X1,additive_inverse(additive_inverse(X1))) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
~ equalish(additive_inverse(additive_inverse(a)),a),
c_0_48 ).
cnf(c_0_51,plain,
( ~ defined(X1)
| equalish(additive_inverse(additive_inverse(X1)),X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_49]) ).
cnf(c_0_52,hypothesis,
defined(a),
a_is_defined ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD007-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.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 15:38:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 59.88/9.21 % Version: 3.5.1
% 59.88/9.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 59.88/9.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.88/9.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.88/9.21 % Starting new_bool_3 with 300s (1) cores
% 59.88/9.21 % Starting new_bool_1 with 300s (1) cores
% 59.88/9.21 % Starting sh5l with 300s (1) cores
% 59.88/9.21 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 463615 completed with status 0
% 59.88/9.21 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 59.88/9.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 59.88/9.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.88/9.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.88/9.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 59.88/9.21 % No SInE strategy applied
% 59.88/9.21 % Search class: FGUNF-FFMS21-SFFFFFNN
% 59.88/9.21 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 59.88/9.21 % Starting SubtermCWHack with 136s (1) cores
% 59.88/9.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 59.88/9.21 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 59.88/9.21 % Starting U----_206e_02_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 59.88/9.21 % Starting G-E--_208_C02CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 59.88/9.21 % G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with pid 463622 completed with status 0
% 59.88/9.21 % Result found by G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c
% 59.88/9.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 59.88/9.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 59.88/9.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 59.88/9.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 59.88/9.21 % No SInE strategy applied
% 59.88/9.21 % Search class: FGUNF-FFMS21-SFFFFFNN
% 59.88/9.21 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 59.88/9.21 % Starting SubtermCWHack with 136s (1) cores
% 59.88/9.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 59.88/9.21 % Starting G-E--_208_C18_SOS_F1_SE_CS_SP_PS_S4c with 136s (1) cores
% 59.88/9.21 % Preprocessing time : 0.002 s
% 59.88/9.21 % Presaturation interreduction done
% 59.88/9.21
% 59.88/9.21 % Proof found!
% 59.88/9.21 % SZS status Unsatisfiable
% 59.88/9.21 % SZS output start CNFRefutation
% See solution above
% 59.88/9.21 % Parsed axioms : 29
% 59.88/9.21 % Removed by relevancy pruning/SinE : 0
% 59.88/9.21 % Initial clauses : 29
% 59.88/9.21 % Removed in clause preprocessing : 0
% 59.88/9.21 % Initial clauses in saturation : 29
% 59.88/9.21 % Processed clauses : 17105
% 59.88/9.21 % ...of these trivial : 2673
% 59.88/9.21 % ...subsumed : 7565
% 59.88/9.21 % ...remaining for further processing : 6867
% 59.88/9.21 % Other redundant clauses eliminated : 0
% 59.88/9.21 % Clauses deleted for lack of memory : 0
% 59.88/9.21 % Backward-subsumed : 318
% 59.88/9.21 % Backward-rewritten : 636
% 59.88/9.21 % Generated clauses : 367853
% 59.88/9.21 % ...of the previous two non-redundant : 325080
% 59.88/9.21 % ...aggressively subsumed : 0
% 59.88/9.21 % Contextual simplify-reflections : 194
% 59.88/9.21 % Paramodulations : 367837
% 59.88/9.21 % Factorizations : 16
% 59.88/9.21 % NegExts : 0
% 59.88/9.21 % Equation resolutions : 0
% 59.88/9.21 % Disequality decompositions : 0
% 59.88/9.21 % Total rewrite steps : 141932
% 59.88/9.21 % ...of those cached : 140939
% 59.88/9.21 % Propositional unsat checks : 0
% 59.88/9.21 % Propositional check models : 0
% 59.88/9.21 % Propositional check unsatisfiable : 0
% 59.88/9.21 % Propositional clauses : 0
% 59.88/9.21 % Propositional clauses after purity: 0
% 59.88/9.21 % Propositional unsat core size : 0
% 59.88/9.21 % Propositional preprocessing time : 0.000
% 59.88/9.21 % Propositional encoding time : 0.000
% 59.88/9.21 % Propositional solver time : 0.000
% 59.88/9.21 % Success case prop preproc time : 0.000
% 59.88/9.21 % Success case prop encoding time : 0.000
% 59.88/9.21 % Success case prop solver time : 0.000
% 59.88/9.21 % Current number of processed clauses : 5884
% 59.88/9.21 % Positive orientable unit clauses : 994
% 59.88/9.21 % Positive unorientable unit clauses: 0
% 59.88/9.21 % Negative unit clauses : 2
% 59.88/9.21 % Non-unit-clauses : 4888
% 59.88/9.21 % Current number of unprocessed clauses: 306997
% 59.88/9.21 % ...number of literals in the above : 771560
% 59.88/9.21 % Current number of archived formulas : 0
% 59.88/9.21 % Current number of archived clauses : 983
% 59.88/9.21 % Clause-clause subsumption calls (NU) : 1221246
% 59.88/9.21 % Rec. Clause-clause subsumption calls : 987108
% 59.88/9.21 % Non-unit clause-clause subsumptions : 8077
% 59.88/9.21 % Unit Clause-clause subsumption calls : 67625
% 59.88/9.21 % Rewrite failures with RHS unbound : 0
% 59.88/9.21 % BW rewrite match attempts : 1816
% 59.88/9.21 % BW rewrite match successes : 485
% 59.88/9.21 % Condensation attempts : 0
% 59.88/9.21 % Condensation successes : 0
% 59.88/9.21 % Termbank termtop insertions : 5905818
% 59.88/9.21 % Search garbage collected termcells : 71
% 59.88/9.21
% 59.88/9.21 % -------------------------------------------------
% 59.88/9.21 % User time : 8.210 s
% 59.88/9.21 % System time : 0.295 s
% 59.88/9.21 % Total time : 8.504 s
% 59.88/9.21 % Maximum resident set size: 3660 pages
% 59.88/9.21
% 59.88/9.21 % -------------------------------------------------
% 59.88/9.21 % User time : 40.848 s
% 59.88/9.21 % System time : 1.447 s
% 59.88/9.21 % Total time : 42.295 s
% 59.88/9.21 % Maximum resident set size: 4608 pages
% 59.88/9.21 % E exiting
%------------------------------------------------------------------------------