%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 11:56:07 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 42 ( 12 unt; 8 nHn; 32 RR)
% Number of literals : 85 ( 0 equ; 46 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 57 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(commutativity_of_product,axiom,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_product) ).
cnf(product_to_inverse,axiom,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_inverse) ).
cnf(square_to_0,axiom,
( ~ product(X1,X1,additive_identity)
| ~ product(X1,X2,X3)
| product(X3,X3,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',square_to_0) ).
cnf(inverse_and_identity,axiom,
( product(X1,X1,additive_identity)
| product(X1,multiplicative_inverse(X1),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_and_identity) ).
cnf(not_abelian,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_abelian) ).
cnf(product_and_greater_than_0,axiom,
( ~ greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ product(X1,X2,X3)
| greater_than_0(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_greater_than_0) ).
cnf(right_identity,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(inverse_greater_than_0,axiom,
( ~ greater_than_0(additive_inverse(X1))
| ~ greater_than_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_greater_than_0) ).
cnf(greater_than_0_square,axiom,
( ~ product(X1,X1,additive_identity)
| ~ greater_than_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greater_than_0_square) ).
cnf(product_and_inverse,axiom,
( greater_than_0(additive_inverse(X1))
| product(X1,X1,additive_identity)
| greater_than_0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_and_inverse) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
cnf(a_greater_than_0,hypothesis,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_greater_than_0) ).
cnf(c_0_12,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_product]) ).
cnf(c_0_13,plain,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
inference(fof_simplification,[status(thm)],[product_to_inverse]) ).
cnf(c_0_14,plain,
( ~ product(X1,X1,additive_identity)
| ~ product(X1,X2,X3)
| product(X3,X3,additive_identity) ),
inference(fof_simplification,[status(thm)],[square_to_0]) ).
cnf(c_0_15,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_12 ).
cnf(c_0_16,axiom,
( product(X1,X1,additive_identity)
| product(X1,multiplicative_inverse(X1),multiplicative_identity) ),
inverse_and_identity ).
cnf(c_0_17,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(fof_simplification,[status(thm)],[not_abelian]) ).
cnf(c_0_18,plain,
( ~ greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ product(X1,X2,X3)
| greater_than_0(X3) ),
inference(fof_simplification,[status(thm)],[product_and_greater_than_0]) ).
cnf(c_0_19,plain,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
c_0_13 ).
cnf(c_0_20,axiom,
product(X1,multiplicative_identity,X1),
right_identity ).
cnf(c_0_21,plain,
( ~ greater_than_0(additive_inverse(X1))
| ~ greater_than_0(X1) ),
inference(fof_simplification,[status(thm)],[inverse_greater_than_0]) ).
cnf(c_0_22,plain,
( ~ product(X1,X1,additive_identity)
| ~ product(X1,X2,X3)
| product(X3,X3,additive_identity) ),
c_0_14 ).
cnf(c_0_23,plain,
( product(X1,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
c_0_17 ).
cnf(c_0_25,plain,
( ~ product(X1,X1,additive_identity)
| ~ greater_than_0(X1) ),
inference(fof_simplification,[status(thm)],[greater_than_0_square]) ).
cnf(c_0_26,plain,
( ~ greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ product(X1,X2,X3)
| greater_than_0(X3) ),
c_0_18 ).
cnf(c_0_27,plain,
product(X1,additive_inverse(multiplicative_identity),additive_inverse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_28,plain,
( ~ greater_than_0(additive_inverse(X1))
| ~ greater_than_0(X1) ),
c_0_21 ).
cnf(c_0_29,plain,
( ~ product(multiplicative_inverse(X1),multiplicative_inverse(X1),additive_identity)
| product(X1,X1,additive_identity) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,axiom,
( greater_than_0(additive_inverse(X1))
| product(X1,X1,additive_identity)
| greater_than_0(X1) ),
product_and_inverse ).
cnf(c_0_31,plain,
( product(X1,X1,additive_identity)
| product(X1,additive_inverse(multiplicative_inverse(X1)),additive_inverse(multiplicative_identity)) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_32,plain,
( ~ product(X1,X1,additive_identity)
| ~ greater_than_0(X1) ),
c_0_25 ).
cnf(c_0_33,plain,
( ~ greater_than_0(X1)
| ~ greater_than_0(additive_inverse(multiplicative_identity)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_34,plain,
( product(X1,X1,additive_identity)
| greater_than_0(multiplicative_inverse(X1))
| greater_than_0(additive_inverse(multiplicative_inverse(X1))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
inference(fof_simplification,[status(thm)],[prove_a_inverse_greater_than_0]) ).
cnf(c_0_36,plain,
( ~ greater_than_0(X1)
| ~ greater_than_0(additive_inverse(multiplicative_inverse(X1))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_31]),c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
( ~ greater_than_0(X1)
| greater_than_0(multiplicative_inverse(X1))
| greater_than_0(additive_inverse(multiplicative_inverse(X1))) ),
inference(spm,[status(thm)],[c_0_32,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
c_0_35 ).
cnf(c_0_39,plain,
( ~ greater_than_0(X1)
| greater_than_0(multiplicative_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,hypothesis,
greater_than_0(a),
a_greater_than_0 ).
cnf(c_0_41,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 21 12:54:14 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.12/0.44 % Version: 3.5.1
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.44 % Starting sh5l with 300s (1) cores
% 0.12/0.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1926093 completed with status 0
% 0.12/0.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.44 % No SInE strategy applied
% 0.12/0.44 % Search class: FGHNF-FFSF11-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.12/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.44 % Starting new_bool_1 with 136s (1) cores
% 0.12/0.44 % new_bool_3 with pid 1926102 completed with status 0
% 0.12/0.44 % Result found by new_bool_3
% 0.12/0.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.12/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.12/0.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.44 % No SInE strategy applied
% 0.12/0.44 % Search class: FGHNF-FFSF11-SFFFFFNN
% 0.12/0.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.44 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.12/0.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.12/0.44 % Starting new_bool_3 with 136s (1) cores
% 0.12/0.44 % Preprocessing time : 0.001 s
% 0.12/0.44 % Presaturation interreduction done
% 0.12/0.44
% 0.12/0.44 % Proof found!
% 0.12/0.44 % SZS status Unsatisfiable
% 0.12/0.44 % SZS output start CNFRefutation
% See solution above
% 0.12/0.44 % Parsed axioms : 14
% 0.12/0.44 % Removed by relevancy pruning/SinE : 0
% 0.12/0.44 % Initial clauses : 14
% 0.12/0.44 % Removed in clause preprocessing : 0
% 0.12/0.44 % Initial clauses in saturation : 14
% 0.12/0.44 % Processed clauses : 81
% 0.12/0.44 % ...of these trivial : 2
% 0.12/0.44 % ...subsumed : 20
% 0.12/0.44 % ...remaining for further processing : 59
% 0.12/0.44 % Other redundant clauses eliminated : 0
% 0.12/0.44 % Clauses deleted for lack of memory : 0
% 0.12/0.44 % Backward-subsumed : 3
% 0.12/0.44 % Backward-rewritten : 0
% 0.12/0.44 % Generated clauses : 146
% 0.12/0.44 % ...of the previous two non-redundant : 111
% 0.12/0.44 % ...aggressively subsumed : 0
% 0.12/0.44 % Contextual simplify-reflections : 6
% 0.12/0.44 % Paramodulations : 146
% 0.12/0.44 % Factorizations : 0
% 0.12/0.44 % NegExts : 0
% 0.12/0.44 % Equation resolutions : 0
% 0.12/0.44 % Disequality decompositions : 0
% 0.12/0.44 % Total rewrite steps : 18
% 0.12/0.44 % ...of those cached : 4
% 0.12/0.44 % Propositional unsat checks : 0
% 0.12/0.44 % Propositional check models : 0
% 0.12/0.44 % Propositional check unsatisfiable : 0
% 0.12/0.44 % Propositional clauses : 0
% 0.12/0.44 % Propositional clauses after purity: 0
% 0.12/0.44 % Propositional unsat core size : 0
% 0.12/0.44 % Propositional preprocessing time : 0.000
% 0.12/0.44 % Propositional encoding time : 0.000
% 0.12/0.44 % Propositional solver time : 0.000
% 0.12/0.44 % Success case prop preproc time : 0.000
% 0.12/0.44 % Success case prop encoding time : 0.000
% 0.12/0.44 % Success case prop solver time : 0.000
% 0.12/0.44 % Current number of processed clauses : 42
% 0.12/0.44 % Positive orientable unit clauses : 10
% 0.12/0.44 % Positive unorientable unit clauses: 0
% 0.12/0.44 % Negative unit clauses : 2
% 0.12/0.44 % Non-unit-clauses : 30
% 0.12/0.44 % Current number of unprocessed clauses: 56
% 0.12/0.44 % ...number of literals in the above : 148
% 0.12/0.44 % Current number of archived formulas : 0
% 0.12/0.44 % Current number of archived clauses : 17
% 0.12/0.44 % Clause-clause subsumption calls (NU) : 143
% 0.12/0.44 % Rec. Clause-clause subsumption calls : 130
% 0.12/0.44 % Non-unit clause-clause subsumptions : 27
% 0.12/0.44 % Unit Clause-clause subsumption calls : 2
% 0.12/0.44 % Rewrite failures with RHS unbound : 0
% 0.12/0.44 % BW rewrite match attempts : 7
% 0.12/0.44 % BW rewrite match successes : 1
% 0.12/0.44 % Condensation attempts : 0
% 0.12/0.44 % Condensation successes : 0
% 0.12/0.44 % Termbank termtop insertions : 2425
% 0.12/0.44 % Search garbage collected termcells : 22
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.005 s
% 0.12/0.44 % System time : 0.005 s
% 0.12/0.44 % Total time : 0.010 s
% 0.12/0.44 % Maximum resident set size: 3636 pages
% 0.12/0.44
% 0.12/0.44 % -------------------------------------------------
% 0.12/0.44 % User time : 0.032 s
% 0.12/0.44 % System time : 0.017 s
% 0.12/0.44 % Total time : 0.050 s
% 0.12/0.44 % Maximum resident set size: 4608 pages
% 0.12/0.44 % E exiting
%------------------------------------------------------------------------------