%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 11:50:12 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.52s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of clauses : 41 ( 11 unt; 8 nHn; 33 RR)
% Number of literals : 88 ( 0 equ; 49 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 : 60 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',product_and_greater_than_0) ).
cnf(product_to_inverse,axiom,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',square_to_0) ).
cnf(commutativity_of_product,axiom,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_product) ).
cnf(inverse_greater_than_0,axiom,
( ~ greater_than_0(additive_inverse(X1))
| ~ greater_than_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_greater_than_0) ).
cnf(product_and_inverse,axiom,
( greater_than_0(additive_inverse(X1))
| product(X1,X1,additive_identity)
| greater_than_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_inverse) ).
cnf(inverse_and_identity,axiom,
( product(X1,X1,additive_identity)
| product(X1,multiplicative_inverse(X1),multiplicative_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_and_identity) ).
cnf(not_abelian,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_abelian) ).
cnf(greater_than_0_square,axiom,
( ~ product(X1,X1,additive_identity)
| ~ greater_than_0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greater_than_0_square) ).
cnf(right_identity,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(prove_a_inverse_greater_than_0,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
cnf(a_greater_than_0,hypothesis,
greater_than_0(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_greater_than_0) ).
cnf(c_0_12,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_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) ),
inference(fof_simplification,[status(thm)],[commutativity_of_product]) ).
cnf(c_0_16,plain,
( ~ greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ product(X1,X2,X3)
| greater_than_0(X3) ),
c_0_12 ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X3)
| product(X1,additive_inverse(X2),additive_inverse(X3)) ),
c_0_13 ).
cnf(c_0_18,plain,
( ~ greater_than_0(additive_inverse(X1))
| ~ greater_than_0(X1) ),
inference(fof_simplification,[status(thm)],[inverse_greater_than_0]) ).
cnf(c_0_19,plain,
( ~ product(X1,X1,additive_identity)
| ~ product(X1,X2,X3)
| product(X3,X3,additive_identity) ),
c_0_14 ).
cnf(c_0_20,axiom,
( greater_than_0(additive_inverse(X1))
| product(X1,X1,additive_identity)
| greater_than_0(X1) ),
product_and_inverse ).
cnf(c_0_21,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_15 ).
cnf(c_0_22,axiom,
( product(X1,X1,additive_identity)
| product(X1,multiplicative_inverse(X1),multiplicative_identity) ),
inverse_and_identity ).
cnf(c_0_23,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(fof_simplification,[status(thm)],[not_abelian]) ).
cnf(c_0_24,plain,
( ~ product(X1,X1,additive_identity)
| ~ greater_than_0(X1) ),
inference(fof_simplification,[status(thm)],[greater_than_0_square]) ).
cnf(c_0_25,plain,
( ~ product(X3,X2,X1)
| ~ greater_than_0(X3)
| ~ greater_than_0(additive_inverse(X2))
| greater_than_0(additive_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,axiom,
product(X1,multiplicative_identity,X1),
right_identity ).
cnf(c_0_27,plain,
( ~ greater_than_0(additive_inverse(X1))
| ~ greater_than_0(X1) ),
c_0_18 ).
cnf(c_0_28,plain,
( ~ product(X1,X3,X2)
| product(X2,X2,additive_identity)
| greater_than_0(X1)
| greater_than_0(additive_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,plain,
( product(X1,X1,additive_identity)
| product(multiplicative_inverse(X1),X1,multiplicative_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
c_0_23 ).
cnf(c_0_31,plain,
( ~ product(X1,X1,additive_identity)
| ~ greater_than_0(X1) ),
c_0_24 ).
cnf(c_0_32,plain,
( ~ greater_than_0(X1)
| ~ greater_than_0(additive_inverse(multiplicative_identity)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_33,plain,
( product(X1,X1,additive_identity)
| greater_than_0(multiplicative_inverse(X1))
| greater_than_0(additive_inverse(multiplicative_inverse(X1))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
inference(fof_simplification,[status(thm)],[prove_a_inverse_greater_than_0]) ).
cnf(c_0_35,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_25,c_0_22]),c_0_31]),c_0_32]) ).
cnf(c_0_36,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_31,c_0_33]) ).
cnf(c_0_37,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
c_0_34 ).
cnf(c_0_38,plain,
( ~ greater_than_0(X1)
| greater_than_0(multiplicative_inverse(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,hypothesis,
greater_than_0(a),
a_greater_than_0 ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]),
[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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.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 12:52:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.46 Running first-order theorem proving
% 0.14/0.46 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
% 0.14/0.52 % Version: 3.5.1
% 0.14/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.52 % Starting sh5l with 300s (1) cores
% 0.14/0.52 % new_bool_3 with pid 912428 completed with status 0
% 0.14/0.52 % Result found by new_bool_3
% 0.14/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.52 % Search class: FGHNF-FFSF11-SFFFFFNN
% 0.14/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.52 % SubtermCWHack with pid 912431 completed with status 0
% 0.14/0.52 % Result found by SubtermCWHack
% 0.14/0.52 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.52 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.52 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.52 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.52 % Search class: FGHNF-FFSF11-SFFFFFNN
% 0.14/0.52 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.52 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.52 % Preprocessing time : 0.002 s
% 0.14/0.52
% 0.14/0.52 % Proof found!
% 0.14/0.52 % SZS status Unsatisfiable
% 0.14/0.52 % SZS output start CNFRefutation
% See solution above
% 0.14/0.52 % Parsed axioms : 14
% 0.14/0.52 % Removed by relevancy pruning/SinE : 0
% 0.14/0.52 % Initial clauses : 14
% 0.14/0.52 % Removed in clause preprocessing : 0
% 0.14/0.52 % Initial clauses in saturation : 14
% 0.14/0.52 % Processed clauses : 256
% 0.14/0.52 % ...of these trivial : 4
% 0.14/0.52 % ...subsumed : 162
% 0.14/0.52 % ...remaining for further processing : 90
% 0.14/0.52 % Other redundant clauses eliminated : 0
% 0.14/0.52 % Clauses deleted for lack of memory : 0
% 0.14/0.52 % Backward-subsumed : 2
% 0.14/0.52 % Backward-rewritten : 4
% 0.14/0.52 % Generated clauses : 694
% 0.14/0.52 % ...of the previous two non-redundant : 622
% 0.14/0.52 % ...aggressively subsumed : 0
% 0.14/0.52 % Contextual simplify-reflections : 7
% 0.14/0.52 % Paramodulations : 694
% 0.14/0.52 % Factorizations : 0
% 0.14/0.52 % NegExts : 0
% 0.14/0.52 % Equation resolutions : 0
% 0.14/0.52 % Disequality decompositions : 0
% 0.14/0.52 % Total rewrite steps : 64
% 0.14/0.52 % ...of those cached : 53
% 0.14/0.52 % Propositional unsat checks : 0
% 0.14/0.52 % Propositional check models : 0
% 0.14/0.52 % Propositional check unsatisfiable : 0
% 0.14/0.52 % Propositional clauses : 0
% 0.14/0.52 % Propositional clauses after purity: 0
% 0.14/0.52 % Propositional unsat core size : 0
% 0.14/0.52 % Propositional preprocessing time : 0.000
% 0.14/0.52 % Propositional encoding time : 0.000
% 0.14/0.52 % Propositional solver time : 0.000
% 0.14/0.52 % Success case prop preproc time : 0.000
% 0.14/0.52 % Success case prop encoding time : 0.000
% 0.14/0.52 % Success case prop solver time : 0.000
% 0.14/0.52 % Current number of processed clauses : 84
% 0.14/0.52 % Positive orientable unit clauses : 12
% 0.14/0.52 % Positive unorientable unit clauses: 0
% 0.14/0.52 % Negative unit clauses : 2
% 0.14/0.52 % Non-unit-clauses : 70
% 0.14/0.52 % Current number of unprocessed clauses: 378
% 0.14/0.52 % ...number of literals in the above : 1144
% 0.14/0.52 % Current number of archived formulas : 0
% 0.14/0.52 % Current number of archived clauses : 6
% 0.14/0.52 % Clause-clause subsumption calls (NU) : 1720
% 0.14/0.52 % Rec. Clause-clause subsumption calls : 1703
% 0.14/0.52 % Non-unit clause-clause subsumptions : 171
% 0.14/0.52 % Unit Clause-clause subsumption calls : 0
% 0.14/0.52 % Rewrite failures with RHS unbound : 0
% 0.14/0.52 % BW rewrite match attempts : 30
% 0.14/0.52 % BW rewrite match successes : 1
% 0.14/0.52 % Condensation attempts : 0
% 0.14/0.52 % Condensation successes : 0
% 0.14/0.52 % Termbank termtop insertions : 10062
% 0.14/0.52 % Search garbage collected termcells : 22
% 0.14/0.52
% 0.14/0.52 % -------------------------------------------------
% 0.14/0.52 % User time : 0.023 s
% 0.14/0.52 % System time : 0.004 s
% 0.14/0.52 % Total time : 0.028 s
% 0.14/0.52 % Maximum resident set size: 3636 pages
% 0.14/0.52
% 0.14/0.52 % -------------------------------------------------
% 0.14/0.52 % User time : 0.027 s
% 0.14/0.52 % System time : 0.009 s
% 0.14/0.52 % Total time : 0.036 s
% 0.14/0.52 % Maximum resident set size: 4608 pages
% 0.14/0.52 % E exiting
%------------------------------------------------------------------------------