%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG037-2 : 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 : 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 02:06:08 PM UTC 2026
% Result : Unsatisfiable 19.21s 3.21s
% Output : CNFRefutation 19.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 52 ( 24 unt; 0 nHn; 37 RR)
% Number of literals : 104 ( 0 equ; 55 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 119 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(sum_substitution3,axiom,
( ~ sum(X3,X4,X1)
| ~ equalish(X1,X2)
| sum(X3,X4,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution3) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(sum_substitution2,axiom,
( ~ sum(X3,X1,X4)
| ~ equalish(X1,X2)
| sum(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_substitution2) ).
cnf(additive_inverse2,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(product_substitution2,axiom,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution2) ).
cnf(additive_inverse_substitution,axiom,
( ~ equalish(X1,X2)
| equalish(additive_inverse(X1),additive_inverse(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_substitution) ).
cnf(multiplicative_identity2,axiom,
product(X1,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
cnf(a_inverse_times_b,hypothesis,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
cnf(prove_sum_is_additive_identity,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
cnf(a_times_b,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(c_0_14,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_15,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_16,plain,
( ~ sum(X3,X4,X1)
| ~ equalish(X1,X2)
| sum(X3,X4,X2) ),
inference(fof_simplification,[status(thm)],[sum_substitution3]) ).
cnf(c_0_17,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| equalish(X3,X4) ),
c_0_14 ).
cnf(c_0_18,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_19,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_15 ).
cnf(c_0_20,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_21,plain,
( ~ sum(X3,X4,X1)
| ~ equalish(X1,X2)
| sum(X3,X4,X2) ),
c_0_16 ).
cnf(c_0_22,plain,
( ~ sum(X2,additive_identity,X1)
| equalish(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
sum(X1,X2,add(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( ~ sum(X3,X1,X4)
| ~ equalish(X1,X2)
| sum(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[sum_substitution2]) ).
cnf(c_0_25,axiom,
sum(X1,additive_inverse(X1),additive_identity),
additive_inverse2 ).
cnf(c_0_26,plain,
( ~ equalish(X1,X2)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_27,plain,
equalish(add(additive_identity,X1),X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_29,plain,
( ~ sum(X3,X1,X4)
| ~ equalish(X1,X2)
| sum(X3,X2,X4) ),
c_0_24 ).
cnf(c_0_30,plain,
sum(additive_inverse(X1),X1,additive_identity),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_31,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
inference(fof_simplification,[status(thm)],[product_substitution2]) ).
cnf(c_0_32,plain,
( ~ equalish(X1,X2)
| equalish(additive_inverse(X1),additive_inverse(X2)) ),
inference(fof_simplification,[status(thm)],[additive_inverse_substitution]) ).
cnf(c_0_33,plain,
sum(add(additive_identity,X1),additive_identity,X1),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_28 ).
cnf(c_0_35,axiom,
product(X1,additive_identity,additive_identity),
multiplicative_identity2 ).
cnf(c_0_36,plain,
( ~ equalish(X1,X2)
| sum(additive_inverse(X1),X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( ~ product(X3,X1,X4)
| ~ equalish(X1,X2)
| product(X3,X2,X4) ),
c_0_31 ).
cnf(c_0_38,hypothesis,
product(a,additive_inverse(b),c),
a_inverse_times_b ).
cnf(c_0_39,plain,
( ~ equalish(X1,X2)
| equalish(additive_inverse(X1),additive_inverse(X2)) ),
c_0_32 ).
cnf(c_0_40,plain,
equalish(X1,add(additive_identity,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_41,plain,
( ~ sum(X5,X4,additive_identity)
| ~ product(X3,X5,X1)
| ~ product(X3,X4,X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
sum(additive_inverse(add(additive_identity,X1)),X1,additive_identity),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_43,hypothesis,
( ~ equalish(additive_inverse(b),X1)
| product(a,X1,c) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
equalish(additive_inverse(X1),additive_inverse(add(additive_identity,X1))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
( ~ product(X3,X4,X2)
| ~ product(X3,additive_inverse(add(additive_identity,X4)),X1)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,hypothesis,
product(a,additive_inverse(add(additive_identity,b)),c),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
~ sum(c,d,additive_identity),
inference(fof_simplification,[status(thm)],[prove_sum_is_additive_identity]) ).
cnf(c_0_48,hypothesis,
( ~ product(a,b,X1)
| sum(c,X1,additive_identity) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,hypothesis,
product(a,b,d),
a_times_b ).
cnf(c_0_50,negated_conjecture,
~ sum(c,d,additive_identity),
c_0_47 ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG037-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n012.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:14:52 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 19.21/3.21 % Version: 3.5.1
% 19.21/3.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.21/3.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.21/3.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.21/3.21 % Starting new_bool_3 with 300s (1) cores
% 19.21/3.21 % Starting new_bool_1 with 300s (1) cores
% 19.21/3.21 % Starting sh5l with 300s (1) cores
% 19.21/3.21 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1539871 completed with status 0
% 19.21/3.21 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 19.21/3.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.21/3.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.21/3.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.21/3.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.21/3.21 % No SInE strategy applied
% 19.21/3.21 % Search class: FHUNM-FFMF21-SFFFFFNN
% 19.21/3.21 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 19.21/3.21 % Starting SubtermCWHack with 136s (1) cores
% 19.21/3.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.21/3.21 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 19.21/3.21 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 19.21/3.21 % Starting new_bool_3 with 136s (1) cores
% 19.21/3.21 % G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with pid 1539880 completed with status 0
% 19.21/3.21 % Result found by G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A
% 19.21/3.21 % Preprocessing class: FSMSSMSSSSSNFFN.
% 19.21/3.21 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 19.21/3.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 19.21/3.21 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 19.21/3.21 % No SInE strategy applied
% 19.21/3.21 % Search class: FHUNM-FFMF21-SFFFFFNN
% 19.21/3.21 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 19.21/3.21 % Starting SubtermCWHack with 136s (1) cores
% 19.21/3.21 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 19.21/3.21 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 19.21/3.21 % Starting G-E--_107_C09_12_F1_PI_AE_Q4_CS_SP_PS_S064A with 136s (1) cores
% 19.21/3.21 % Preprocessing time : 0.001 s
% 19.21/3.21 % Presaturation interreduction done
% 19.21/3.21
% 19.21/3.21 % Proof found!
% 19.21/3.21 % SZS status Unsatisfiable
% 19.21/3.21 % SZS output start CNFRefutation
% See solution above
% 19.21/3.21 % Parsed axioms : 29
% 19.21/3.21 % Removed by relevancy pruning/SinE : 0
% 19.21/3.21 % Initial clauses : 29
% 19.21/3.21 % Removed in clause preprocessing : 0
% 19.21/3.21 % Initial clauses in saturation : 29
% 19.21/3.21 % Processed clauses : 8852
% 19.21/3.21 % ...of these trivial : 2980
% 19.21/3.21 % ...subsumed : 2777
% 19.21/3.21 % ...remaining for further processing : 3095
% 19.21/3.21 % Other redundant clauses eliminated : 0
% 19.21/3.21 % Clauses deleted for lack of memory : 0
% 19.21/3.21 % Backward-subsumed : 223
% 19.21/3.21 % Backward-rewritten : 258
% 19.21/3.21 % Generated clauses : 290834
% 19.21/3.21 % ...of the previous two non-redundant : 255516
% 19.21/3.21 % ...aggressively subsumed : 0
% 19.21/3.21 % Contextual simplify-reflections : 0
% 19.21/3.21 % Paramodulations : 290834
% 19.21/3.21 % Factorizations : 0
% 19.21/3.21 % NegExts : 0
% 19.21/3.21 % Equation resolutions : 0
% 19.21/3.21 % Disequality decompositions : 0
% 19.21/3.21 % Total rewrite steps : 39224
% 19.21/3.21 % ...of those cached : 34335
% 19.21/3.21 % Propositional unsat checks : 0
% 19.21/3.21 % Propositional check models : 0
% 19.21/3.21 % Propositional check unsatisfiable : 0
% 19.21/3.21 % Propositional clauses : 0
% 19.21/3.21 % Propositional clauses after purity: 0
% 19.21/3.21 % Propositional unsat core size : 0
% 19.21/3.21 % Propositional preprocessing time : 0.000
% 19.21/3.21 % Propositional encoding time : 0.000
% 19.21/3.21 % Propositional solver time : 0.000
% 19.21/3.21 % Success case prop preproc time : 0.000
% 19.21/3.21 % Success case prop encoding time : 0.000
% 19.21/3.21 % Success case prop solver time : 0.000
% 19.21/3.21 % Current number of processed clauses : 2585
% 19.21/3.21 % Positive orientable unit clauses : 991
% 19.21/3.21 % Positive unorientable unit clauses: 0
% 19.21/3.21 % Negative unit clauses : 1
% 19.21/3.21 % Non-unit-clauses : 1593
% 19.21/3.21 % Current number of unprocessed clauses: 245278
% 19.21/3.21 % ...number of literals in the above : 306665
% 19.21/3.21 % Current number of archived formulas : 0
% 19.21/3.21 % Current number of archived clauses : 510
% 19.21/3.21 % Clause-clause subsumption calls (NU) : 582215
% 19.21/3.21 % Rec. Clause-clause subsumption calls : 513238
% 19.21/3.21 % Non-unit clause-clause subsumptions : 3000
% 19.21/3.21 % Unit Clause-clause subsumption calls : 4828
% 19.21/3.21 % Rewrite failures with RHS unbound : 0
% 19.21/3.21 % BW rewrite match attempts : 30173
% 19.21/3.21 % BW rewrite match successes : 258
% 19.21/3.21 % Condensation attempts : 0
% 19.21/3.21 % Condensation successes : 0
% 19.21/3.21 % Termbank termtop insertions : 3517930
% 19.21/3.21 % Search garbage collected termcells : 90
% 19.21/3.21
% 19.21/3.21 % -------------------------------------------------
% 19.21/3.21 % User time : 2.589 s
% 19.21/3.21 % System time : 0.129 s
% 19.21/3.21 % Total time : 2.719 s
% 19.21/3.21 % Maximum resident set size: 3656 pages
% 19.21/3.21
% 19.21/3.21 % -------------------------------------------------
% 19.21/3.21 % User time : 12.918 s
% 19.21/3.21 % System time : 0.597 s
% 19.21/3.21 % Total time : 13.515 s
% 19.21/3.21 % Maximum resident set size: 4864 pages
% 19.21/3.21 % E exiting
%------------------------------------------------------------------------------