%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG038-1 : 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 : n004.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 02:05:36 PM UTC 2026
% Result : Unsatisfiable 0.26s 0.56s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 55 ( 25 unt; 0 nHn; 37 RR)
% Number of literals : 117 ( 22 equ; 65 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(some_property,hypothesis,
( X1 != additive_identity
| product(X1,h(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',some_property) ).
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/Axioms/RNG001-0.ax',distributivity1) ).
cnf(associativity_of_addition2,axiom,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(associativity_of_multiplication2,axiom,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
cnf(a_times_b,hypothesis,
product(a,b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(left_inverse,axiom,
sum(additive_inverse(X1),X1,additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',left_inverse) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(prove_b_is_additive_identity,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
cnf(c_0_13,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_14,hypothesis,
( X1 != additive_identity
| product(X1,h(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[some_property]) ).
cnf(c_0_15,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_16,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition2]) ).
cnf(c_0_17,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_13 ).
cnf(c_0_18,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_19,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_multiplication2]) ).
cnf(c_0_20,hypothesis,
( X1 != additive_identity
| product(X1,h(X1,X2),X2) ),
c_0_14 ).
cnf(c_0_21,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_15 ).
cnf(c_0_22,hypothesis,
product(a,b,additive_identity),
a_times_b ).
cnf(c_0_23,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
c_0_16 ).
cnf(c_0_24,axiom,
sum(additive_inverse(X1),X1,additive_identity),
left_inverse ).
cnf(c_0_25,plain,
( ~ sum(X2,additive_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_27,plain,
( ~ product(X1,X5,X6)
| ~ product(X2,X4,X5)
| ~ product(X1,X2,X3)
| product(X3,X4,X6) ),
c_0_19 ).
cnf(c_0_28,hypothesis,
product(additive_identity,h(additive_identity,X1),X1),
inference(er,[status(thm)],[c_0_20]) ).
cnf(c_0_29,hypothesis,
( ~ sum(X4,X3,b)
| ~ product(a,X4,X1)
| ~ product(a,X3,X2)
| sum(X1,X2,additive_identity) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( ~ sum(X4,additive_identity,X3)
| ~ sum(X4,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_33,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_34,hypothesis,
( ~ product(X4,X2,X3)
| ~ product(X4,additive_identity,X1)
| product(X1,h(additive_identity,X2),X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,hypothesis,
( ~ sum(X2,b,b)
| ~ product(a,X2,X1)
| sum(X1,additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_36,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_37,plain,
( ~ sum(X3,additive_inverse(X2),X1)
| sum(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_31]) ).
cnf(c_0_38,plain,
( ~ sum(X2,additive_inverse(X2),X1)
| X1 = additive_identity ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_39,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_33 ).
cnf(c_0_40,hypothesis,
( ~ product(a,additive_identity,X1)
| product(X1,h(additive_identity,b),additive_identity) ),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_41,hypothesis,
( ~ sum(X1,b,b)
| sum(multiply(a,X1),additive_identity,additive_identity) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_42,plain,
sum(add(X1,additive_inverse(X2)),X2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_26]) ).
cnf(c_0_43,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_44,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_36]) ).
cnf(c_0_45,hypothesis,
product(multiply(a,additive_identity),h(additive_identity,b),additive_identity),
inference(spm,[status(thm)],[c_0_40,c_0_36]) ).
cnf(c_0_46,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_47,hypothesis,
sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_48,hypothesis,
( ~ product(additive_identity,h(additive_identity,X2),X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_39,c_0_28]) ).
cnf(c_0_49,negated_conjecture,
b != additive_identity,
inference(fof_simplification,[status(thm)],[prove_b_is_additive_identity]) ).
cnf(c_0_50,hypothesis,
multiply(multiply(a,additive_identity),h(additive_identity,b)) = additive_identity,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,hypothesis,
multiply(a,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_31]) ).
cnf(c_0_52,hypothesis,
multiply(additive_identity,h(additive_identity,X1)) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
cnf(c_0_53,negated_conjecture,
b != additive_identity,
c_0_49 ).
cnf(c_0_54,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 04:14:50 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.56 % Version: 3.5.1
% 0.26/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.26/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.26/0.56 % Starting sh5l with 300s (1) cores
% 0.26/0.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2220245 completed with status 0
% 0.26/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.26/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.56 % No SInE strategy applied
% 0.26/0.56 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.26/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.26/0.56 % Starting new_bool_3 with 136s (1) cores
% 0.26/0.56 % Starting new_bool_1 with 136s (1) cores
% 0.26/0.56 % G-E--_208_C18_F1_SE_CS_SP_PS_S4d with pid 2220252 completed with status 0
% 0.26/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4d
% 0.26/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.26/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.26/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.26/0.56 % No SInE strategy applied
% 0.26/0.56 % Search class: FHUSM-FFMF21-SFFFFFNN
% 0.26/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.26/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.26/0.56 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 0.26/0.56 % Preprocessing time : 0.002 s
% 0.26/0.56 % Presaturation interreduction done
% 0.26/0.56
% 0.26/0.56 % Proof found!
% 0.26/0.56 % SZS status Unsatisfiable
% 0.26/0.56 % SZS output start CNFRefutation
% See solution above
% 0.26/0.56 % Parsed axioms : 21
% 0.26/0.56 % Removed by relevancy pruning/SinE : 0
% 0.26/0.56 % Initial clauses : 21
% 0.26/0.56 % Removed in clause preprocessing : 0
% 0.26/0.56 % Initial clauses in saturation : 21
% 0.26/0.56 % Processed clauses : 238
% 0.26/0.56 % ...of these trivial : 9
% 0.26/0.56 % ...subsumed : 76
% 0.26/0.56 % ...remaining for further processing : 153
% 0.26/0.56 % Other redundant clauses eliminated : 1
% 0.26/0.56 % Clauses deleted for lack of memory : 0
% 0.26/0.56 % Backward-subsumed : 1
% 0.26/0.56 % Backward-rewritten : 8
% 0.26/0.56 % Generated clauses : 706
% 0.26/0.56 % ...of the previous two non-redundant : 445
% 0.26/0.56 % ...aggressively subsumed : 0
% 0.26/0.56 % Contextual simplify-reflections : 0
% 0.26/0.56 % Paramodulations : 705
% 0.26/0.56 % Factorizations : 0
% 0.26/0.56 % NegExts : 0
% 0.26/0.56 % Equation resolutions : 1
% 0.26/0.56 % Disequality decompositions : 0
% 0.26/0.56 % Total rewrite steps : 467
% 0.26/0.56 % ...of those cached : 399
% 0.26/0.56 % Propositional unsat checks : 0
% 0.26/0.56 % Propositional check models : 0
% 0.26/0.56 % Propositional check unsatisfiable : 0
% 0.26/0.56 % Propositional clauses : 0
% 0.26/0.56 % Propositional clauses after purity: 0
% 0.26/0.56 % Propositional unsat core size : 0
% 0.26/0.56 % Propositional preprocessing time : 0.000
% 0.26/0.56 % Propositional encoding time : 0.000
% 0.26/0.56 % Propositional solver time : 0.000
% 0.26/0.56 % Success case prop preproc time : 0.000
% 0.26/0.56 % Success case prop encoding time : 0.000
% 0.26/0.56 % Success case prop solver time : 0.000
% 0.26/0.56 % Current number of processed clauses : 122
% 0.26/0.56 % Positive orientable unit clauses : 33
% 0.26/0.56 % Positive unorientable unit clauses: 1
% 0.26/0.56 % Negative unit clauses : 2
% 0.26/0.56 % Non-unit-clauses : 86
% 0.26/0.56 % Current number of unprocessed clauses: 235
% 0.26/0.56 % ...number of literals in the above : 551
% 0.26/0.56 % Current number of archived formulas : 0
% 0.26/0.56 % Current number of archived clauses : 30
% 0.26/0.56 % Clause-clause subsumption calls (NU) : 1707
% 0.26/0.56 % Rec. Clause-clause subsumption calls : 1392
% 0.26/0.56 % Non-unit clause-clause subsumptions : 73
% 0.26/0.56 % Unit Clause-clause subsumption calls : 3
% 0.26/0.56 % Rewrite failures with RHS unbound : 0
% 0.26/0.56 % BW rewrite match attempts : 66
% 0.26/0.56 % BW rewrite match successes : 18
% 0.26/0.56 % Condensation attempts : 0
% 0.26/0.56 % Condensation successes : 0
% 0.26/0.56 % Termbank termtop insertions : 7929
% 0.26/0.56 % Search garbage collected termcells : 66
% 0.26/0.56
% 0.26/0.56 % -------------------------------------------------
% 0.26/0.56 % User time : 0.027 s
% 0.26/0.56 % System time : 0.005 s
% 0.26/0.56 % Total time : 0.033 s
% 0.26/0.56 % Maximum resident set size: 3648 pages
% 0.26/0.56
% 0.26/0.56 % -------------------------------------------------
% 0.26/0.56 % User time : 0.133 s
% 0.26/0.56 % System time : 0.023 s
% 0.26/0.56 % Total time : 0.156 s
% 0.26/0.56 % Maximum resident set size: 4864 pages
% 0.26/0.56 % E exiting
%------------------------------------------------------------------------------