%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : RNG006-3 : 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 : n015.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 02:06:00 PM UTC 2026
% Result : Unsatisfiable 1.37s 0.68s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of clauses : 52 ( 30 unt; 0 nHn; 41 RR)
% Number of literals : 97 ( 9 equ; 48 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 103 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_of_addition1,axiom,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition1) ).
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(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
cnf(a_times_b,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
cnf(right_inverse,axiom,
sum(X1,additive_inverse(X1),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
cnf(b_plus_inverse_c,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
cnf(a_times_c,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
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(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(aPb_plus_IaPc,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
cnf(prove_a_times_bS_Ic_is_aPb_S__IaPc,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
cnf(c_0_14,plain,
( ~ sum(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
inference(fof_simplification,[status(thm)],[associativity_of_addition1]) ).
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(X3,X4,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X1,X5,X6) ),
c_0_14 ).
cnf(c_0_17,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_18,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_19,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_20,hypothesis,
product(a,b,aPb),
a_times_b ).
cnf(c_0_21,plain,
( ~ sum(X4,X3,X2)
| ~ sum(X1,X4,additive_identity)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
sum(X1,additive_inverse(X1),additive_identity),
right_inverse ).
cnf(c_0_23,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_18 ).
cnf(c_0_24,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
b_plus_inverse_c ).
cnf(c_0_25,hypothesis,
( ~ sum(X4,X3,b)
| ~ product(a,X4,X1)
| ~ product(a,X3,X2)
| sum(X1,X2,aPb) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,hypothesis,
product(a,c,aPc),
a_times_c ).
cnf(c_0_27,plain,
( ~ sum(additive_inverse(X1),X3,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,hypothesis,
sum(additive_inverse(c),b,bS_Ic),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_30,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_31,hypothesis,
( ~ sum(X2,c,b)
| ~ product(a,X2,X1)
| sum(X1,aPc,aPb) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_33,hypothesis,
sum(c,bS_Ic,b),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_29 ).
cnf(c_0_35,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
aPb_plus_IaPc ).
cnf(c_0_36,plain,
( ~ sum(X1,X5,X3)
| ~ sum(X5,X4,X2)
| sum(X1,X2,add(X3,X4)) ),
inference(spm,[status(thm)],[c_0_16,c_0_30]) ).
cnf(c_0_37,hypothesis,
( ~ sum(X1,c,b)
| sum(multiply(a,X1),aPc,aPb) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,hypothesis,
sum(bS_Ic,c,b),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_39,hypothesis,
( ~ sum(aPb,additive_inverse(aPc),X1)
| X1 = aPb_S_IaPc ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_41,plain,
( ~ sum(X1,X3,X2)
| sum(X1,additive_identity,add(X2,additive_inverse(X3))) ),
inference(spm,[status(thm)],[c_0_36,c_0_22]) ).
cnf(c_0_42,hypothesis,
sum(multiply(a,bS_Ic),aPc,aPb),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
add(aPb,additive_inverse(aPc)) = aPb_S_IaPc,
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_44,plain,
( ~ sum(X2,additive_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_45,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_46,hypothesis,
sum(multiply(a,bS_Ic),additive_identity,aPb_S_IaPc),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_47,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_30]) ).
cnf(c_0_48,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(fof_simplification,[status(thm)],[prove_a_times_bS_Ic_is_aPb_S__IaPc]) ).
cnf(c_0_49,hypothesis,
multiply(a,bS_Ic) = aPb_S_IaPc,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_50,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
c_0_48 ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_49]),c_0_50]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.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 04:13:20 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.44 Running first-order theorem proving
% 0.12/0.44 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
% 1.37/0.68 % Version: 3.5.1
% 1.37/0.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.37/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.37/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.37/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.37/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.37/0.68 % Starting sh5l with 300s (1) cores
% 1.37/0.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 529708 completed with status 0
% 1.37/0.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 1.37/0.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.37/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.37/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.37/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.37/0.68 % No SInE strategy applied
% 1.37/0.68 % Search class: FHUSM-FFMS21-SFFFFFNN
% 1.37/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.37/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.37/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.37/0.68 % Starting G-E--_301_C18_F1_URBAN_S0Y with 136s (1) cores
% 1.37/0.68 % Starting new_bool_3 with 136s (1) cores
% 1.37/0.68 % Starting new_bool_1 with 136s (1) cores
% 1.37/0.68 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 529713 completed with status 0
% 1.37/0.68 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 1.37/0.68 % Preprocessing class: FSMSSMSMSSSNFFN.
% 1.37/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.37/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 1.37/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.37/0.68 % No SInE strategy applied
% 1.37/0.68 % Search class: FHUSM-FFMS21-SFFFFFNN
% 1.37/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.37/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.37/0.68 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 1.37/0.68 % Preprocessing time : 0.001 s
% 1.37/0.68 % Presaturation interreduction done
% 1.37/0.68
% 1.37/0.68 % Proof found!
% 1.37/0.68 % SZS status Unsatisfiable
% 1.37/0.68 % SZS output start CNFRefutation
% See solution above
% 1.37/0.68 % Parsed axioms : 22
% 1.37/0.68 % Removed by relevancy pruning/SinE : 0
% 1.37/0.68 % Initial clauses : 22
% 1.37/0.68 % Removed in clause preprocessing : 0
% 1.37/0.68 % Initial clauses in saturation : 22
% 1.37/0.68 % Processed clauses : 1796
% 1.37/0.68 % ...of these trivial : 177
% 1.37/0.68 % ...subsumed : 614
% 1.37/0.68 % ...remaining for further processing : 1005
% 1.37/0.68 % Other redundant clauses eliminated : 0
% 1.37/0.68 % Clauses deleted for lack of memory : 0
% 1.37/0.68 % Backward-subsumed : 35
% 1.37/0.68 % Backward-rewritten : 82
% 1.37/0.68 % Generated clauses : 7184
% 1.37/0.68 % ...of the previous two non-redundant : 4796
% 1.37/0.68 % ...aggressively subsumed : 0
% 1.37/0.68 % Contextual simplify-reflections : 0
% 1.37/0.68 % Paramodulations : 7184
% 1.37/0.68 % Factorizations : 0
% 1.37/0.68 % NegExts : 0
% 1.37/0.68 % Equation resolutions : 0
% 1.37/0.68 % Disequality decompositions : 0
% 1.37/0.68 % Total rewrite steps : 5133
% 1.37/0.68 % ...of those cached : 4660
% 1.37/0.68 % Propositional unsat checks : 0
% 1.37/0.68 % Propositional check models : 0
% 1.37/0.68 % Propositional check unsatisfiable : 0
% 1.37/0.68 % Propositional clauses : 0
% 1.37/0.68 % Propositional clauses after purity: 0
% 1.37/0.68 % Propositional unsat core size : 0
% 1.37/0.68 % Propositional preprocessing time : 0.000
% 1.37/0.68 % Propositional encoding time : 0.000
% 1.37/0.68 % Propositional solver time : 0.000
% 1.37/0.68 % Success case prop preproc time : 0.000
% 1.37/0.68 % Success case prop encoding time : 0.000
% 1.37/0.68 % Success case prop solver time : 0.000
% 1.37/0.68 % Current number of processed clauses : 866
% 1.37/0.68 % Positive orientable unit clauses : 155
% 1.37/0.68 % Positive unorientable unit clauses: 1
% 1.37/0.68 % Negative unit clauses : 2
% 1.37/0.68 % Non-unit-clauses : 708
% 1.37/0.68 % Current number of unprocessed clauses: 2798
% 1.37/0.68 % ...number of literals in the above : 5918
% 1.37/0.68 % Current number of archived formulas : 0
% 1.37/0.68 % Current number of archived clauses : 139
% 1.37/0.68 % Clause-clause subsumption calls (NU) : 55315
% 1.37/0.68 % Rec. Clause-clause subsumption calls : 44754
% 1.37/0.68 % Non-unit clause-clause subsumptions : 642
% 1.37/0.68 % Unit Clause-clause subsumption calls : 147
% 1.37/0.68 % Rewrite failures with RHS unbound : 0
% 1.37/0.68 % BW rewrite match attempts : 319
% 1.37/0.68 % BW rewrite match successes : 69
% 1.37/0.68 % Condensation attempts : 0
% 1.37/0.68 % Condensation successes : 0
% 1.37/0.68 % Termbank termtop insertions : 87465
% 1.37/0.68 % Search garbage collected termcells : 61
% 1.37/0.68
% 1.37/0.68 % -------------------------------------------------
% 1.37/0.68 % User time : 0.144 s
% 1.37/0.68 % System time : 0.013 s
% 1.37/0.68 % Total time : 0.156 s
% 1.37/0.68 % Maximum resident set size: 3648 pages
% 1.37/0.68
% 1.37/0.68 % -------------------------------------------------
% 1.37/0.68 % User time : 0.831 s
% 1.37/0.68 % System time : 0.052 s
% 1.37/0.68 % Total time : 0.884 s
% 1.37/0.68 % Maximum resident set size: 4864 pages
% 1.37/0.68 % E exiting
%------------------------------------------------------------------------------