%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG039-1 : 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 : n009.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 0.14s 0.73s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of clauses : 74 ( 54 unt; 0 nHn; 45 RR)
% Number of literals : 107 ( 34 equ; 38 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',multiplication_is_well_defined) ).
cnf(clause40,axiom,
product(b,d,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
cnf(clause44,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
cnf(clause37,axiom,
multiply(b,a) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
cnf(clause35,axiom,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_multiplication) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
cnf(absorbtion2,axiom,
sum(add(X1,X2),X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion2) ).
cnf(clause71,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
cnf(clause38,axiom,
sum(X1,X2,add(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',closure_of_addition) ).
cnf(a_times_b,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
cnf(associativity_of_addition2,axiom,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
cnf(clause68,axiom,
product(add(b,a),b,add(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
cnf(prove_c_equals_d,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(clause70,axiom,
product(add(a,b),a,add(a,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
cnf(absorbtion1,axiom,
sum(X1,add(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion1) ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_18,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_17 ).
cnf(c_0_19,axiom,
product(b,d,d),
clause40 ).
cnf(c_0_20,axiom,
product(a,multiply(b,X1),multiply(X2,X1)),
clause44 ).
cnf(c_0_21,axiom,
multiply(b,a) = d,
clause37 ).
cnf(c_0_22,axiom,
multiply(X1,X1) = X1,
clause35 ).
cnf(c_0_23,plain,
( ~ product(b,d,X1)
| X1 = d ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_25,plain,
product(a,d,d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_26,plain,
product(a,multiply(b,X1),X1),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_27,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_28,plain,
multiply(b,d) = d,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( ~ product(a,d,X1)
| X1 = d ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_30,plain,
product(a,d,a),
inference(spm,[status(thm)],[c_0_26,c_0_21]) ).
cnf(c_0_31,plain,
product(a,b,b),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_32,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_27 ).
cnf(c_0_33,axiom,
sum(add(X1,X2),X2,X1),
absorbtion2 ).
cnf(c_0_34,axiom,
product(X1,X1,X1),
clause71 ).
cnf(c_0_35,plain,
product(a,d,multiply(X1,d)),
inference(spm,[status(thm)],[c_0_20,c_0_28]) ).
cnf(c_0_36,plain,
d = a,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
( ~ product(a,b,X1)
| X1 = b ),
inference(spm,[status(thm)],[c_0_18,c_0_31]) ).
cnf(c_0_38,plain,
product(a,b,multiply(X1,b)),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_39,plain,
( ~ sum(add(X2,X3),X3,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,axiom,
sum(X1,X2,add(X2,X1)),
clause38 ).
cnf(c_0_41,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_42,negated_conjecture,
product(a,b,c),
a_times_b ).
cnf(c_0_43,plain,
( ~ product(X2,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_44,plain,
product(a,a,multiply(X1,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_36]) ).
cnf(c_0_45,plain,
multiply(X1,b) = b,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_46,plain,
add(X1,add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
add(add(X1,X2),X2) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( ~ product(a,b,X1)
| X1 = c ),
inference(spm,[status(thm)],[c_0_18,c_0_42]) ).
cnf(c_0_49,plain,
multiply(X1,a) = a,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,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_51,plain,
product(X1,b,b),
inference(spm,[status(thm)],[c_0_24,c_0_45]) ).
cnf(c_0_52,axiom,
product(add(b,a),b,add(b,c)),
clause68 ).
cnf(c_0_53,plain,
add(X1,X2) = add(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
c = b,
inference(spm,[status(thm)],[c_0_48,c_0_31]) ).
cnf(c_0_55,plain,
product(X1,a,a),
inference(spm,[status(thm)],[c_0_24,c_0_49]) ).
cnf(c_0_56,plain,
( ~ sum(X1,X5,X6)
| ~ sum(X2,X4,X5)
| ~ sum(X1,X2,X3)
| sum(X3,X4,X6) ),
c_0_50 ).
cnf(c_0_57,plain,
( ~ product(X2,b,X1)
| X1 = b ),
inference(spm,[status(thm)],[c_0_18,c_0_51]) ).
cnf(c_0_58,plain,
product(add(a,b),b,add(b,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_59,negated_conjecture,
c != d,
inference(fof_simplification,[status(thm)],[prove_c_equals_d]) ).
cnf(c_0_60,plain,
( ~ product(X2,a,X1)
| X1 = a ),
inference(spm,[status(thm)],[c_0_18,c_0_55]) ).
cnf(c_0_61,axiom,
product(add(a,b),a,add(a,d)),
clause70 ).
cnf(c_0_62,plain,
( ~ sum(X4,X5,X3)
| ~ sum(X4,add(X5,X2),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_56,c_0_33]) ).
cnf(c_0_63,axiom,
sum(X1,add(X1,X2),X2),
absorbtion1 ).
cnf(c_0_64,plain,
add(b,b) = b,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,negated_conjecture,
c != d,
c_0_59 ).
cnf(c_0_66,plain,
add(a,a) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_36]) ).
cnf(c_0_67,plain,
( ~ sum(X3,X3,X2)
| sum(X1,X1,X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_68,plain,
sum(b,b,b),
inference(spm,[status(thm)],[c_0_40,c_0_64]) ).
cnf(c_0_69,negated_conjecture,
c != a,
inference(rw,[status(thm)],[c_0_65,c_0_36]) ).
cnf(c_0_70,plain,
( ~ sum(a,a,X1)
| X1 = a ),
inference(spm,[status(thm)],[c_0_39,c_0_66]) ).
cnf(c_0_71,plain,
sum(X1,X1,b),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,negated_conjecture,
b != a,
inference(rw,[status(thm)],[c_0_69,c_0_54]) ).
cnf(c_0_73,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.58 % Computer : n009.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Mon Sep 21 04:14:58 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.65 Running first-order theorem proving
% 0.14/0.65 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
% 0.14/0.73 % Version: 3.5.1
% 0.14/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.73 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.73 % Starting sh5l with 300s (1) cores
% 0.14/0.73 % new_bool_3 with pid 821835 completed with status 0
% 0.14/0.73 % Result found by new_bool_3
% 0.14/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.73 % Search class: FHUSM-FFMM22-SFFFFFNN
% 0.14/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.73 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.73 % SubtermCWHack with pid 821840 completed with status 0
% 0.14/0.73 % Result found by SubtermCWHack
% 0.14/0.73 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.73 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.73 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.73 % Search class: FHUSM-FFMM22-SFFFFFNN
% 0.14/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.73 % Starting SubtermCWHack with 31s (1) cores
% 0.14/0.73 % Preprocessing time : 0.001 s
% 0.14/0.73
% 0.14/0.73 % Proof found!
% 0.14/0.73 % SZS status Unsatisfiable
% 0.14/0.73 % SZS output start CNFRefutation
% See solution above
% 0.14/0.73 % Parsed axioms : 60
% 0.14/0.73 % Removed by relevancy pruning/SinE : 7
% 0.14/0.73 % Initial clauses : 53
% 0.14/0.73 % Removed in clause preprocessing : 0
% 0.14/0.73 % Initial clauses in saturation : 53
% 0.14/0.73 % Processed clauses : 189
% 0.14/0.73 % ...of these trivial : 31
% 0.14/0.73 % ...subsumed : 32
% 0.14/0.73 % ...remaining for further processing : 126
% 0.14/0.73 % Other redundant clauses eliminated : 0
% 0.14/0.73 % Clauses deleted for lack of memory : 0
% 0.14/0.73 % Backward-subsumed : 7
% 0.14/0.73 % Backward-rewritten : 77
% 0.14/0.73 % Generated clauses : 500
% 0.14/0.73 % ...of the previous two non-redundant : 340
% 0.14/0.73 % ...aggressively subsumed : 0
% 0.14/0.73 % Contextual simplify-reflections : 0
% 0.14/0.73 % Paramodulations : 500
% 0.14/0.73 % Factorizations : 0
% 0.14/0.73 % NegExts : 0
% 0.14/0.73 % Equation resolutions : 0
% 0.14/0.73 % Disequality decompositions : 0
% 0.14/0.73 % Total rewrite steps : 455
% 0.14/0.73 % ...of those cached : 345
% 0.14/0.73 % Propositional unsat checks : 0
% 0.14/0.73 % Propositional check models : 0
% 0.14/0.73 % Propositional check unsatisfiable : 0
% 0.14/0.73 % Propositional clauses : 0
% 0.14/0.73 % Propositional clauses after purity: 0
% 0.14/0.73 % Propositional unsat core size : 0
% 0.14/0.73 % Propositional preprocessing time : 0.000
% 0.14/0.73 % Propositional encoding time : 0.000
% 0.14/0.73 % Propositional solver time : 0.000
% 0.14/0.73 % Success case prop preproc time : 0.000
% 0.14/0.73 % Success case prop encoding time : 0.000
% 0.14/0.73 % Success case prop solver time : 0.000
% 0.14/0.73 % Current number of processed clauses : 42
% 0.14/0.73 % Positive orientable unit clauses : 18
% 0.14/0.73 % Positive unorientable unit clauses: 1
% 0.14/0.73 % Negative unit clauses : 1
% 0.14/0.73 % Non-unit-clauses : 22
% 0.14/0.73 % Current number of unprocessed clauses: 148
% 0.14/0.73 % ...number of literals in the above : 477
% 0.14/0.73 % Current number of archived formulas : 0
% 0.14/0.73 % Current number of archived clauses : 84
% 0.14/0.73 % Clause-clause subsumption calls (NU) : 351
% 0.14/0.73 % Rec. Clause-clause subsumption calls : 234
% 0.14/0.73 % Non-unit clause-clause subsumptions : 36
% 0.14/0.73 % Unit Clause-clause subsumption calls : 15
% 0.14/0.73 % Rewrite failures with RHS unbound : 0
% 0.14/0.73 % BW rewrite match attempts : 199
% 0.14/0.73 % BW rewrite match successes : 63
% 0.14/0.73 % Condensation attempts : 0
% 0.14/0.73 % Condensation successes : 0
% 0.14/0.73 % Termbank termtop insertions : 5529
% 0.14/0.73 % Search garbage collected termcells : 77
% 0.14/0.73
% 0.14/0.73 % -------------------------------------------------
% 0.14/0.73 % User time : 0.011 s
% 0.14/0.73 % System time : 0.003 s
% 0.14/0.73 % Total time : 0.015 s
% 0.14/0.73 % Maximum resident set size: 3668 pages
% 0.14/0.73
% 0.14/0.73 % -------------------------------------------------
% 0.14/0.73 % User time : 0.014 s
% 0.14/0.73 % System time : 0.010 s
% 0.14/0.73 % Total time : 0.024 s
% 0.14/0.73 % Maximum resident set size: 4864 pages
% 0.14/0.73 % E exiting
%------------------------------------------------------------------------------