%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG008-3 : 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 : n018.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 02:05:28 PM UTC 2026
% Result : Unsatisfiable 0.26s 0.56s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 18 RR)
% Number of literals : 65 ( 64 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 75 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply_additive_inverse1,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse1) ).
cnf(boolean_ring,hypothesis,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
cnf(associative_multiplication,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_multiplication) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',additive_inverse_additive_inverse) ).
cnf(multiply_additive_inverse2,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_inverse2) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute2) ).
cnf(commutative_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
cnf(right_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(multiply_additive_id2,axiom,
multiply(additive_identity,X1) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_id2) ).
cnf(multiply_additive_id1,axiom,
multiply(X1,additive_identity) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',multiply_additive_id1) ).
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',distribute1) ).
cnf(right_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(associative_addition,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',associative_addition) ).
cnf(left_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',left_identity) ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_16,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse1 ).
cnf(c_0_17,hypothesis,
multiply(X1,X1) = X1,
boolean_ring ).
cnf(c_0_18,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associative_multiplication ).
cnf(c_0_19,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_20,hypothesis,
multiply(X1,additive_inverse(X1)) = additive_inverse(X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_22,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse2 ).
cnf(c_0_23,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,hypothesis,
multiply(additive_inverse(X1),X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_26,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_27,hypothesis,
multiply(c,b) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_17]),c_0_19]) ).
cnf(c_0_28,axiom,
add(X1,X2) = add(X2,X1),
commutative_addition ).
cnf(c_0_29,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_inverse ).
cnf(c_0_30,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_20]) ).
cnf(c_0_31,hypothesis,
add(c,multiply(X1,b)) = multiply(add(X1,c),b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,plain,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
multiply(add(a,c),b) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_19]),c_0_32]) ).
cnf(c_0_34,axiom,
multiply(additive_identity,X1) = additive_identity,
multiply_additive_id2 ).
cnf(c_0_35,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_36,negated_conjecture,
multiply(add(a,c),multiply(b,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_33]),c_0_34]) ).
cnf(c_0_37,axiom,
multiply(X1,additive_identity) = additive_identity,
multiply_additive_id1 ).
cnf(c_0_38,hypothesis,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_39,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_40,hypothesis,
multiply(c,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_41,hypothesis,
multiply(b,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_42,negated_conjecture,
multiply(a,c) = c,
inference(spm,[status(thm)],[c_0_38,c_0_19]) ).
cnf(c_0_43,hypothesis,
add(X1,multiply(X1,X2)) = multiply(X1,add(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_17]),c_0_28]) ).
cnf(c_0_44,hypothesis,
multiply(c,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_37]) ).
cnf(c_0_45,axiom,
add(X1,additive_identity) = X1,
right_identity ).
cnf(c_0_46,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associative_addition ).
cnf(c_0_47,negated_conjecture,
add(c,multiply(a,X1)) = multiply(a,add(X1,c)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_42]),c_0_28]) ).
cnf(c_0_48,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]),c_0_32]),c_0_45]) ).
cnf(c_0_49,hypothesis,
multiply(a,add(a,c)) = add(a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_17]),c_0_28]) ).
cnf(c_0_50,negated_conjecture,
multiply(a,add(X1,c)) = multiply(a,add(X1,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_28]),c_0_47]) ).
cnf(c_0_51,hypothesis,
multiply(c,multiply(a,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_18,c_0_48]) ).
cnf(c_0_52,hypothesis,
multiply(a,add(a,b)) = add(a,c),
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,hypothesis,
multiply(c,add(a,b)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_44]) ).
cnf(c_0_54,axiom,
add(additive_identity,X1) = X1,
left_identity ).
cnf(c_0_55,hypothesis,
multiply(c,multiply(add(a,b),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_53]),c_0_34]) ).
cnf(c_0_56,plain,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_32]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_58,negated_conjecture,
multiply(b,a) != c,
inference(fof_simplification,[status(thm)],[prove_commutativity]) ).
cnf(c_0_59,negated_conjecture,
add(c,multiply(X1,c)) = multiply(add(X1,a),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_42]),c_0_28]) ).
cnf(c_0_60,hypothesis,
multiply(add(a,b),c) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_55]),c_0_37]) ).
cnf(c_0_61,plain,
add(X1,add(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_56,c_0_28]) ).
cnf(c_0_62,negated_conjecture,
multiply(b,c) = multiply(b,a),
inference(rw,[status(thm)],[c_0_57,c_0_48]) ).
cnf(c_0_63,negated_conjecture,
multiply(b,a) != c,
c_0_58 ).
cnf(c_0_64,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_45]),c_0_46]),c_0_61]),c_0_62]),c_0_63]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 04:12:28 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.50 Running first-order theorem proving
% 0.17/0.50 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 % new_bool_1 with pid 941428 completed with status 0
% 0.26/0.56 % Result found by new_bool_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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.56 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.26/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.56 % SubtermCWHack with pid 941434 completed with status 0
% 0.26/0.56 % Result found by SubtermCWHack
% 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 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.26/0.56 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.26/0.56 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.26/0.56 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.26/0.56 % Starting SubtermCWHack with 31s (1) cores
% 0.26/0.56 % Preprocessing time : 0.002 s
% 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 : 19
% 0.26/0.56 % Removed by relevancy pruning/SinE : 0
% 0.26/0.56 % Initial clauses : 19
% 0.26/0.56 % Removed in clause preprocessing : 0
% 0.26/0.56 % Initial clauses in saturation : 19
% 0.26/0.56 % Processed clauses : 168
% 0.26/0.56 % ...of these trivial : 23
% 0.26/0.56 % ...subsumed : 58
% 0.26/0.56 % ...remaining for further processing : 87
% 0.26/0.56 % Other redundant clauses eliminated : 0
% 0.26/0.56 % Clauses deleted for lack of memory : 0
% 0.26/0.56 % Backward-subsumed : 0
% 0.26/0.56 % Backward-rewritten : 18
% 0.26/0.56 % Generated clauses : 1790
% 0.26/0.56 % ...of the previous two non-redundant : 1061
% 0.26/0.56 % ...aggressively subsumed : 0
% 0.26/0.56 % Contextual simplify-reflections : 0
% 0.26/0.56 % Paramodulations : 1790
% 0.26/0.56 % Factorizations : 0
% 0.26/0.56 % NegExts : 0
% 0.26/0.56 % Equation resolutions : 0
% 0.26/0.56 % Disequality decompositions : 0
% 0.26/0.56 % Total rewrite steps : 2441
% 0.26/0.56 % ...of those cached : 1743
% 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 : 69
% 0.26/0.56 % Positive orientable unit clauses : 62
% 0.26/0.56 % Positive unorientable unit clauses: 6
% 0.26/0.56 % Negative unit clauses : 1
% 0.26/0.56 % Non-unit-clauses : 0
% 0.26/0.56 % Current number of unprocessed clauses: 891
% 0.26/0.56 % ...number of literals in the above : 891
% 0.26/0.56 % Current number of archived formulas : 0
% 0.26/0.56 % Current number of archived clauses : 18
% 0.26/0.56 % Clause-clause subsumption calls (NU) : 0
% 0.26/0.56 % Rec. Clause-clause subsumption calls : 0
% 0.26/0.56 % Non-unit clause-clause subsumptions : 0
% 0.26/0.56 % Unit Clause-clause subsumption calls : 10
% 0.26/0.56 % Rewrite failures with RHS unbound : 0
% 0.26/0.56 % BW rewrite match attempts : 90
% 0.26/0.56 % BW rewrite match successes : 61
% 0.26/0.56 % Condensation attempts : 0
% 0.26/0.56 % Condensation successes : 0
% 0.26/0.56 % Termbank termtop insertions : 17322
% 0.26/0.56 % Search garbage collected termcells : 2
% 0.26/0.56
% 0.26/0.56 % -------------------------------------------------
% 0.26/0.56 % User time : 0.027 s
% 0.26/0.56 % System time : 0.006 s
% 0.26/0.56 % Total time : 0.034 s
% 0.26/0.56 % Maximum resident set size: 3640 pages
% 0.26/0.56
% 0.26/0.56 % -------------------------------------------------
% 0.26/0.56 % User time : 0.028 s
% 0.26/0.56 % System time : 0.014 s
% 0.26/0.56 % Total time : 0.042 s
% 0.26/0.56 % Maximum resident set size: 4608 pages
% 0.26/0.56 % E exiting
%------------------------------------------------------------------------------