%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG008-7 : 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 : 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 02:05:29 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.46s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of clauses : 64 ( 64 unt; 0 nHn; 13 RR)
% Number of literals : 64 ( 63 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 87 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distribute1,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute1) ).
cnf(boolean_ring,hypothesis,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',boolean_ring) ).
cnf(commutativity_for_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',commutativity_for_addition) ).
cnf(associativity_for_addition,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_addition) ).
cnf(right_additive_inverse,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_inverse) ).
cnf(left_additive_identity,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',left_additive_identity) ).
cnf(distribute2,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',distribute2) ).
cnf(associativity_for_multiplication,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',associativity_for_multiplication) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(right_additive_identity,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/RNG005-0.ax',right_additive_identity) ).
cnf(prove_commutativity,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_11,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_12,hypothesis,
multiply(X1,X1) = X1,
boolean_ring ).
cnf(c_0_13,axiom,
add(X1,X2) = add(X2,X1),
commutativity_for_addition ).
cnf(c_0_14,axiom,
add(X1,add(X2,X3)) = add(add(X1,X2),X3),
associativity_for_addition ).
cnf(c_0_15,axiom,
add(X1,additive_inverse(X1)) = additive_identity,
right_additive_inverse ).
cnf(c_0_16,axiom,
add(additive_identity,X1) = X1,
left_additive_identity ).
cnf(c_0_17,hypothesis,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_18,plain,
add(X1,add(additive_inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_20,plain,
add(X1,add(X2,additive_inverse(add(X1,X2)))) = additive_identity,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_21,hypothesis,
add(X1,multiply(X1,additive_identity)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_12]) ).
cnf(c_0_22,plain,
add(X1,add(X2,additive_inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_23,axiom,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X2),X3),
associativity_for_multiplication ).
cnf(c_0_24,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_25,hypothesis,
multiply(add(X1,X2),X2) = add(X2,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_13]) ).
cnf(c_0_26,hypothesis,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_27,hypothesis,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,axiom,
add(X1,additive_identity) = X1,
right_additive_identity ).
cnf(c_0_29,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,hypothesis,
add(X1,multiply(additive_identity,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_12]) ).
cnf(c_0_32,hypothesis,
add(X1,multiply(X1,additive_inverse(X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_15]),c_0_27]) ).
cnf(c_0_33,plain,
additive_inverse(additive_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_28]) ).
cnf(c_0_34,negated_conjecture,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
add(multiply(X1,X2),multiply(X3,multiply(X4,X2))) = multiply(add(X1,multiply(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_36,hypothesis,
multiply(add(X1,X2),X1) = add(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_37,hypothesis,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_31]),c_0_22]) ).
cnf(c_0_38,hypothesis,
multiply(additive_inverse(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_32]),c_0_28]),c_0_33]) ).
cnf(c_0_39,negated_conjecture,
multiply(c,multiply(X1,multiply(b,X1))) = multiply(c,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_29]),c_0_30]) ).
cnf(c_0_40,negated_conjecture,
multiply(b,multiply(c,multiply(a,X1))) = multiply(b,multiply(a,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_23]),c_0_23]) ).
cnf(c_0_41,hypothesis,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_42,negated_conjecture,
multiply(add(c,multiply(X1,b)),X2) = multiply(add(a,X1),multiply(b,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_30]),c_0_35]) ).
cnf(c_0_43,hypothesis,
multiply(c,b) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_12]),c_0_24]) ).
cnf(c_0_44,hypothesis,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_15]),c_0_37]),c_0_38]) ).
cnf(c_0_45,negated_conjecture,
multiply(c,multiply(a,multiply(X1,multiply(b,multiply(a,X1))))) = multiply(c,multiply(a,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_23]),c_0_23]),c_0_41]),c_0_41]) ).
cnf(c_0_46,hypothesis,
multiply(add(a,c),multiply(b,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_37]) ).
cnf(c_0_47,negated_conjecture,
multiply(a,c) = c,
inference(spm,[status(thm)],[c_0_41,c_0_24]) ).
cnf(c_0_48,hypothesis,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_44]),c_0_16]) ).
cnf(c_0_49,negated_conjecture,
add(c,multiply(c,a)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_27]),c_0_27]),c_0_26]),c_0_47]),c_0_17]) ).
cnf(c_0_50,hypothesis,
multiply(c,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_23,c_0_43]) ).
cnf(c_0_51,plain,
add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_52,hypothesis,
multiply(c,a) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_28]) ).
cnf(c_0_53,hypothesis,
multiply(c,add(multiply(b,X1),X2)) = multiply(c,add(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_50]),c_0_11]) ).
cnf(c_0_54,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_44]),c_0_28]) ).
cnf(c_0_55,hypothesis,
add(X1,add(X2,X1)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_44]),c_0_28]) ).
cnf(c_0_56,negated_conjecture,
multiply(b,c) = multiply(b,a),
inference(rw,[status(thm)],[c_0_34,c_0_52]) ).
cnf(c_0_57,hypothesis,
multiply(c,add(X1,multiply(b,X1))) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_20]),c_0_27]),c_0_54]),c_0_55]) ).
cnf(c_0_58,negated_conjecture,
multiply(b,multiply(c,X1)) = multiply(b,multiply(a,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_56]),c_0_23]) ).
cnf(c_0_59,negated_conjecture,
multiply(c,multiply(add(c,multiply(b,a)),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_35]) ).
cnf(c_0_60,negated_conjecture,
multiply(b,a) != c,
inference(fof_simplification,[status(thm)],[prove_commutativity]) ).
cnf(c_0_61,hypothesis,
add(c,multiply(b,a)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_59]),c_0_27]),c_0_36]),c_0_23]),c_0_47]),c_0_56]) ).
cnf(c_0_62,negated_conjecture,
multiply(b,a) != c,
c_0_60 ).
cnf(c_0_63,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_61]),c_0_28]),c_0_62]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG008-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/5.36 % Computer : n004.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 04:10:55 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/5.40 Running first-order theorem proving
% 0.12/5.40 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
% 0.12/5.46 % Version: 3.5.1
% 0.12/5.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/5.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/5.46 % Starting new_bool_3 with 300s (1) cores
% 0.12/5.46 % Starting new_bool_1 with 300s (1) cores
% 0.12/5.46 % Starting sh5l with 300s (1) cores
% 0.12/5.46 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2216317 completed with status 0
% 0.12/5.46 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.12/5.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/5.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/5.46 % No SInE strategy applied
% 0.12/5.46 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.12/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.12/5.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.12/5.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.12/5.46 % Starting new_bool_3 with 136s (1) cores
% 0.12/5.46 % Starting new_bool_1 with 136s (1) cores
% 0.12/5.46 % SAT001_MinMin_p005000_rr_RG with pid 2216325 completed with status 0
% 0.12/5.46 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.12/5.46 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/5.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/5.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/5.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/5.46 % No SInE strategy applied
% 0.12/5.46 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.12/5.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/5.46 % Starting SubtermCWHack with 136s (1) cores
% 0.12/5.46 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.12/5.46 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.12/5.46 % Preprocessing time : 0.001 s
% 0.12/5.46 % Presaturation interreduction done
% 0.12/5.46
% 0.12/5.46 % Proof found!
% 0.12/5.46 % SZS status Unsatisfiable
% 0.12/5.46 % SZS output start CNFRefutation
% See solution above
% 0.12/5.46 % Parsed axioms : 12
% 0.12/5.46 % Removed by relevancy pruning/SinE : 0
% 0.12/5.46 % Initial clauses : 12
% 0.12/5.46 % Removed in clause preprocessing : 0
% 0.12/5.46 % Initial clauses in saturation : 12
% 0.12/5.46 % Processed clauses : 267
% 0.12/5.46 % ...of these trivial : 74
% 0.12/5.46 % ...subsumed : 35
% 0.12/5.46 % ...remaining for further processing : 158
% 0.12/5.46 % Other redundant clauses eliminated : 0
% 0.12/5.46 % Clauses deleted for lack of memory : 0
% 0.12/5.46 % Backward-subsumed : 0
% 0.12/5.46 % Backward-rewritten : 67
% 0.12/5.46 % Generated clauses : 3283
% 0.12/5.46 % ...of the previous two non-redundant : 2035
% 0.12/5.46 % ...aggressively subsumed : 0
% 0.12/5.46 % Contextual simplify-reflections : 0
% 0.12/5.46 % Paramodulations : 3283
% 0.12/5.46 % Factorizations : 0
% 0.12/5.46 % NegExts : 0
% 0.12/5.46 % Equation resolutions : 0
% 0.12/5.46 % Disequality decompositions : 0
% 0.12/5.46 % Total rewrite steps : 5204
% 0.12/5.46 % ...of those cached : 3976
% 0.12/5.46 % Propositional unsat checks : 0
% 0.12/5.46 % Propositional check models : 0
% 0.12/5.46 % Propositional check unsatisfiable : 0
% 0.12/5.46 % Propositional clauses : 0
% 0.12/5.46 % Propositional clauses after purity: 0
% 0.12/5.46 % Propositional unsat core size : 0
% 0.12/5.46 % Propositional preprocessing time : 0.000
% 0.12/5.46 % Propositional encoding time : 0.000
% 0.12/5.46 % Propositional solver time : 0.000
% 0.12/5.46 % Success case prop preproc time : 0.000
% 0.12/5.46 % Success case prop encoding time : 0.000
% 0.12/5.46 % Success case prop solver time : 0.000
% 0.12/5.46 % Current number of processed clauses : 80
% 0.12/5.46 % Positive orientable unit clauses : 76
% 0.12/5.46 % Positive unorientable unit clauses: 3
% 0.12/5.46 % Negative unit clauses : 1
% 0.12/5.46 % Non-unit-clauses : 0
% 0.12/5.46 % Current number of unprocessed clauses: 1739
% 0.12/5.46 % ...number of literals in the above : 1739
% 0.12/5.46 % Current number of archived formulas : 0
% 0.12/5.46 % Current number of archived clauses : 78
% 0.12/5.46 % Clause-clause subsumption calls (NU) : 0
% 0.12/5.46 % Rec. Clause-clause subsumption calls : 0
% 0.12/5.46 % Non-unit clause-clause subsumptions : 0
% 0.12/5.46 % Unit Clause-clause subsumption calls : 17
% 0.12/5.46 % Rewrite failures with RHS unbound : 0
% 0.12/5.46 % BW rewrite match attempts : 238
% 0.12/5.46 % BW rewrite match successes : 86
% 0.12/5.46 % Condensation attempts : 0
% 0.12/5.46 % Condensation successes : 0
% 0.12/5.46 % Termbank termtop insertions : 38040
% 0.12/5.46 % Search garbage collected termcells : 2
% 0.12/5.46
% 0.12/5.46 % -------------------------------------------------
% 0.12/5.46 % User time : 0.036 s
% 0.12/5.46 % System time : 0.007 s
% 0.12/5.46 % Total time : 0.043 s
% 0.12/5.46 % Maximum resident set size: 3640 pages
% 0.12/5.46
% 0.12/5.46 % -------------------------------------------------
% 0.12/5.46 % User time : 0.180 s
% 0.12/5.46 % System time : 0.032 s
% 0.12/5.46 % Total time : 0.211 s
% 0.12/5.46 % Maximum resident set size: 4608 pages
% 0.12/5.46 % E exiting
%------------------------------------------------------------------------------