%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG008-4 : 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 : n010.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 0.23s 0.57s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 56 ( 56 unt; 0 nHn; 16 RR)
% Number of literals : 56 ( 55 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 : 68 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(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(boolean_ring,hypothesis,
multiply(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
cnf(left_additive_inverse,axiom,
add(additive_inverse(X1),X1) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',left_additive_inverse) ).
cnf(commutative_addition,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG002-0.ax',commutative_addition) ).
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(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(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
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(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(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_15,axiom,
multiply(additive_inverse(X1),X2) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse2 ).
cnf(c_0_16,axiom,
multiply(X1,additive_inverse(X2)) = additive_inverse(multiply(X1,X2)),
multiply_additive_inverse1 ).
cnf(c_0_17,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associative_multiplication ).
cnf(c_0_18,hypothesis,
multiply(X1,X1) = X1,
boolean_ring ).
cnf(c_0_19,axiom,
add(additive_inverse(X1),X1) = additive_identity,
left_additive_inverse ).
cnf(c_0_20,axiom,
add(X1,X2) = add(X2,X1),
commutative_addition ).
cnf(c_0_21,plain,
multiply(additive_inverse(X1),X2) = multiply(X1,additive_inverse(X2)),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,axiom,
additive_inverse(additive_inverse(X1)) = X1,
additive_inverse_additive_inverse ).
cnf(c_0_23,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distribute1 ).
cnf(c_0_24,negated_conjecture,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_25,hypothesis,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,plain,
add(X1,additive_inverse(X1)) = additive_identity,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,hypothesis,
additive_inverse(X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_22]),c_0_18]) ).
cnf(c_0_28,negated_conjecture,
add(c,multiply(a,X1)) = multiply(a,add(X1,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]) ).
cnf(c_0_29,negated_conjecture,
multiply(a,c) = c,
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
add(X1,X1) = additive_identity,
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
multiply(a,add(b,c)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_20]) ).
cnf(c_0_32,axiom,
multiply(additive_identity,X1) = additive_identity,
multiply_additive_id2 ).
cnf(c_0_33,hypothesis,
multiply(X1,multiply(X2,multiply(X1,X2))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_34,negated_conjecture,
multiply(a,multiply(add(b,c),X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_31]),c_0_32]) ).
cnf(c_0_35,axiom,
multiply(X1,additive_identity) = additive_identity,
multiply_additive_id1 ).
cnf(c_0_36,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distribute2 ).
cnf(c_0_37,hypothesis,
multiply(a,add(a,b)) = add(a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_20]) ).
cnf(c_0_38,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associative_addition ).
cnf(c_0_39,axiom,
add(additive_identity,X1) = X1,
left_identity ).
cnf(c_0_40,hypothesis,
multiply(add(b,c),a) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_41,hypothesis,
add(X1,multiply(X2,X1)) = multiply(add(X2,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_18]),c_0_20]) ).
cnf(c_0_42,hypothesis,
multiply(a,add(a,c)) = add(a,c),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_43,plain,
add(X1,add(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_30]),c_0_39]) ).
cnf(c_0_44,hypothesis,
multiply(add(b,c),multiply(a,X1)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_40]),c_0_32]) ).
cnf(c_0_45,negated_conjecture,
multiply(a,multiply(b,X1)) = multiply(c,X1),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_46,hypothesis,
add(X1,multiply(X1,X2)) = multiply(X1,add(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_18]),c_0_20]) ).
cnf(c_0_47,hypothesis,
multiply(c,add(a,c)) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_30]),c_0_43]) ).
cnf(c_0_48,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_49,negated_conjecture,
multiply(add(b,c),c) = additive_identity,
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_50,negated_conjecture,
multiply(b,a) != c,
inference(fof_simplification,[status(thm)],[prove_commutativity]) ).
cnf(c_0_51,negated_conjecture,
multiply(b,multiply(c,a)) = multiply(b,a),
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_52,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_46,c_0_47]),c_0_48]),c_0_38]),c_0_30]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
multiply(b,c) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_49]),c_0_48]),c_0_38]),c_0_30]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
multiply(b,a) != c,
c_0_50 ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.46 % Computer : n010.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 04:10:39 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.52 Running first-order theorem proving
% 0.23/0.52 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
% 0.23/0.57 % Version: 3.5.1
% 0.23/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.57 % Starting sh5l with 300s (1) cores
% 0.23/0.57 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4192763 completed with status 0
% 0.23/0.57 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.57 % No SInE strategy applied
% 0.23/0.57 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.23/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.57 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.23/0.57 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.57 % Starting new_bool_1 with 136s (1) cores
% 0.23/0.57 % SAT001_MinMin_p005000_rr_RG with pid 4192769 completed with status 0
% 0.23/0.57 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.23/0.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.57 % No SInE strategy applied
% 0.23/0.57 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.23/0.57 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.57 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.57 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.23/0.57 % Preprocessing time : 0.002 s
% 0.23/0.57 % Presaturation interreduction done
% 0.23/0.57
% 0.23/0.57 % Proof found!
% 0.23/0.57 % SZS status Unsatisfiable
% 0.23/0.57 % SZS output start CNFRefutation
% See solution above
% 0.23/0.57 % Parsed axioms : 17
% 0.23/0.57 % Removed by relevancy pruning/SinE : 0
% 0.23/0.57 % Initial clauses : 17
% 0.23/0.57 % Removed in clause preprocessing : 0
% 0.23/0.57 % Initial clauses in saturation : 17
% 0.23/0.57 % Processed clauses : 93
% 0.23/0.57 % ...of these trivial : 8
% 0.23/0.57 % ...subsumed : 11
% 0.23/0.57 % ...remaining for further processing : 74
% 0.23/0.57 % Other redundant clauses eliminated : 0
% 0.23/0.57 % Clauses deleted for lack of memory : 0
% 0.23/0.57 % Backward-subsumed : 0
% 0.23/0.57 % Backward-rewritten : 11
% 0.23/0.57 % Generated clauses : 608
% 0.23/0.57 % ...of the previous two non-redundant : 365
% 0.23/0.57 % ...aggressively subsumed : 0
% 0.23/0.57 % Contextual simplify-reflections : 0
% 0.23/0.57 % Paramodulations : 608
% 0.23/0.57 % Factorizations : 0
% 0.23/0.57 % NegExts : 0
% 0.23/0.57 % Equation resolutions : 0
% 0.23/0.57 % Disequality decompositions : 0
% 0.23/0.57 % Total rewrite steps : 796
% 0.23/0.57 % ...of those cached : 474
% 0.23/0.57 % Propositional unsat checks : 0
% 0.23/0.57 % Propositional check models : 0
% 0.23/0.57 % Propositional check unsatisfiable : 0
% 0.23/0.57 % Propositional clauses : 0
% 0.23/0.57 % Propositional clauses after purity: 0
% 0.23/0.57 % Propositional unsat core size : 0
% 0.23/0.57 % Propositional preprocessing time : 0.000
% 0.23/0.57 % Propositional encoding time : 0.000
% 0.23/0.57 % Propositional solver time : 0.000
% 0.23/0.57 % Success case prop preproc time : 0.000
% 0.23/0.57 % Success case prop encoding time : 0.000
% 0.23/0.58 % Success case prop solver time : 0.000
% 0.23/0.58 % Current number of processed clauses : 46
% 0.23/0.58 % Positive orientable unit clauses : 42
% 0.23/0.58 % Positive unorientable unit clauses: 3
% 0.23/0.58 % Negative unit clauses : 1
% 0.23/0.58 % Non-unit-clauses : 0
% 0.23/0.58 % Current number of unprocessed clauses: 293
% 0.23/0.58 % ...number of literals in the above : 293
% 0.23/0.58 % Current number of archived formulas : 0
% 0.23/0.58 % Current number of archived clauses : 28
% 0.23/0.58 % Clause-clause subsumption calls (NU) : 0
% 0.23/0.58 % Rec. Clause-clause subsumption calls : 0
% 0.23/0.58 % Non-unit clause-clause subsumptions : 0
% 0.23/0.58 % Unit Clause-clause subsumption calls : 3
% 0.23/0.58 % Rewrite failures with RHS unbound : 0
% 0.23/0.58 % BW rewrite match attempts : 64
% 0.23/0.58 % BW rewrite match successes : 34
% 0.23/0.58 % Condensation attempts : 0
% 0.23/0.58 % Condensation successes : 0
% 0.23/0.58 % Termbank termtop insertions : 5965
% 0.23/0.58 % Search garbage collected termcells : 2
% 0.23/0.58
% 0.23/0.58 % -------------------------------------------------
% 0.23/0.58 % User time : 0.015 s
% 0.23/0.58 % System time : 0.004 s
% 0.23/0.58 % Total time : 0.019 s
% 0.23/0.58 % Maximum resident set size: 3640 pages
% 0.23/0.58
% 0.23/0.58 % -------------------------------------------------
% 0.23/0.58 % User time : 0.041 s
% 0.23/0.58 % System time : 0.018 s
% 0.23/0.58 % Total time : 0.059 s
% 0.23/0.58 % Maximum resident set size: 4864 pages
% 0.23/0.58 % E exiting
%------------------------------------------------------------------------------