%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO008-4 : TPTP v9.3.1. Released v1.1.0.
% 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 12:06:56 PM UTC 2026
% Result : Unsatisfiable 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 7 RR)
% Number of literals : 52 ( 51 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
cnf(distributivity2,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
cnf(prove_associativity,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
cnf(c_0_9,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity1 ).
cnf(c_0_10,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_11,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_12,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_13,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_14,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_15,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_16,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_17,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_18,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity2 ).
cnf(c_0_19,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_21,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_22,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_14]) ).
cnf(c_0_23,plain,
inverse(additive_identity) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_24,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_20]),c_0_10]) ).
cnf(c_0_25,plain,
add(X1,multiply(X1,X2)) = add(X1,multiply(additive_identity,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_14]),c_0_21]) ).
cnf(c_0_26,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_11]) ).
cnf(c_0_27,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_28,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_14]) ).
cnf(c_0_29,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_16]) ).
cnf(c_0_30,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_13]),c_0_14]) ).
cnf(c_0_32,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_13]),c_0_19]) ).
cnf(c_0_33,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_16]) ).
cnf(c_0_34,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_35,plain,
multiply(X1,add(add(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_28]) ).
cnf(c_0_36,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
inference(fof_simplification,[status(thm)],[prove_associativity]) ).
cnf(c_0_38,plain,
multiply(X1,add(add(X2,inverse(X1)),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_18]) ).
cnf(c_0_39,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_10]),c_0_11]),c_0_33]) ).
cnf(c_0_40,plain,
add(X1,add(add(X2,X1),X3)) = add(add(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_15]) ).
cnf(c_0_41,plain,
multiply(X1,add(add(X1,X2),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_36]),c_0_28]) ).
cnf(c_0_42,plain,
add(X1,add(X2,X1)) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_15]) ).
cnf(c_0_43,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
c_0_37 ).
cnf(c_0_44,plain,
add(add(X1,X2),X3) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_29]),c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
multiply(X1,add(X2,add(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
add(c,add(a,b)) != add(a,add(b,c)),
inference(rw,[status(thm)],[c_0_43,c_0_15]) ).
cnf(c_0_47,plain,
add(X1,add(X2,X3)) = add(X3,add(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_44]) ).
cnf(c_0_48,plain,
add(X1,add(X2,add(X1,X3))) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_45]),c_0_15]) ).
cnf(c_0_49,negated_conjecture,
add(b,add(a,c)) != add(a,add(b,c)),
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_42]),c_0_44]),c_0_44]),c_0_48]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO008-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 13:47:56 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 0.18/0.52 % Version: 3.5.1
% 0.18/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.52 % Starting new_bool_3 with 300s (1) cores
% 0.18/0.52 % Starting new_bool_1 with 300s (1) cores
% 0.18/0.52 % Starting sh5l with 300s (1) cores
% 0.18/0.52 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1022201 completed with status 0
% 0.18/0.52 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.18/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.52 % No SInE strategy applied
% 0.18/0.52 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.18/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.18/0.52 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.18/0.52 % Starting new_bool_3 with 136s (1) cores
% 0.18/0.52 % Starting new_bool_1 with 136s (1) cores
% 0.18/0.52 % new_bool_3 with pid 1022211 completed with status 0
% 0.18/0.52 % Result found by new_bool_3
% 0.18/0.52 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.18/0.52 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.18/0.52 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.18/0.52 % No SInE strategy applied
% 0.18/0.52 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.18/0.52 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.18/0.52 % Starting SubtermCWHack with 136s (1) cores
% 0.18/0.52 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.18/0.52 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.18/0.52 % Starting new_bool_3 with 136s (1) cores
% 0.18/0.52 % Preprocessing time : 0.001 s
% 0.18/0.52 % Presaturation interreduction done
% 0.18/0.52
% 0.18/0.52 % Proof found!
% 0.18/0.52 % SZS status Unsatisfiable
% 0.18/0.52 % SZS output start CNFRefutation
% See solution above
% 0.18/0.52 % Parsed axioms : 9
% 0.18/0.52 % Removed by relevancy pruning/SinE : 0
% 0.18/0.52 % Initial clauses : 9
% 0.18/0.52 % Removed in clause preprocessing : 0
% 0.18/0.52 % Initial clauses in saturation : 9
% 0.18/0.52 % Processed clauses : 553
% 0.18/0.52 % ...of these trivial : 272
% 0.18/0.52 % ...subsumed : 130
% 0.18/0.52 % ...remaining for further processing : 151
% 0.18/0.52 % Other redundant clauses eliminated : 0
% 0.18/0.52 % Clauses deleted for lack of memory : 0
% 0.18/0.52 % Backward-subsumed : 0
% 0.18/0.52 % Backward-rewritten : 44
% 0.18/0.52 % Generated clauses : 10796
% 0.18/0.52 % ...of the previous two non-redundant : 5126
% 0.18/0.52 % ...aggressively subsumed : 0
% 0.18/0.52 % Contextual simplify-reflections : 0
% 0.18/0.52 % Paramodulations : 10796
% 0.18/0.52 % Factorizations : 0
% 0.18/0.52 % NegExts : 0
% 0.18/0.52 % Equation resolutions : 0
% 0.18/0.52 % Disequality decompositions : 0
% 0.18/0.52 % Total rewrite steps : 12299
% 0.18/0.52 % ...of those cached : 10436
% 0.18/0.52 % Propositional unsat checks : 0
% 0.18/0.52 % Propositional check models : 0
% 0.18/0.52 % Propositional check unsatisfiable : 0
% 0.18/0.52 % Propositional clauses : 0
% 0.18/0.52 % Propositional clauses after purity: 0
% 0.18/0.52 % Propositional unsat core size : 0
% 0.18/0.52 % Propositional preprocessing time : 0.000
% 0.18/0.52 % Propositional encoding time : 0.000
% 0.18/0.52 % Propositional solver time : 0.000
% 0.18/0.52 % Success case prop preproc time : 0.000
% 0.18/0.52 % Success case prop encoding time : 0.000
% 0.18/0.52 % Success case prop solver time : 0.000
% 0.18/0.52 % Current number of processed clauses : 98
% 0.18/0.52 % Positive orientable unit clauses : 94
% 0.18/0.52 % Positive unorientable unit clauses: 4
% 0.18/0.52 % Negative unit clauses : 0
% 0.18/0.52 % Non-unit-clauses : 0
% 0.18/0.52 % Current number of unprocessed clauses: 4474
% 0.18/0.52 % ...number of literals in the above : 4474
% 0.18/0.52 % Current number of archived formulas : 0
% 0.18/0.52 % Current number of archived clauses : 53
% 0.18/0.52 % Clause-clause subsumption calls (NU) : 0
% 0.18/0.52 % Rec. Clause-clause subsumption calls : 0
% 0.18/0.52 % Non-unit clause-clause subsumptions : 0
% 0.18/0.52 % Unit Clause-clause subsumption calls : 10
% 0.18/0.52 % Rewrite failures with RHS unbound : 0
% 0.18/0.52 % BW rewrite match attempts : 381
% 0.18/0.52 % BW rewrite match successes : 179
% 0.18/0.52 % Condensation attempts : 0
% 0.18/0.52 % Condensation successes : 0
% 0.18/0.52 % Termbank termtop insertions : 79372
% 0.18/0.52 % Search garbage collected termcells : 2
% 0.18/0.52
% 0.18/0.52 % -------------------------------------------------
% 0.18/0.52 % User time : 0.063 s
% 0.18/0.52 % System time : 0.010 s
% 0.18/0.52 % Total time : 0.073 s
% 0.18/0.52 % Maximum resident set size: 3596 pages
% 0.18/0.52
% 0.18/0.52 % -------------------------------------------------
% 0.18/0.52 % User time : 0.337 s
% 0.18/0.52 % System time : 0.033 s
% 0.18/0.52 % Total time : 0.371 s
% 0.18/0.52 % Maximum resident set size: 4864 pages
% 0.18/0.52 % E exiting
%------------------------------------------------------------------------------