%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO008-2 : 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 : 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 12:06:55 PM UTC 2026
% Result : Unsatisfiable 0.65s 0.59s
% Output : CNFRefutation 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 6 RR)
% Number of literals : 48 ( 47 equ; 4 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(distributivity1,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(additive_id2,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(distributivity3,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',distributivity3) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
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_13,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2 ).
cnf(c_0_14,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_15,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_16,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_17,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_18,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_19,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
distributivity1 ).
cnf(c_0_20,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_22,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4 ).
cnf(c_0_23,axiom,
add(additive_identity,X1) = X1,
additive_id2 ).
cnf(c_0_24,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_25,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_17]),c_0_18]) ).
cnf(c_0_27,plain,
inverse(additive_identity) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_28,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_24]),c_0_14]) ).
cnf(c_0_29,plain,
add(X1,multiply(X1,X2)) = add(multiply(additive_identity,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_25]) ).
cnf(c_0_30,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_15]) ).
cnf(c_0_31,axiom,
multiply(add(X1,X2),X3) = add(multiply(X1,X3),multiply(X2,X3)),
distributivity3 ).
cnf(c_0_32,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_23]) ).
cnf(c_0_33,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_20]) ).
cnf(c_0_34,plain,
add(multiply(X1,add(X2,X3)),add(X2,multiply(X4,X3))) = multiply(add(X1,add(X2,X4)),add(X2,X3)),
inference(spm,[status(thm)],[c_0_31,c_0_13]) ).
cnf(c_0_35,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_36,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_37,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_38,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_39,plain,
add(X1,add(X2,multiply(X3,X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_40,plain,
add(add(X1,X2),add(X3,X2)) = add(add(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
inference(fof_simplification,[status(thm)],[prove_associativity]) ).
cnf(c_0_42,plain,
add(add(X1,X2),X3) = add(add(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_40]),c_0_40]) ).
cnf(c_0_43,negated_conjecture,
add(a,add(b,c)) != add(add(a,b),c),
c_0_41 ).
cnf(c_0_44,plain,
add(add(X1,X2),X3) = add(X1,add(X3,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
add(c,add(a,b)) != add(a,add(b,c)),
inference(rw,[status(thm)],[c_0_43,c_0_21]) ).
cnf(c_0_46,plain,
add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_44]),c_0_44]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:47:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.65/0.59 % Version: 3.5.1
% 0.65/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.65/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.65/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.65/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.65/0.59 % Starting sh5l with 300s (1) cores
% 0.65/0.59 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3291286 completed with status 0
% 0.65/0.59 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.65/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.65/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.65/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.59 % No SInE strategy applied
% 0.65/0.59 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.65/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.65/0.59 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.65/0.59 % Starting new_bool_3 with 136s (1) cores
% 0.65/0.59 % Starting new_bool_1 with 136s (1) cores
% 0.65/0.59 % SAT001_MinMin_p005000_rr_RG with pid 3291293 completed with status 0
% 0.65/0.59 % Result found by SAT001_MinMin_p005000_rr_RG
% 0.65/0.59 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.65/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.65/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.65/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.65/0.59 % No SInE strategy applied
% 0.65/0.59 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.65/0.59 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.65/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.65/0.59 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.65/0.59 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.65/0.59 % Preprocessing time : 0.001 s
% 0.65/0.59 % Presaturation interreduction done
% 0.65/0.59
% 0.65/0.59 % Proof found!
% 0.65/0.59 % SZS status Unsatisfiable
% 0.65/0.59 % SZS output start CNFRefutation
% See solution above
% 0.65/0.59 % Parsed axioms : 15
% 0.65/0.59 % Removed by relevancy pruning/SinE : 0
% 0.65/0.59 % Initial clauses : 15
% 0.65/0.59 % Removed in clause preprocessing : 0
% 0.65/0.59 % Initial clauses in saturation : 15
% 0.65/0.59 % Processed clauses : 687
% 0.65/0.59 % ...of these trivial : 373
% 0.65/0.59 % ...subsumed : 128
% 0.65/0.59 % ...remaining for further processing : 186
% 0.65/0.59 % Other redundant clauses eliminated : 0
% 0.65/0.59 % Clauses deleted for lack of memory : 0
% 0.65/0.59 % Backward-subsumed : 0
% 0.65/0.59 % Backward-rewritten : 52
% 0.65/0.59 % Generated clauses : 18497
% 0.65/0.59 % ...of the previous two non-redundant : 9934
% 0.65/0.59 % ...aggressively subsumed : 0
% 0.65/0.59 % Contextual simplify-reflections : 0
% 0.65/0.59 % Paramodulations : 18497
% 0.65/0.59 % Factorizations : 0
% 0.65/0.59 % NegExts : 0
% 0.65/0.59 % Equation resolutions : 0
% 0.65/0.59 % Disequality decompositions : 0
% 0.65/0.59 % Total rewrite steps : 18930
% 0.65/0.59 % ...of those cached : 15909
% 0.65/0.59 % Propositional unsat checks : 0
% 0.65/0.59 % Propositional check models : 0
% 0.65/0.59 % Propositional check unsatisfiable : 0
% 0.65/0.59 % Propositional clauses : 0
% 0.65/0.59 % Propositional clauses after purity: 0
% 0.65/0.59 % Propositional unsat core size : 0
% 0.65/0.59 % Propositional preprocessing time : 0.000
% 0.65/0.59 % Propositional encoding time : 0.000
% 0.65/0.59 % Propositional solver time : 0.000
% 0.65/0.59 % Success case prop preproc time : 0.000
% 0.65/0.59 % Success case prop encoding time : 0.000
% 0.65/0.59 % Success case prop solver time : 0.000
% 0.65/0.59 % Current number of processed clauses : 121
% 0.65/0.59 % Positive orientable unit clauses : 118
% 0.65/0.59 % Positive unorientable unit clauses: 3
% 0.65/0.59 % Negative unit clauses : 0
% 0.65/0.59 % Non-unit-clauses : 0
% 0.65/0.59 % Current number of unprocessed clauses: 9219
% 0.65/0.59 % ...number of literals in the above : 9219
% 0.65/0.59 % Current number of archived formulas : 0
% 0.65/0.59 % Current number of archived clauses : 65
% 0.65/0.59 % Clause-clause subsumption calls (NU) : 0
% 0.65/0.59 % Rec. Clause-clause subsumption calls : 0
% 0.65/0.59 % Non-unit clause-clause subsumptions : 0
% 0.65/0.59 % Unit Clause-clause subsumption calls : 25
% 0.65/0.59 % Rewrite failures with RHS unbound : 0
% 0.65/0.59 % BW rewrite match attempts : 562
% 0.65/0.59 % BW rewrite match successes : 230
% 0.65/0.59 % Condensation attempts : 0
% 0.65/0.59 % Condensation successes : 0
% 0.65/0.59 % Termbank termtop insertions : 150392
% 0.65/0.59 % Search garbage collected termcells : 2
% 0.65/0.59
% 0.65/0.59 % -------------------------------------------------
% 0.65/0.59 % User time : 0.144 s
% 0.65/0.59 % System time : 0.015 s
% 0.65/0.59 % Total time : 0.159 s
% 0.65/0.59 % Maximum resident set size: 3640 pages
% 0.65/0.59
% 0.65/0.59 % -------------------------------------------------
% 0.65/0.59 % User time : 0.705 s
% 0.65/0.59 % System time : 0.051 s
% 0.65/0.59 % Total time : 0.755 s
% 0.65/0.59 % Maximum resident set size: 4608 pages
% 0.65/0.59 % E exiting
%------------------------------------------------------------------------------