%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO007-4 : 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 : n015.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 0.25s 0.65s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 50 ( 50 unt; 0 nHn; 5 RR)
% Number of literals : 50 ( 49 equ; 4 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 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
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(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(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
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(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
cnf(prove_associativity,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity) ).
cnf(c_0_9,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_10,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_11,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity2 ).
cnf(c_0_12,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_13,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity1 ).
cnf(c_0_14,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_15,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_16,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,plain,
add(X1,multiply(X1,X2)) = multiply(X1,add(X2,multiplicative_identity)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_10]) ).
cnf(c_0_18,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_12]) ).
cnf(c_0_19,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_20,plain,
multiply(additive_identity,add(X1,multiplicative_identity)) = multiply(additive_identity,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_14]) ).
cnf(c_0_22,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_23,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21]),c_0_12]) ).
cnf(c_0_24,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_19]) ).
cnf(c_0_25,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_26,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_9]),c_0_23]),c_0_9]) ).
cnf(c_0_27,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_9]) ).
cnf(c_0_28,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_25]),c_0_9]) ).
cnf(c_0_29,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_25]),c_0_16]) ).
cnf(c_0_30,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_15]) ).
cnf(c_0_31,plain,
multiply(multiply(X1,add(X2,X3)),add(multiply(X1,X2),X4)) = add(multiply(X1,X2),multiply(multiply(X1,X3),X4)),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_32,plain,
add(multiplicative_identity,X1) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_10,c_0_21]) ).
cnf(c_0_33,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_28]),c_0_17]),c_0_21]),c_0_12]) ).
cnf(c_0_34,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_21]),c_0_12]) ).
cnf(c_0_35,plain,
add(X1,multiply(multiply(X2,inverse(X1)),X3)) = add(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_13]) ).
cnf(c_0_36,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_12]),c_0_30]) ).
cnf(c_0_37,plain,
add(X1,multiply(multiply(X1,X2),X3)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_12]),c_0_32]),c_0_12]),c_0_33]) ).
cnf(c_0_38,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
inference(fof_simplification,[status(thm)],[prove_associativity]) ).
cnf(c_0_39,plain,
multiply(X1,multiply(X1,X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_34]),c_0_15]) ).
cnf(c_0_40,plain,
multiply(X1,multiply(multiply(X2,X1),X3)) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_35]),c_0_29]),c_0_36]) ).
cnf(c_0_41,plain,
multiply(X1,multiply(multiply(X1,X2),X3)) = multiply(multiply(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_15]) ).
cnf(c_0_42,plain,
add(X1,multiply(X2,multiply(X3,inverse(X1)))) = add(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_13]) ).
cnf(c_0_43,negated_conjecture,
multiply(a,multiply(b,c)) != multiply(multiply(a,b),c),
c_0_38 ).
cnf(c_0_44,plain,
multiply(X1,multiply(X2,X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_39,c_0_15]) ).
cnf(c_0_45,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_15]),c_0_41]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(X2,multiply(X3,X1))) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_42]),c_0_29]),c_0_36]) ).
cnf(c_0_47,negated_conjecture,
multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_43,c_0_15]) ).
cnf(c_0_48,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_15]),c_0_48]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO007-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n015.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Mon Sep 21 13:50:21 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.52 Running first-order theorem proving
% 0.25/0.52 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
% 0.25/0.65 % Version: 3.5.1
% 0.25/0.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.25/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.25/0.65 % Starting sh5l with 300s (1) cores
% 0.25/0.65 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1622133 completed with status 0
% 0.25/0.65 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.25/0.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.65 % No SInE strategy applied
% 0.25/0.65 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.25/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.65 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.25/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.25/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.25/0.65 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1622139 completed with status 0
% 0.25/0.65 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.25/0.65 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.25/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.25/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/0.65 % No SInE strategy applied
% 0.25/0.65 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.25/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.25/0.65 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.25/0.65 % Preprocessing time : 0.002 s
% 0.25/0.65
% 0.25/0.65 % Proof found!
% 0.25/0.65 % SZS status Unsatisfiable
% 0.25/0.65 % SZS output start CNFRefutation
% See solution above
% 0.25/0.65 % Parsed axioms : 9
% 0.25/0.65 % Removed by relevancy pruning/SinE : 0
% 0.25/0.65 % Initial clauses : 9
% 0.25/0.65 % Removed in clause preprocessing : 0
% 0.25/0.65 % Initial clauses in saturation : 9
% 0.25/0.65 % Processed clauses : 225
% 0.25/0.65 % ...of these trivial : 83
% 0.25/0.65 % ...subsumed : 53
% 0.25/0.65 % ...remaining for further processing : 89
% 0.25/0.65 % Other redundant clauses eliminated : 0
% 0.25/0.65 % Clauses deleted for lack of memory : 0
% 0.25/0.65 % Backward-subsumed : 0
% 0.25/0.65 % Backward-rewritten : 24
% 0.25/0.65 % Generated clauses : 3992
% 0.25/0.65 % ...of the previous two non-redundant : 2632
% 0.25/0.65 % ...aggressively subsumed : 0
% 0.25/0.65 % Contextual simplify-reflections : 0
% 0.25/0.65 % Paramodulations : 3992
% 0.25/0.65 % Factorizations : 0
% 0.25/0.65 % NegExts : 0
% 0.25/0.65 % Equation resolutions : 0
% 0.25/0.65 % Disequality decompositions : 0
% 0.25/0.65 % Total rewrite steps : 4994
% 0.25/0.65 % ...of those cached : 3927
% 0.25/0.65 % Propositional unsat checks : 0
% 0.25/0.65 % Propositional check models : 0
% 0.25/0.65 % Propositional check unsatisfiable : 0
% 0.25/0.65 % Propositional clauses : 0
% 0.25/0.65 % Propositional clauses after purity: 0
% 0.25/0.65 % Propositional unsat core size : 0
% 0.25/0.65 % Propositional preprocessing time : 0.000
% 0.25/0.65 % Propositional encoding time : 0.000
% 0.25/0.65 % Propositional solver time : 0.000
% 0.25/0.65 % Success case prop preproc time : 0.000
% 0.25/0.65 % Success case prop encoding time : 0.000
% 0.25/0.65 % Success case prop solver time : 0.000
% 0.25/0.65 % Current number of processed clauses : 65
% 0.25/0.65 % Positive orientable unit clauses : 62
% 0.25/0.65 % Positive unorientable unit clauses: 3
% 0.25/0.65 % Negative unit clauses : 0
% 0.25/0.65 % Non-unit-clauses : 0
% 0.25/0.65 % Current number of unprocessed clauses: 2341
% 0.25/0.65 % ...number of literals in the above : 2341
% 0.25/0.65 % Current number of archived formulas : 0
% 0.25/0.65 % Current number of archived clauses : 24
% 0.25/0.65 % Clause-clause subsumption calls (NU) : 0
% 0.25/0.65 % Rec. Clause-clause subsumption calls : 0
% 0.25/0.65 % Non-unit clause-clause subsumptions : 0
% 0.25/0.65 % Unit Clause-clause subsumption calls : 7
% 0.25/0.65 % Rewrite failures with RHS unbound : 0
% 0.25/0.65 % BW rewrite match attempts : 202
% 0.25/0.65 % BW rewrite match successes : 71
% 0.25/0.65 % Condensation attempts : 0
% 0.25/0.65 % Condensation successes : 0
% 0.25/0.65 % Termbank termtop insertions : 38244
% 0.25/0.65 % Search garbage collected termcells : 2
% 0.25/0.65
% 0.25/0.65 % -------------------------------------------------
% 0.25/0.65 % User time : 0.081 s
% 0.25/0.65 % System time : 0.008 s
% 0.25/0.65 % Total time : 0.089 s
% 0.25/0.65 % Maximum resident set size: 3636 pages
% 0.25/0.65
% 0.25/0.65 % -------------------------------------------------
% 0.25/0.65 % User time : 0.392 s
% 0.25/0.65 % System time : 0.040 s
% 0.25/0.65 % Total time : 0.431 s
% 0.25/0.65 % Maximum resident set size: 4608 pages
% 0.25/0.65 % E exiting
%------------------------------------------------------------------------------