%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO013-3 : 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 12:06:58 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.65s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of clauses : 53 ( 30 unt; 0 nHn; 42 RR)
% Number of literals : 95 ( 15 equ; 45 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity1) ).
cnf(commutativity_of_addition,axiom,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_addition) ).
cnf(multiplicative_identity2,axiom,
product(X1,multiplicative_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity2) ).
cnf(sum_to_multiplicative_identity2,negated_conjecture,
sum(x,z,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity2) ).
cnf(commutativity_of_multiplication,axiom,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',commutativity_of_multiplication) ).
cnf(product_to_additive_identity1,negated_conjecture,
product(x,y,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity1) ).
cnf(addition_is_well_defined,axiom,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',addition_is_well_defined) ).
cnf(sum_to_multiplicative_identity1,negated_conjecture,
sum(x,y,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_to_multiplicative_identity1) ).
cnf(multiplication_is_well_defined,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplication_is_well_defined) ).
cnf(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
cnf(product_to_additive_identity2,negated_conjecture,
product(x,z,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_to_additive_identity2) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(prove_both_inverse_are_equal,negated_conjecture,
y != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_both_inverse_are_equal) ).
cnf(c_0_14,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
inference(fof_simplification,[status(thm)],[distributivity1]) ).
cnf(c_0_15,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_16,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_14 ).
cnf(c_0_17,axiom,
product(X1,multiplicative_identity,X1),
multiplicative_identity2 ).
cnf(c_0_18,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_15 ).
cnf(c_0_19,negated_conjecture,
sum(x,z,multiplicative_identity),
sum_to_multiplicative_identity2 ).
cnf(c_0_20,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_multiplication]) ).
cnf(c_0_21,plain,
( ~ sum(X5,X4,multiplicative_identity)
| ~ product(X3,X5,X1)
| ~ product(X3,X4,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
sum(z,x,multiplicative_identity),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( ~ product(X1,X2,X3)
| product(X2,X1,X3) ),
c_0_20 ).
cnf(c_0_24,negated_conjecture,
product(x,y,additive_identity),
product_to_additive_identity1 ).
cnf(c_0_25,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_26,negated_conjecture,
sum(x,y,multiplicative_identity),
sum_to_multiplicative_identity1 ).
cnf(c_0_27,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_28,negated_conjecture,
( ~ product(X3,z,X1)
| ~ product(X3,x,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
product(y,x,additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_25 ).
cnf(c_0_31,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_32,negated_conjecture,
sum(y,x,multiplicative_identity),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
product(x,z,additive_identity),
product_to_additive_identity2 ).
cnf(c_0_34,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_27 ).
cnf(c_0_35,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_36,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_37,negated_conjecture,
( ~ product(y,z,X1)
| sum(X1,additive_identity,y) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
( ~ sum(X2,additive_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( ~ product(X3,y,X1)
| ~ product(X3,x,X2)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
product(z,x,additive_identity),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_41,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,plain,
product(X1,X2,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_43,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
sum(multiply(y,z),additive_identity,y),
inference(spm,[status(thm)],[c_0_37,c_0_35]) ).
cnf(c_0_45,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( ~ product(z,y,X1)
| sum(X1,additive_identity,z) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_47,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
multiply(y,z) = y,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_49,negated_conjecture,
y != z,
inference(fof_simplification,[status(thm)],[prove_both_inverse_are_equal]) ).
cnf(c_0_50,negated_conjecture,
sum(y,additive_identity,z),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_35]),c_0_47]),c_0_48]) ).
cnf(c_0_51,negated_conjecture,
y != z,
c_0_49 ).
cnf(c_0_52,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_50]),c_0_45]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.57 % Computer : n004.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Mon Sep 21 13:47:50 UTC 2026
% 0.11/0.57 % CPUTime :
% 0.11/0.57 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.61 Running first-order theorem proving
% 0.11/0.61 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
% 0.14/0.65 % Version: 3.5.1
% 0.14/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.65 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.65 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.65 % Starting sh5l with 300s (1) cores
% 0.14/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3292109 completed with status 0
% 0.14/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.65 % No SInE strategy applied
% 0.14/0.65 % Search class: FHUSM-FFMS21-SFFFFFNN
% 0.14/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.65 % Starting G-E--_301_C18_F1_URBAN_S0Y with 136s (1) cores
% 0.14/0.65 % Starting new_bool_3 with 136s (1) cores
% 0.14/0.65 % Starting new_bool_1 with 136s (1) cores
% 0.14/0.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3292116 completed with status 0
% 0.14/0.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/0.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/0.65 % No SInE strategy applied
% 0.14/0.65 % Search class: FHUSM-FFMS21-SFFFFFNN
% 0.14/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/0.65 % Starting SubtermCWHack with 136s (1) cores
% 0.14/0.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/0.65 % Preprocessing time : 0.001 s
% 0.14/0.65 % Presaturation interreduction done
% 0.14/0.65
% 0.14/0.65 % Proof found!
% 0.14/0.65 % SZS status Unsatisfiable
% 0.14/0.65 % SZS output start CNFRefutation
% See solution above
% 0.14/0.65 % Parsed axioms : 28
% 0.14/0.65 % Removed by relevancy pruning/SinE : 0
% 0.14/0.65 % Initial clauses : 28
% 0.14/0.65 % Removed in clause preprocessing : 0
% 0.14/0.65 % Initial clauses in saturation : 28
% 0.14/0.65 % Processed clauses : 383
% 0.14/0.65 % ...of these trivial : 37
% 0.14/0.65 % ...subsumed : 112
% 0.14/0.65 % ...remaining for further processing : 234
% 0.14/0.65 % Other redundant clauses eliminated : 0
% 0.14/0.65 % Clauses deleted for lack of memory : 0
% 0.14/0.65 % Backward-subsumed : 1
% 0.14/0.65 % Backward-rewritten : 10
% 0.14/0.65 % Generated clauses : 916
% 0.14/0.65 % ...of the previous two non-redundant : 709
% 0.14/0.65 % ...aggressively subsumed : 0
% 0.14/0.65 % Contextual simplify-reflections : 0
% 0.14/0.65 % Paramodulations : 916
% 0.14/0.65 % Factorizations : 0
% 0.14/0.65 % NegExts : 0
% 0.14/0.65 % Equation resolutions : 0
% 0.14/0.65 % Disequality decompositions : 0
% 0.14/0.65 % Total rewrite steps : 356
% 0.14/0.65 % ...of those cached : 255
% 0.14/0.65 % Propositional unsat checks : 0
% 0.14/0.65 % Propositional check models : 0
% 0.14/0.65 % Propositional check unsatisfiable : 0
% 0.14/0.65 % Propositional clauses : 0
% 0.14/0.65 % Propositional clauses after purity: 0
% 0.14/0.65 % Propositional unsat core size : 0
% 0.14/0.65 % Propositional preprocessing time : 0.000
% 0.14/0.65 % Propositional encoding time : 0.000
% 0.14/0.65 % Propositional solver time : 0.000
% 0.14/0.65 % Success case prop preproc time : 0.000
% 0.14/0.65 % Success case prop encoding time : 0.000
% 0.14/0.65 % Success case prop solver time : 0.000
% 0.14/0.65 % Current number of processed clauses : 195
% 0.14/0.65 % Positive orientable unit clauses : 47
% 0.14/0.65 % Positive unorientable unit clauses: 2
% 0.14/0.65 % Negative unit clauses : 1
% 0.14/0.65 % Non-unit-clauses : 145
% 0.14/0.65 % Current number of unprocessed clauses: 364
% 0.14/0.65 % ...number of literals in the above : 1183
% 0.14/0.65 % Current number of archived formulas : 0
% 0.14/0.65 % Current number of archived clauses : 39
% 0.14/0.65 % Clause-clause subsumption calls (NU) : 3666
% 0.14/0.65 % Rec. Clause-clause subsumption calls : 3019
% 0.14/0.65 % Non-unit clause-clause subsumptions : 111
% 0.14/0.65 % Unit Clause-clause subsumption calls : 2
% 0.14/0.65 % Rewrite failures with RHS unbound : 0
% 0.14/0.65 % BW rewrite match attempts : 159
% 0.14/0.65 % BW rewrite match successes : 48
% 0.14/0.65 % Condensation attempts : 0
% 0.14/0.65 % Condensation successes : 0
% 0.14/0.65 % Termbank termtop insertions : 10965
% 0.14/0.65 % Search garbage collected termcells : 68
% 0.14/0.65
% 0.14/0.65 % -------------------------------------------------
% 0.14/0.65 % User time : 0.015 s
% 0.14/0.65 % System time : 0.002 s
% 0.14/0.65 % Total time : 0.017 s
% 0.14/0.65 % Maximum resident set size: 3652 pages
% 0.14/0.65
% 0.14/0.65 % -------------------------------------------------
% 0.14/0.65 % User time : 0.068 s
% 0.14/0.65 % System time : 0.013 s
% 0.14/0.65 % Total time : 0.082 s
% 0.14/0.65 % Maximum resident set size: 4608 pages
% 0.14/0.65 % E exiting
%------------------------------------------------------------------------------