%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:06:57 PM UTC 2026
% Result : Unsatisfiable 7.98s 1.54s
% Output : CNFRefutation 7.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of clauses : 56 ( 29 unt; 0 nHn; 31 RR)
% Number of literals : 113 ( 17 equ; 60 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 6 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(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_inverse1,axiom,
sum(inverse(X1),X1,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_inverse1) ).
cnf(sum_product_dual2,axiom,
( ~ sum(X1,X2,X3)
| product(X1,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_product_dual2) ).
cnf(sum_and_multiply,axiom,
sum(X1,multiply(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_and_multiply) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_identity1) ).
cnf(multiplicative_inverse2,axiom,
product(X1,inverse(X1),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',multiplicative_inverse2) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_multiplication) ).
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(additive_identity2,axiom,
sum(X1,additive_identity,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity2) ).
cnf(distributivity4,axiom,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',distributivity4) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',closure_of_addition) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO002-0.ax',additive_identity1) ).
cnf(prove_inverse_is_an_involution,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
cnf(c_0_15,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_16,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
inference(fof_simplification,[status(thm)],[commutativity_of_addition]) ).
cnf(c_0_17,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[multiplication_is_well_defined]) ).
cnf(c_0_18,plain,
( ~ product(X1,X6,X7)
| ~ sum(X2,X4,X6)
| ~ product(X1,X4,X5)
| ~ product(X1,X2,X3)
| sum(X3,X5,X7) ),
c_0_15 ).
cnf(c_0_19,axiom,
sum(inverse(X1),X1,multiplicative_identity),
additive_inverse1 ).
cnf(c_0_20,plain,
( ~ sum(X1,X2,X3)
| product(X1,X3,X1) ),
inference(fof_simplification,[status(thm)],[sum_product_dual2]) ).
cnf(c_0_21,plain,
( ~ sum(X1,X2,X3)
| sum(X2,X1,X3) ),
c_0_16 ).
cnf(c_0_22,axiom,
sum(X1,multiply(X1,X2),X1),
sum_and_multiply ).
cnf(c_0_23,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| X3 = X4 ),
c_0_17 ).
cnf(c_0_24,axiom,
product(multiplicative_identity,X1,X1),
multiplicative_identity1 ).
cnf(c_0_25,plain,
( ~ product(X4,X5,X2)
| ~ product(X4,multiplicative_identity,X3)
| ~ product(X4,inverse(X5),X1)
| sum(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,axiom,
product(X1,inverse(X1),additive_identity),
multiplicative_inverse2 ).
cnf(c_0_27,plain,
( ~ sum(X1,X2,X3)
| product(X1,X3,X1) ),
c_0_20 ).
cnf(c_0_28,plain,
sum(multiply(X1,X2),X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( ~ product(multiplicative_identity,X2,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,axiom,
product(X1,X2,multiply(X1,X2)),
closure_of_multiplication ).
cnf(c_0_31,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
inference(fof_simplification,[status(thm)],[addition_is_well_defined]) ).
cnf(c_0_32,plain,
( ~ product(X3,multiplicative_identity,X2)
| ~ product(X3,inverse(inverse(X3)),X1)
| sum(X1,additive_identity,X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
product(multiply(X1,X2),X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ~ sum(X1,X2,X4)
| ~ sum(X1,X2,X3)
| X3 = X4 ),
c_0_31 ).
cnf(c_0_36,axiom,
sum(X1,additive_identity,X1),
additive_identity2 ).
cnf(c_0_37,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
inference(fof_simplification,[status(thm)],[distributivity4]) ).
cnf(c_0_38,axiom,
sum(X1,X2,add(X1,X2)),
closure_of_addition ).
cnf(c_0_39,plain,
( ~ product(X2,inverse(inverse(X2)),X1)
| sum(X1,additive_identity,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_40,plain,
( ~ sum(X2,additive_identity,X1)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( ~ sum(X3,X5,X7)
| ~ sum(X1,X4,X6)
| ~ product(X4,X2,X5)
| ~ product(X1,X2,X3)
| product(X6,X2,X7) ),
c_0_37 ).
cnf(c_0_42,axiom,
sum(additive_identity,X1,X1),
additive_identity1 ).
cnf(c_0_43,plain,
( ~ sum(X2,X3,X1)
| X1 = add(X2,X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_38]) ).
cnf(c_0_44,plain,
sum(multiply(X1,inverse(inverse(X1))),additive_identity,X1),
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_45,plain,
add(X1,additive_identity) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_46,plain,
( ~ sum(X4,X5,X1)
| ~ product(X5,X2,X3)
| ~ product(X4,X2,additive_identity)
| product(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
multiply(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_48,plain,
( ~ product(X3,X1,X2)
| ~ product(inverse(X3),X1,additive_identity)
| product(multiplicative_identity,X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_19]) ).
cnf(c_0_49,plain,
product(X1,inverse(inverse(X1)),X1),
inference(spm,[status(thm)],[c_0_30,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
inverse(inverse(x)) != x,
inference(fof_simplification,[status(thm)],[prove_inverse_is_an_involution]) ).
cnf(c_0_51,plain,
( ~ product(X2,X3,X1)
| X1 = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_52,plain,
product(multiplicative_identity,inverse(inverse(X1)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_26])]) ).
cnf(c_0_53,negated_conjecture,
inverse(inverse(x)) != x,
c_0_50 ).
cnf(c_0_54,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:50:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 7.98/1.54 % Version: 3.5.1
% 7.98/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.98/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.98/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.98/1.54 % Starting new_bool_3 with 300s (1) cores
% 7.98/1.54 % Starting new_bool_1 with 300s (1) cores
% 7.98/1.54 % Starting sh5l with 300s (1) cores
% 7.98/1.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3443129 completed with status 0
% 7.98/1.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.98/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.98/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.98/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.98/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.98/1.54 % No SInE strategy applied
% 7.98/1.54 % Search class: FHUSM-FFMF21-SFFFFFNN
% 7.98/1.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.98/1.54 % Starting SubtermCWHack with 136s (1) cores
% 7.98/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.98/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 7.98/1.54 % Starting new_bool_3 with 136s (1) cores
% 7.98/1.54 % Starting new_bool_1 with 136s (1) cores
% 7.98/1.54 % new_bool_3 with pid 3443136 completed with status 0
% 7.98/1.54 % Result found by new_bool_3
% 7.98/1.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.98/1.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.98/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.98/1.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.98/1.54 % No SInE strategy applied
% 7.98/1.54 % Search class: FHUSM-FFMF21-SFFFFFNN
% 7.98/1.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.98/1.54 % Starting SubtermCWHack with 136s (1) cores
% 7.98/1.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.98/1.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4d with 136s (1) cores
% 7.98/1.54 % Starting new_bool_3 with 136s (1) cores
% 7.98/1.54 % Preprocessing time : 0.001 s
% 7.98/1.54 % Presaturation interreduction done
% 7.98/1.54
% 7.98/1.54 % Proof found!
% 7.98/1.54 % SZS status Unsatisfiable
% 7.98/1.54 % SZS output start CNFRefutation
% See solution above
% 7.98/1.54 % Parsed axioms : 35
% 7.98/1.54 % Removed by relevancy pruning/SinE : 0
% 7.98/1.54 % Initial clauses : 35
% 7.98/1.54 % Removed in clause preprocessing : 0
% 7.98/1.54 % Initial clauses in saturation : 35
% 7.98/1.54 % Processed clauses : 11360
% 7.98/1.54 % ...of these trivial : 539
% 7.98/1.54 % ...subsumed : 9327
% 7.98/1.54 % ...remaining for further processing : 1494
% 7.98/1.54 % Other redundant clauses eliminated : 0
% 7.98/1.54 % Clauses deleted for lack of memory : 0
% 7.98/1.54 % Backward-subsumed : 36
% 7.98/1.54 % Backward-rewritten : 196
% 7.98/1.54 % Generated clauses : 65956
% 7.98/1.54 % ...of the previous two non-redundant : 48527
% 7.98/1.54 % ...aggressively subsumed : 0
% 7.98/1.54 % Contextual simplify-reflections : 0
% 7.98/1.54 % Paramodulations : 65956
% 7.98/1.54 % Factorizations : 0
% 7.98/1.54 % NegExts : 0
% 7.98/1.54 % Equation resolutions : 0
% 7.98/1.54 % Disequality decompositions : 0
% 7.98/1.54 % Total rewrite steps : 95867
% 7.98/1.54 % ...of those cached : 93553
% 7.98/1.54 % Propositional unsat checks : 0
% 7.98/1.54 % Propositional check models : 0
% 7.98/1.54 % Propositional check unsatisfiable : 0
% 7.98/1.54 % Propositional clauses : 0
% 7.98/1.54 % Propositional clauses after purity: 0
% 7.98/1.54 % Propositional unsat core size : 0
% 7.98/1.54 % Propositional preprocessing time : 0.000
% 7.98/1.54 % Propositional encoding time : 0.000
% 7.98/1.54 % Propositional solver time : 0.000
% 7.98/1.54 % Success case prop preproc time : 0.000
% 7.98/1.54 % Success case prop encoding time : 0.000
% 7.98/1.54 % Success case prop solver time : 0.000
% 7.98/1.54 % Current number of processed clauses : 1229
% 7.98/1.54 % Positive orientable unit clauses : 145
% 7.98/1.54 % Positive unorientable unit clauses: 2
% 7.98/1.54 % Negative unit clauses : 0
% 7.98/1.54 % Non-unit-clauses : 1082
% 7.98/1.54 % Current number of unprocessed clauses: 37057
% 7.98/1.54 % ...number of literals in the above : 89828
% 7.98/1.54 % Current number of archived formulas : 0
% 7.98/1.54 % Current number of archived clauses : 265
% 7.98/1.54 % Clause-clause subsumption calls (NU) : 490094
% 7.98/1.54 % Rec. Clause-clause subsumption calls : 382461
% 7.98/1.54 % Non-unit clause-clause subsumptions : 9319
% 7.98/1.54 % Unit Clause-clause subsumption calls : 5
% 7.98/1.54 % Rewrite failures with RHS unbound : 0
% 7.98/1.54 % BW rewrite match attempts : 1513
% 7.98/1.54 % BW rewrite match successes : 105
% 7.98/1.54 % Condensation attempts : 0
% 7.98/1.54 % Condensation successes : 0
% 7.98/1.54 % Termbank termtop insertions : 874829
% 7.98/1.54 % Search garbage collected termcells : 84
% 7.98/1.54
% 7.98/1.54 % -------------------------------------------------
% 7.98/1.54 % User time : 0.870 s
% 7.98/1.54 % System time : 0.023 s
% 7.98/1.54 % Total time : 0.893 s
% 7.98/1.54 % Maximum resident set size: 3656 pages
% 7.98/1.54
% 7.98/1.54 % -------------------------------------------------
% 7.98/1.54 % User time : 4.919 s
% 7.98/1.54 % System time : 0.193 s
% 7.98/1.54 % Total time : 5.112 s
% 7.98/1.54 % Maximum resident set size: 4608 pages
% 7.98/1.54 % E exiting
%------------------------------------------------------------------------------