%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO015-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:06:59 PM UTC 2026
% Result : Unsatisfiable 0.25s 10.69s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 73 ( 73 unt; 0 nHn; 26 RR)
% Number of literals : 73 ( 72 equ; 3 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 77 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity2,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity2) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id1) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id1) ).
cnf(distributivity4,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity4) ).
cnf(additive_id2,axiom,
add(additive_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',additive_id2) ).
cnf(multiplicative_id2,axiom,
multiply(multiplicative_identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',multiplicative_id2) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_multiply) ).
cnf(a_inverse_plus_b_inverse_is_d,hypothesis,
add(inverse(a),inverse(b)) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_plus_b_inverse_is_d) ).
cnf(distributivity1,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',distributivity1) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO003-0.ax',commutativity_of_add) ).
cnf(a_times_b_is_c,hypothesis,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(prove_c_inverse_is_d,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_0_14,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity2 ).
cnf(c_0_15,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_16,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_17,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_18,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_19,axiom,
add(X1,additive_identity) = X1,
additive_id1 ).
cnf(c_0_20,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity4 ).
cnf(c_0_22,axiom,
add(additive_identity,X1) = X1,
additive_id2 ).
cnf(c_0_23,axiom,
multiply(multiplicative_identity,X1) = X1,
multiplicative_id2 ).
cnf(c_0_24,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_25,plain,
multiply(X1,add(X1,X2)) = add(X1,multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_26,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_19]) ).
cnf(c_0_27,hypothesis,
add(inverse(a),inverse(b)) = d,
a_inverse_plus_b_inverse_is_d ).
cnf(c_0_28,plain,
inverse(additive_identity) = multiplicative_identity,
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_29,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_15]) ).
cnf(c_0_30,axiom,
add(multiply(X1,X2),X3) = multiply(add(X1,X3),add(X2,X3)),
distributivity1 ).
cnf(c_0_31,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_32,plain,
add(X1,multiply(X1,X2)) = add(X1,multiply(X2,additive_identity)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_24]),c_0_25]) ).
cnf(c_0_33,plain,
multiply(X1,additive_identity) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_22]),c_0_18]) ).
cnf(c_0_34,hypothesis,
add(inverse(a),multiply(X1,inverse(b))) = multiply(d,add(inverse(a),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_27]),c_0_24]) ).
cnf(c_0_35,plain,
multiply(additive_identity,X1) = additive_identity,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_29]),c_0_16]) ).
cnf(c_0_36,plain,
multiply(X1,add(X2,X1)) = add(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_31]) ).
cnf(c_0_37,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_19]) ).
cnf(c_0_38,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_23]) ).
cnf(c_0_39,hypothesis,
multiply(d,inverse(a)) = inverse(a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19]),c_0_19]) ).
cnf(c_0_40,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_18]),c_0_19]) ).
cnf(c_0_42,hypothesis,
add(a,d) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_39]),c_0_15]) ).
cnf(c_0_43,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_22]) ).
cnf(c_0_44,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_24]) ).
cnf(c_0_45,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_24]) ).
cnf(c_0_46,hypothesis,
multiply(a,b) = c,
a_times_b_is_c ).
cnf(c_0_47,hypothesis,
add(d,multiply(a,X1)) = add(X1,d),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_42]),c_0_23]),c_0_31]) ).
cnf(c_0_48,hypothesis,
multiply(d,inverse(b)) = inverse(b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_24]) ).
cnf(c_0_49,plain,
multiply(X1,multiply(inverse(X1),X2)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_37]),c_0_18]) ).
cnf(c_0_50,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_15]),c_0_16]),c_0_44]) ).
cnf(c_0_51,hypothesis,
add(b,c) = b,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,hypothesis,
add(c,d) = add(b,d),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_46]),c_0_31]) ).
cnf(c_0_53,hypothesis,
add(b,d) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_48]),c_0_15]) ).
cnf(c_0_54,plain,
multiply(inverse(X1),multiply(X1,X2)) = additive_identity,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_55,hypothesis,
multiply(b,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_51]),c_0_24]) ).
cnf(c_0_56,hypothesis,
add(a,c) = a,
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_57,hypothesis,
add(c,d) = multiplicative_identity,
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,plain,
add(multiply(X1,X2),inverse(X1)) = add(X2,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_15]),c_0_23]) ).
cnf(c_0_59,hypothesis,
multiply(c,inverse(b)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_24]) ).
cnf(c_0_60,hypothesis,
multiply(a,c) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_56]),c_0_24]) ).
cnf(c_0_61,hypothesis,
add(d,multiply(c,X1)) = add(X1,d),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_57]),c_0_23]),c_0_31]) ).
cnf(c_0_62,plain,
multiply(X1,add(X1,X2)) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_63,hypothesis,
add(inverse(b),inverse(c)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_22]) ).
cnf(c_0_64,hypothesis,
multiply(c,inverse(a)) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_60]),c_0_24]) ).
cnf(c_0_65,hypothesis,
add(d,inverse(c)) = d,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_18]),c_0_19]),c_0_31]) ).
cnf(c_0_66,negated_conjecture,
inverse(c) != d,
inference(fof_simplification,[status(thm)],[prove_c_inverse_is_d]) ).
cnf(c_0_67,hypothesis,
add(inverse(a),multiply(inverse(b),X1)) = multiply(d,add(inverse(a),X1)),
inference(spm,[status(thm)],[c_0_14,c_0_27]) ).
cnf(c_0_68,hypothesis,
multiply(inverse(b),inverse(c)) = inverse(b),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,hypothesis,
add(inverse(a),inverse(c)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_64]),c_0_22]) ).
cnf(c_0_70,hypothesis,
multiply(d,inverse(c)) = inverse(c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_65]),c_0_24]) ).
cnf(c_0_71,negated_conjecture,
inverse(c) != d,
c_0_66 ).
cnf(c_0_72,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_27]),c_0_69]),c_0_70]),c_0_71]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO015-2 : TPTP v9.3.1. Bugfixed v1.0.1.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/10.49 % Computer : n008.cluster.edu
% 0.20/10.49 % Model : x86_64 x86_64
% 0.20/10.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/10.49 % Memory : 8046.5625MB
% 0.20/10.49 % OS : Linux 6.8.0-71-generic
% 0.20/10.49 % CPULimit : 300
% 0.20/10.49 % WCLimit : 300
% 0.20/10.49 % DateTime : Mon Sep 21 13:49:20 UTC 2026
% 0.20/10.49 % CPUTime :
% 0.20/10.49 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/10.57 Running first-order theorem proving
% 0.25/10.57 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
% 0.25/10.69 % Version: 3.5.1
% 0.25/10.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/10.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/10.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/10.69 % Starting new_bool_3 with 300s (1) cores
% 0.25/10.69 % Starting new_bool_1 with 300s (1) cores
% 0.25/10.69 % Starting sh5l with 300s (1) cores
% 0.25/10.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1142887 completed with status 0
% 0.25/10.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/10.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/10.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/10.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/10.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/10.69 % No SInE strategy applied
% 0.25/10.69 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.25/10.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/10.69 % Starting SubtermCWHack with 136s (1) cores
% 0.25/10.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/10.69 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.25/10.69 % Starting new_bool_3 with 136s (1) cores
% 0.25/10.69 % Starting new_bool_1 with 136s (1) cores
% 0.25/10.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1142892 completed with status 0
% 0.25/10.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.25/10.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.25/10.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.25/10.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.25/10.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.25/10.69 % No SInE strategy applied
% 0.25/10.69 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.25/10.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.25/10.69 % Starting SubtermCWHack with 136s (1) cores
% 0.25/10.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.25/10.69 % Preprocessing time : 0.002 s
% 0.25/10.69 % Presaturation interreduction done
% 0.25/10.69
% 0.25/10.69 % Proof found!
% 0.25/10.69 % SZS status Unsatisfiable
% 0.25/10.69 % SZS output start CNFRefutation
% See solution above
% 0.25/10.70 % Parsed axioms : 17
% 0.25/10.70 % Removed by relevancy pruning/SinE : 0
% 0.25/10.70 % Initial clauses : 17
% 0.25/10.70 % Removed in clause preprocessing : 0
% 0.25/10.70 % Initial clauses in saturation : 17
% 0.25/10.70 % Processed clauses : 508
% 0.25/10.70 % ...of these trivial : 256
% 0.25/10.70 % ...subsumed : 27
% 0.25/10.70 % ...remaining for further processing : 225
% 0.25/10.70 % Other redundant clauses eliminated : 0
% 0.25/10.70 % Clauses deleted for lack of memory : 0
% 0.25/10.70 % Backward-subsumed : 0
% 0.25/10.70 % Backward-rewritten : 41
% 0.25/10.70 % Generated clauses : 7834
% 0.25/10.70 % ...of the previous two non-redundant : 4579
% 0.25/10.70 % ...aggressively subsumed : 0
% 0.25/10.70 % Contextual simplify-reflections : 0
% 0.25/10.70 % Paramodulations : 7834
% 0.25/10.70 % Factorizations : 0
% 0.25/10.70 % NegExts : 0
% 0.25/10.70 % Equation resolutions : 0
% 0.25/10.70 % Disequality decompositions : 0
% 0.25/10.70 % Total rewrite steps : 8318
% 0.25/10.70 % ...of those cached : 6877
% 0.25/10.70 % Propositional unsat checks : 0
% 0.25/10.70 % Propositional check models : 0
% 0.25/10.70 % Propositional check unsatisfiable : 0
% 0.25/10.70 % Propositional clauses : 0
% 0.25/10.70 % Propositional clauses after purity: 0
% 0.25/10.70 % Propositional unsat core size : 0
% 0.25/10.70 % Propositional preprocessing time : 0.000
% 0.25/10.70 % Propositional encoding time : 0.000
% 0.25/10.70 % Propositional solver time : 0.000
% 0.25/10.70 % Success case prop preproc time : 0.000
% 0.25/10.70 % Success case prop encoding time : 0.000
% 0.25/10.70 % Success case prop solver time : 0.000
% 0.25/10.70 % Current number of processed clauses : 169
% 0.25/10.70 % Positive orientable unit clauses : 166
% 0.25/10.70 % Positive unorientable unit clauses: 2
% 0.25/10.70 % Negative unit clauses : 1
% 0.25/10.70 % Non-unit-clauses : 0
% 0.25/10.70 % Current number of unprocessed clauses: 4068
% 0.25/10.70 % ...number of literals in the above : 4068
% 0.25/10.70 % Current number of archived formulas : 0
% 0.25/10.70 % Current number of archived clauses : 56
% 0.25/10.70 % Clause-clause subsumption calls (NU) : 0
% 0.25/10.70 % Rec. Clause-clause subsumption calls : 0
% 0.25/10.70 % Non-unit clause-clause subsumptions : 0
% 0.25/10.70 % Unit Clause-clause subsumption calls : 2
% 0.25/10.70 % Rewrite failures with RHS unbound : 0
% 0.25/10.70 % BW rewrite match attempts : 280
% 0.25/10.70 % BW rewrite match successes : 70
% 0.25/10.70 % Condensation attempts : 0
% 0.25/10.70 % Condensation successes : 0
% 0.25/10.70 % Termbank termtop insertions : 72443
% 0.25/10.70 % Search garbage collected termcells : 2
% 0.25/10.70
% 0.25/10.70 % -------------------------------------------------
% 0.25/10.70 % User time : 0.074 s
% 0.25/10.70 % System time : 0.011 s
% 0.25/10.70 % Total time : 0.085 s
% 0.25/10.70 % Maximum resident set size: 3588 pages
% 0.25/10.70
% 0.25/10.70 % -------------------------------------------------
% 0.25/10.70 % User time : 0.308 s
% 0.25/10.70 % System time : 0.035 s
% 0.25/10.70 % Total time : 0.343 s
% 0.25/10.70 % Maximum resident set size: 4864 pages
% 0.25/10.70 % E exiting
%------------------------------------------------------------------------------