%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO014-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 1.88s 0.73s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 4 RR)
% Number of literals : 58 ( 57 equ; 3 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 102 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity1,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity1) ).
cnf(additive_inverse1,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_inverse1) ).
cnf(multiplicative_id1,axiom,
multiply(X1,multiplicative_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_id1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_multiply) ).
cnf(distributivity2,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',distributivity2) ).
cnf(multiplicative_inverse1,axiom,
multiply(X1,inverse(X1)) = additive_identity,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',multiplicative_inverse1) ).
cnf(additive_id1,axiom,
add(X1,additive_identity) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',additive_id1) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/BOO004-0.ax',commutativity_of_add) ).
cnf(prove_c_inverse_is_d,negated_conjecture,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_is_d) ).
cnf(c_0_9,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X1,X2),add(X1,X3)),
distributivity1 ).
cnf(c_0_10,axiom,
add(X1,inverse(X1)) = multiplicative_identity,
additive_inverse1 ).
cnf(c_0_11,axiom,
multiply(X1,multiplicative_identity) = X1,
multiplicative_id1 ).
cnf(c_0_12,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_13,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X1,X2),multiply(X1,X3)),
distributivity2 ).
cnf(c_0_14,axiom,
multiply(X1,inverse(X1)) = additive_identity,
multiplicative_inverse1 ).
cnf(c_0_15,axiom,
add(X1,additive_identity) = X1,
additive_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_9,c_0_10]),c_0_11]) ).
cnf(c_0_17,plain,
multiply(multiplicative_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
add(X1,multiplicative_identity) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_10]) ).
cnf(c_0_20,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_21,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_10]),c_0_11]) ).
cnf(c_0_22,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_11]),c_0_19]),c_0_11]),c_0_20]) ).
cnf(c_0_23,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_17]) ).
cnf(c_0_24,plain,
add(additive_identity,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_25,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_20]),c_0_22]) ).
cnf(c_0_26,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_14]),c_0_15]) ).
cnf(c_0_27,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_24]) ).
cnf(c_0_28,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_12]) ).
cnf(c_0_29,plain,
multiply(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_12]) ).
cnf(c_0_30,plain,
multiply(add(X1,X2),add(X3,X1)) = add(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(X2,inverse(X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_14]) ).
cnf(c_0_32,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_10]),c_0_11]),c_0_29]) ).
cnf(c_0_33,plain,
add(X1,multiply(multiply(X1,X2),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_25]) ).
cnf(c_0_34,plain,
multiply(inverse(X1),multiply(X2,X1)) = additive_identity,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
add(X1,add(X2,inverse(X1))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_25]),c_0_10]) ).
cnf(c_0_36,plain,
add(X1,inverse(inverse(multiply(X1,X2)))) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_37,plain,
multiply(X1,inverse(add(X2,X1))) = additive_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_25]),c_0_12]) ).
cnf(c_0_38,plain,
add(X1,inverse(multiply(X1,X2))) = multiplicative_identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_20]) ).
cnf(c_0_39,plain,
add(inverse(X1),multiply(X2,X1)) = add(inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_10]),c_0_11]) ).
cnf(c_0_40,plain,
add(X1,inverse(add(X2,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_37]),c_0_15]) ).
cnf(c_0_41,plain,
add(X1,multiply(add(X2,inverse(X1)),X3)) = add(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_35]),c_0_17]) ).
cnf(c_0_42,plain,
multiply(inverse(X1),add(X2,X1)) = multiply(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_43,plain,
multiply(X1,inverse(multiply(inverse(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_38]),c_0_11]) ).
cnf(c_0_44,plain,
multiply(add(X1,X2),add(X2,X3)) = add(X2,multiply(X1,X3)),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_45,plain,
add(multiply(X1,X2),inverse(add(X2,inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_18]),c_0_20]),c_0_40]),c_0_20]) ).
cnf(c_0_46,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_41]),c_0_27]),c_0_32]) ).
cnf(c_0_47,plain,
multiply(add(X1,X2),inverse(multiply(inverse(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_23]),c_0_12]),c_0_43]),c_0_12]) ).
cnf(c_0_48,plain,
add(inverse(X1),multiply(X1,X2)) = add(inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_10]),c_0_17]) ).
cnf(c_0_49,plain,
add(multiply(X1,X2),inverse(add(X1,inverse(X2)))) = X2,
inference(spm,[status(thm)],[c_0_45,c_0_12]) ).
cnf(c_0_50,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
add(multiply(X1,X2),inverse(X1)) = add(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_48]) ).
cnf(c_0_52,plain,
inverse(multiply(inverse(X1),X2)) = add(inverse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_32]),c_0_28]),c_0_51]) ).
cnf(c_0_53,negated_conjecture,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
inference(fof_simplification,[status(thm)],[prove_c_inverse_is_d]) ).
cnf(c_0_54,plain,
inverse(add(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
inverse(add(a,b)) != multiply(inverse(a),inverse(b)),
c_0_53 ).
cnf(c_0_56,plain,
multiply(inverse(X1),inverse(X2)) = inverse(add(X2,X1)),
inference(spm,[status(thm)],[c_0_54,c_0_32]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO014-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:46:06 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 1.88/0.73 % Version: 3.5.1
% 1.88/0.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.88/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.88/0.73 % Starting new_bool_3 with 300s (1) cores
% 1.88/0.73 % Starting new_bool_1 with 300s (1) cores
% 1.88/0.73 % Starting sh5l with 300s (1) cores
% 1.88/0.73 % new_bool_3 with pid 1244673 completed with status 0
% 1.88/0.73 % Result found by new_bool_3
% 1.88/0.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.88/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.88/0.73 % Starting new_bool_3 with 300s (1) cores
% 1.88/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.88/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.88/0.73 % Search class: FUUPM-FFSF21-SFFFFFNN
% 1.88/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.88/0.73 % Starting SubtermCWHack with 31s (1) cores
% 1.88/0.73 % SubtermCWHack with pid 1244678 completed with status 0
% 1.88/0.73 % Result found by SubtermCWHack
% 1.88/0.73 % Preprocessing class: FSSSSMSSSSSNFFN.
% 1.88/0.73 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.88/0.73 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.88/0.73 % Starting new_bool_3 with 300s (1) cores
% 1.88/0.73 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 1.88/0.73 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.88/0.73 % Search class: FUUPM-FFSF21-SFFFFFNN
% 1.88/0.73 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.88/0.73 % Starting SubtermCWHack with 31s (1) cores
% 1.88/0.73 % Preprocessing time : 0.001 s
% 1.88/0.73
% 1.88/0.73 % Proof found!
% 1.88/0.73 % SZS status Unsatisfiable
% 1.88/0.73 % SZS output start CNFRefutation
% See solution above
% 1.88/0.73 % Parsed axioms : 9
% 1.88/0.73 % Removed by relevancy pruning/SinE : 0
% 1.88/0.73 % Initial clauses : 9
% 1.88/0.73 % Removed in clause preprocessing : 0
% 1.88/0.73 % Initial clauses in saturation : 9
% 1.88/0.73 % Processed clauses : 2281
% 1.88/0.73 % ...of these trivial : 1363
% 1.88/0.73 % ...subsumed : 580
% 1.88/0.73 % ...remaining for further processing : 338
% 1.88/0.73 % Other redundant clauses eliminated : 0
% 1.88/0.73 % Clauses deleted for lack of memory : 0
% 1.88/0.73 % Backward-subsumed : 0
% 1.88/0.73 % Backward-rewritten : 31
% 1.88/0.73 % Generated clauses : 81775
% 1.88/0.73 % ...of the previous two non-redundant : 34894
% 1.88/0.73 % ...aggressively subsumed : 0
% 1.88/0.73 % Contextual simplify-reflections : 0
% 1.88/0.73 % Paramodulations : 81775
% 1.88/0.73 % Factorizations : 0
% 1.88/0.73 % NegExts : 0
% 1.88/0.73 % Equation resolutions : 0
% 1.88/0.73 % Disequality decompositions : 0
% 1.88/0.73 % Total rewrite steps : 94769
% 1.88/0.73 % ...of those cached : 83394
% 1.88/0.73 % Propositional unsat checks : 0
% 1.88/0.73 % Propositional check models : 0
% 1.88/0.73 % Propositional check unsatisfiable : 0
% 1.88/0.73 % Propositional clauses : 0
% 1.88/0.73 % Propositional clauses after purity: 0
% 1.88/0.73 % Propositional unsat core size : 0
% 1.88/0.73 % Propositional preprocessing time : 0.000
% 1.88/0.73 % Propositional encoding time : 0.000
% 1.88/0.73 % Propositional solver time : 0.000
% 1.88/0.73 % Success case prop preproc time : 0.000
% 1.88/0.73 % Success case prop encoding time : 0.000
% 1.88/0.73 % Success case prop solver time : 0.000
% 1.88/0.73 % Current number of processed clauses : 307
% 1.88/0.73 % Positive orientable unit clauses : 305
% 1.88/0.73 % Positive unorientable unit clauses: 2
% 1.88/0.73 % Negative unit clauses : 0
% 1.88/0.73 % Non-unit-clauses : 0
% 1.88/0.73 % Current number of unprocessed clauses: 32568
% 1.88/0.73 % ...number of literals in the above : 32568
% 1.88/0.73 % Current number of archived formulas : 0
% 1.88/0.73 % Current number of archived clauses : 31
% 1.88/0.73 % Clause-clause subsumption calls (NU) : 0
% 1.88/0.73 % Rec. Clause-clause subsumption calls : 0
% 1.88/0.73 % Non-unit clause-clause subsumptions : 0
% 1.88/0.73 % Unit Clause-clause subsumption calls : 0
% 1.88/0.73 % Rewrite failures with RHS unbound : 0
% 1.88/0.73 % BW rewrite match attempts : 952
% 1.88/0.73 % BW rewrite match successes : 35
% 1.88/0.73 % Condensation attempts : 0
% 1.88/0.73 % Condensation successes : 0
% 1.88/0.73 % Termbank termtop insertions : 647891
% 1.88/0.73 % Search garbage collected termcells : 2
% 1.88/0.73
% 1.88/0.73 % -------------------------------------------------
% 1.88/0.73 % User time : 0.270 s
% 1.88/0.73 % System time : 0.011 s
% 1.88/0.73 % Total time : 0.281 s
% 1.88/0.73 % Maximum resident set size: 3636 pages
% 1.88/0.73
% 1.88/0.73 % -------------------------------------------------
% 1.88/0.73 % User time : 0.271 s
% 1.88/0.73 % System time : 0.014 s
% 1.88/0.73 % Total time : 0.284 s
% 1.88/0.73 % Maximum resident set size: 4608 pages
% 1.88/0.73 % E exiting
%------------------------------------------------------------------------------