%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO020-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:07:00 PM UTC 2026
% Result : Unsatisfiable 2.03s 0.68s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 4
% Syntax : Number of clauses : 61 ( 42 unt; 0 nHn; 22 RR)
% Number of literals : 83 ( 82 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 118 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(frink2,axiom,
( add(add(add(X1,X2),X3),X4) != add(add(X2,X3),X1)
| add(add(add(X1,X2),X3),inverse(X4)) = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',frink2) ).
cnf(frink1,axiom,
add(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',frink1) ).
cnf(frink3,axiom,
( add(add(add(X1,X2),X3),inverse(X4)) != n0
| add(add(add(X1,X2),X3),X4) = add(add(X2,X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',frink3) ).
cnf(prove_huntington,negated_conjecture,
( add(b,a) != add(a,b)
| add(add(a,b),c) != add(a,add(b,c))
| add(inverse(add(a,inverse(b))),inverse(add(inverse(a),inverse(b)))) != b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_huntington) ).
cnf(c_0_4,plain,
( add(add(add(X1,X2),X3),X4) != add(add(X2,X3),X1)
| add(add(add(X1,X2),X3),inverse(X4)) = n0 ),
inference(fof_simplification,[status(thm)],[frink2]) ).
cnf(c_0_5,plain,
( add(add(add(X1,X2),X3),X4) != add(add(X2,X3),X1)
| add(add(add(X1,X2),X3),inverse(X4)) = n0 ),
c_0_4 ).
cnf(c_0_6,axiom,
add(X1,X1) = X1,
frink1 ).
cnf(c_0_7,plain,
( add(add(X1,X2),X3) != add(add(X1,X2),X1)
| add(add(X1,X2),inverse(X3)) = n0 ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
( add(add(add(X1,X2),X3),inverse(X4)) != n0
| add(add(add(X1,X2),X3),X4) = add(add(X2,X3),X1) ),
inference(fof_simplification,[status(thm)],[frink3]) ).
cnf(c_0_9,plain,
( add(X1,X2) != X1
| add(X1,inverse(X2)) = n0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_6]) ).
cnf(c_0_10,plain,
( add(add(add(X1,X2),X3),inverse(X4)) != n0
| add(add(add(X1,X2),X3),X4) = add(add(X2,X3),X1) ),
c_0_8 ).
cnf(c_0_11,plain,
add(add(X1,X2),inverse(X1)) = n0,
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
add(X1,inverse(X1)) = n0,
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_13,plain,
( add(add(X1,X2),inverse(X3)) != n0
| add(add(X1,X2),X3) = add(add(X1,X2),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_14,plain,
add(n0,inverse(X1)) = n0,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( add(add(X1,X2),inverse(X3)) != n0
| add(add(X1,X2),X3) = add(add(X2,add(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_6]) ).
cnf(c_0_16,plain,
add(n0,X1) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_6]),c_0_14])]) ).
cnf(c_0_17,plain,
add(add(X1,add(X2,X1)),X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_6]) ).
cnf(c_0_18,plain,
add(add(X1,X2),n0) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_16]),c_0_16]),c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_19,plain,
( add(X1,inverse(X2)) != n0
| add(X1,X2) = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_6]),c_0_6]) ).
cnf(c_0_20,plain,
add(inverse(X1),X1) = n0,
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_21,plain,
add(X1,n0) = n0,
inference(spm,[status(thm)],[c_0_18,c_0_6]) ).
cnf(c_0_22,plain,
add(inverse(inverse(X1)),X1) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
inverse(inverse(n0)) = n0,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,plain,
add(X1,inverse(n0)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_21])]) ).
cnf(c_0_25,plain,
( add(add(X3,X1),X2) != n0
| add(add(X1,X2),X3) = n0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_21]) ).
cnf(c_0_26,plain,
add(add(X1,inverse(X2)),X2) = n0,
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_27,plain,
( add(X2,X1) != n0
| add(X1,X2) = n0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_24]),c_0_24]) ).
cnf(c_0_28,plain,
add(inverse(inverse(inverse(X1))),X1) = n0,
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_29,plain,
add(X1,inverse(inverse(inverse(X1)))) = n0,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_31,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_30]),c_0_22]),c_0_22]) ).
cnf(c_0_32,plain,
add(add(inverse(X1),X2),X1) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_12]),c_0_16])]) ).
cnf(c_0_33,plain,
( add(X1,X2) != n0
| add(X1,inverse(X2)) = X1 ),
inference(spm,[status(thm)],[c_0_19,c_0_31]) ).
cnf(c_0_34,plain,
add(add(X1,X2),inverse(X2)) = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_32]),c_0_16]),c_0_16])]) ).
cnf(c_0_35,plain,
add(add(X1,X2),X2) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_31]) ).
cnf(c_0_36,plain,
add(add(X1,X2),X3) = add(add(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_12]),c_0_6]) ).
cnf(c_0_37,plain,
add(add(X1,X2),X1) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_12]),c_0_6]) ).
cnf(c_0_38,plain,
add(X1,X2) = add(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_39,plain,
add(X1,add(inverse(X1),X2)) = n0,
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_40,plain,
add(X1,add(X2,inverse(X1))) = n0,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_41,plain,
( add(add(X1,X2),inverse(X3)) != n0
| add(add(X1,X2),X3) = add(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_24]) ).
cnf(c_0_42,plain,
add(add(X1,X2),X3) = add(X2,add(X3,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_38]) ).
cnf(c_0_43,plain,
add(X1,add(X2,add(inverse(add(X1,X2)),X3))) = n0,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_39]),c_0_16]),c_0_16])]),c_0_38]) ).
cnf(c_0_44,plain,
add(X1,inverse(add(X2,inverse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_40]) ).
cnf(c_0_45,plain,
add(inverse(X1),add(X1,X2)) = n0,
inference(spm,[status(thm)],[c_0_27,c_0_11]) ).
cnf(c_0_46,plain,
( add(X1,add(inverse(X2),X3)) != n0
| add(X1,add(X2,X3)) = add(X1,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
cnf(c_0_47,plain,
add(X1,add(X2,inverse(add(X1,X2)))) = n0,
inference(spm,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_48,plain,
add(inverse(add(X1,inverse(X2))),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_44]),c_0_35]) ).
cnf(c_0_49,plain,
add(inverse(X1),inverse(add(X1,X2))) = inverse(X1),
inference(spm,[status(thm)],[c_0_33,c_0_45]) ).
cnf(c_0_50,plain,
add(X1,inverse(add(X1,inverse(X2)))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_44]) ).
cnf(c_0_51,plain,
add(X1,add(X1,X2)) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_31]) ).
cnf(c_0_52,negated_conjecture,
( add(b,a) != add(a,b)
| add(add(a,b),c) != add(a,add(b,c))
| add(inverse(add(a,inverse(b))),inverse(add(inverse(a),inverse(b)))) != b ),
inference(fof_simplification,[status(thm)],[prove_huntington]) ).
cnf(c_0_53,plain,
add(X1,inverse(add(X1,X2))) = add(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_50]),c_0_51]) ).
cnf(c_0_54,plain,
add(inverse(X1),add(X2,X1)) = n0,
inference(spm,[status(thm)],[c_0_27,c_0_34]) ).
cnf(c_0_55,negated_conjecture,
( add(b,a) != add(a,b)
| add(add(a,b),c) != add(a,add(b,c))
| add(inverse(add(a,inverse(b))),inverse(add(inverse(a),inverse(b)))) != b ),
c_0_52 ).
cnf(c_0_56,plain,
add(X1,inverse(add(X2,X1))) = add(X1,inverse(X2)),
inference(spm,[status(thm)],[c_0_53,c_0_38]) ).
cnf(c_0_57,plain,
add(inverse(X1),inverse(add(X2,X1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_33,c_0_54]) ).
cnf(c_0_58,negated_conjecture,
add(inverse(add(a,inverse(b))),inverse(add(inverse(b),inverse(a)))) != b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_36]),c_0_38]),c_0_38]),c_0_38])]) ).
cnf(c_0_59,plain,
add(inverse(add(X1,X2)),inverse(add(X2,inverse(X1)))) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_56]),c_0_38]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO020-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 13:48:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 2.03/0.68 % Version: 3.5.1
% 2.03/0.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.03/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.03/0.68 % Starting new_bool_3 with 300s (1) cores
% 2.03/0.68 % Starting new_bool_1 with 300s (1) cores
% 2.03/0.68 % Starting sh5l with 300s (1) cores
% 2.03/0.68 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1024640 completed with status 0
% 2.03/0.68 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.03/0.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.03/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.03/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.03/0.68 % No SInE strategy applied
% 2.03/0.68 % Search class: FHHPF-FFSF21-MFFFFFNN
% 2.03/0.68 % partial match(1): FUHPF-FFSF21-MFFFFFNN
% 2.03/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.03/0.68 % Starting SubtermCWHack with 136s (1) cores
% 2.03/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.03/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 2.03/0.68 % Starting new_bool_3 with 136s (1) cores
% 2.03/0.68 % Starting new_bool_1 with 136s (1) cores
% 2.03/0.68 % new_bool_1 with pid 1024648 completed with status 0
% 2.03/0.68 % Result found by new_bool_1
% 2.03/0.68 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.03/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.03/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.03/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.03/0.68 % No SInE strategy applied
% 2.03/0.68 % Search class: FHHPF-FFSF21-MFFFFFNN
% 2.03/0.68 % partial match(1): FUHPF-FFSF21-MFFFFFNN
% 2.03/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.03/0.68 % Starting SubtermCWHack with 136s (1) cores
% 2.03/0.68 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.03/0.68 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 2.03/0.68 % Starting new_bool_3 with 136s (1) cores
% 2.03/0.68 % Starting new_bool_1 with 136s (1) cores
% 2.03/0.68 % Preprocessing time : 0.001 s
% 2.03/0.68 % Presaturation interreduction done
% 2.03/0.68
% 2.03/0.68 % Proof found!
% 2.03/0.68 % SZS status Unsatisfiable
% 2.03/0.68 % SZS output start CNFRefutation
% See solution above
% 2.03/0.68 % Parsed axioms : 4
% 2.03/0.68 % Removed by relevancy pruning/SinE : 0
% 2.03/0.68 % Initial clauses : 4
% 2.03/0.68 % Removed in clause preprocessing : 0
% 2.03/0.68 % Initial clauses in saturation : 4
% 2.03/0.68 % Processed clauses : 3560
% 2.03/0.68 % ...of these trivial : 323
% 2.03/0.68 % ...subsumed : 2834
% 2.03/0.68 % ...remaining for further processing : 403
% 2.03/0.68 % Other redundant clauses eliminated : 645
% 2.03/0.68 % Clauses deleted for lack of memory : 0
% 2.03/0.68 % Backward-subsumed : 3
% 2.03/0.68 % Backward-rewritten : 118
% 2.03/0.68 % Generated clauses : 36649
% 2.03/0.68 % ...of the previous two non-redundant : 25330
% 2.03/0.68 % ...aggressively subsumed : 0
% 2.03/0.68 % Contextual simplify-reflections : 0
% 2.03/0.68 % Paramodulations : 36002
% 2.03/0.68 % Factorizations : 0
% 2.03/0.68 % NegExts : 0
% 2.03/0.68 % Equation resolutions : 647
% 2.03/0.68 % Disequality decompositions : 0
% 2.03/0.68 % Total rewrite steps : 83010
% 2.03/0.68 % ...of those cached : 70497
% 2.03/0.68 % Propositional unsat checks : 0
% 2.03/0.68 % Propositional check models : 0
% 2.03/0.68 % Propositional check unsatisfiable : 0
% 2.03/0.68 % Propositional clauses : 0
% 2.03/0.68 % Propositional clauses after purity: 0
% 2.03/0.68 % Propositional unsat core size : 0
% 2.03/0.68 % Propositional preprocessing time : 0.000
% 2.03/0.68 % Propositional encoding time : 0.000
% 2.03/0.68 % Propositional solver time : 0.000
% 2.03/0.68 % Success case prop preproc time : 0.000
% 2.03/0.68 % Success case prop encoding time : 0.000
% 2.03/0.68 % Success case prop solver time : 0.000
% 2.03/0.68 % Current number of processed clauses : 259
% 2.03/0.68 % Positive orientable unit clauses : 52
% 2.03/0.68 % Positive unorientable unit clauses: 12
% 2.03/0.68 % Negative unit clauses : 0
% 2.03/0.68 % Non-unit-clauses : 195
% 2.03/0.68 % Current number of unprocessed clauses: 19975
% 2.03/0.68 % ...number of literals in the above : 32414
% 2.03/0.68 % Current number of archived formulas : 0
% 2.03/0.68 % Current number of archived clauses : 125
% 2.03/0.68 % Clause-clause subsumption calls (NU) : 20574
% 2.03/0.68 % Rec. Clause-clause subsumption calls : 20574
% 2.03/0.68 % Non-unit clause-clause subsumptions : 2609
% 2.03/0.68 % Unit Clause-clause subsumption calls : 254
% 2.03/0.68 % Rewrite failures with RHS unbound : 0
% 2.03/0.68 % BW rewrite match attempts : 1619
% 2.03/0.68 % BW rewrite match successes : 1001
% 2.03/0.68 % Condensation attempts : 0
% 2.03/0.68 % Condensation successes : 0
% 2.03/0.68 % Termbank termtop insertions : 425887
% 2.03/0.68 % Search garbage collected termcells : 12
% 2.03/0.68
% 2.03/0.68 % -------------------------------------------------
% 2.03/0.68 % User time : 0.242 s
% 2.03/0.68 % System time : 0.014 s
% 2.03/0.68 % Total time : 0.256 s
% 2.03/0.68 % Maximum resident set size: 3632 pages
% 2.03/0.68
% 2.03/0.68 % -------------------------------------------------
% 2.03/0.68 % User time : 1.164 s
% 2.03/0.68 % System time : 0.065 s
% 2.03/0.68 % Total time : 1.230 s
% 2.03/0.68 % Maximum resident set size: 4864 pages
% 2.03/0.68 % E exiting
%------------------------------------------------------------------------------