%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO025-1 : 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 : n009.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 12:07:01 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of clauses : 59 ( 59 unt; 0 nHn; 7 RR)
% Number of literals : 59 ( 58 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 98 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(multiply_add,axiom,
multiply(add(X1,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add) ).
cnf(multiply_add_property,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_add_property) ).
cnf(pixley1,axiom,
pixley(X1,X1,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley1) ).
cnf(pixley_defn,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley_defn) ).
cnf(additive_inverse,axiom,
add(X1,inverse(X1)) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_inverse) ).
cnf(pixley2,axiom,
pixley(X1,X2,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pixley2) ).
cnf(prove_equal_identity,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equal_identity) ).
cnf(c_0_7,axiom,
multiply(add(X1,X2),X2) = X2,
multiply_add ).
cnf(c_0_8,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
multiply_add_property ).
cnf(c_0_9,plain,
multiply(multiply(X1,add(X2,X3)),multiply(X3,X1)) = multiply(X3,X1),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,axiom,
pixley(X1,X1,X2) = X2,
pixley1 ).
cnf(c_0_11,axiom,
pixley(X1,X2,X3) = add(multiply(X1,inverse(X2)),add(multiply(X1,X3),multiply(inverse(X2),X3))),
pixley_defn ).
cnf(c_0_12,plain,
multiply(multiply(X1,add(X2,add(X3,X1))),X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_13,plain,
add(multiply(X1,inverse(X1)),add(multiply(X1,X2),multiply(inverse(X1),X2))) = X2,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
add(X1,inverse(X1)) = n1,
additive_inverse ).
cnf(c_0_15,plain,
multiply(multiply(X1,add(X2,multiply(X1,add(X3,add(X4,X1))))),X1) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_16,plain,
add(multiply(X1,inverse(X1)),multiply(X2,n1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_8]),c_0_14]) ).
cnf(c_0_17,plain,
multiply(n1,inverse(X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_18,plain,
multiply(multiply(X1,multiply(add(X2,add(X3,X1)),add(X4,X1))),X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_19,plain,
multiply(X1,multiply(X1,n1)) = multiply(X1,n1),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_20,plain,
add(inverse(n1),multiply(X1,n1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
multiply(multiply(X1,add(X2,X1)),X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_7]) ).
cnf(c_0_22,plain,
multiply(X1,add(multiply(X1,add(X2,add(X3,X1))),X4)) = add(X1,multiply(X4,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_12]) ).
cnf(c_0_23,plain,
add(multiply(X1,n1),multiply(X2,multiply(X1,n1))) = multiply(multiply(X1,n1),add(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_19]) ).
cnf(c_0_24,plain,
add(inverse(n1),n1) = add(X1,n1),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
cnf(c_0_25,plain,
multiply(add(X1,multiply(X1,X1)),X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
multiply(multiply(X1,X2),multiply(multiply(X2,n1),X1)) = multiply(multiply(X2,n1),X1),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_27,plain,
multiply(multiply(X1,n1),add(X1,X1)) = multiply(n1,add(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_8]) ).
cnf(c_0_28,plain,
add(X1,n1) = add(X2,n1),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_29,plain,
add(inverse(n1),n1) = add(n1,multiply(n1,n1)),
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(multiply(X1,n1),add(X2,X1))) = multiply(multiply(X1,n1),add(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_7]) ).
cnf(c_0_31,plain,
add(multiply(X1,X2),X2) = multiply(X2,add(X1,add(X3,X2))),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_32,plain,
multiply(add(X1,X1),add(X2,multiply(X1,n1))) = multiply(add(X1,X1),add(X2,n1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_27]),c_0_8]) ).
cnf(c_0_33,plain,
add(X1,n1) = add(n1,multiply(n1,n1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
multiply(X1,multiply(n1,add(X1,X1))) = multiply(n1,add(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_19]),c_0_8]),c_0_19]),c_0_8]) ).
cnf(c_0_35,plain,
add(X1,n1) = multiply(n1,add(X2,add(X3,n1))),
inference(spm,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_36,plain,
multiply(add(X1,X1),add(n1,multiply(n1,n1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_20]),c_0_7]),c_0_33]) ).
cnf(c_0_37,plain,
multiply(add(X1,n1),add(X2,n1)) = add(X2,n1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
add(n1,n1) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_36]),c_0_37]) ).
cnf(c_0_39,plain,
multiply(n1,n1) = n1,
inference(spm,[status(thm)],[c_0_7,c_0_38]) ).
cnf(c_0_40,plain,
multiply(X1,add(add(X2,X1),X3)) = add(X1,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_41,plain,
multiply(add(X1,X1),n1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_39]),c_0_38]) ).
cnf(c_0_42,plain,
multiply(X1,add(X2,n1)) = add(X1,multiply(n1,X1)),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_43,plain,
add(X1,n1) = n1,
inference(spm,[status(thm)],[c_0_28,c_0_38]) ).
cnf(c_0_44,plain,
add(inverse(n1),X1) = add(X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_45,plain,
add(X1,multiply(n1,X1)) = multiply(X1,n1),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
multiply(n1,add(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_44]),c_0_8]) ).
cnf(c_0_47,axiom,
pixley(X1,X2,X2) = X1,
pixley2 ).
cnf(c_0_48,plain,
add(add(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41]) ).
cnf(c_0_49,plain,
multiply(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_46]),c_0_46]) ).
cnf(c_0_50,plain,
add(multiply(X1,inverse(X2)),add(multiply(X1,X2),multiply(inverse(X2),X2))) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_11]) ).
cnf(c_0_51,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_48]),c_0_49]),c_0_49]) ).
cnf(c_0_52,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
inference(fof_simplification,[status(thm)],[prove_equal_identity]) ).
cnf(c_0_53,plain,
add(multiply(X1,inverse(X2)),multiply(X2,add(X1,inverse(X2)))) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_8]) ).
cnf(c_0_54,plain,
add(inverse(n1),X1) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_51]) ).
cnf(c_0_55,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_51]),c_0_51]) ).
cnf(c_0_56,negated_conjecture,
multiply(b,inverse(b)) != multiply(a,inverse(a)),
c_0_52 ).
cnf(c_0_57,plain,
multiply(X1,inverse(X1)) = inverse(n1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_8]),c_0_54]),c_0_55]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_57]),c_0_57])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO025-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:48:43 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.45 % Version: 3.5.1
% 0.12/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.12/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.12/0.45 % Starting sh5l with 300s (1) cores
% 0.12/0.45 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1917257 completed with status 0
% 0.12/0.45 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.12/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.12/0.45 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.12/0.45 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.12/0.45 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 0.12/0.45 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 0.12/0.45 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 1917264 completed with status 0
% 0.12/0.45 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 0.12/0.45 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.12/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.12/0.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/0.45 % No SInE strategy applied
% 0.12/0.45 % Search class: FUUPM-FFSF21-MFFFFFNN
% 0.12/0.45 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/0.45 % Starting SubtermCWHack with 136s (1) cores
% 0.12/0.45 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.12/0.45 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 0.12/0.45 % Preprocessing time : 0.001 s
% 0.12/0.45
% 0.12/0.45 % Proof found!
% 0.12/0.45 % SZS status Unsatisfiable
% 0.12/0.45 % SZS output start CNFRefutation
% See solution above
% 0.12/0.45 % Parsed axioms : 8
% 0.12/0.45 % Removed by relevancy pruning/SinE : 0
% 0.12/0.45 % Initial clauses : 8
% 0.12/0.45 % Removed in clause preprocessing : 1
% 0.12/0.45 % Initial clauses in saturation : 7
% 0.12/0.45 % Processed clauses : 200
% 0.12/0.45 % ...of these trivial : 50
% 0.12/0.45 % ...subsumed : 49
% 0.12/0.45 % ...remaining for further processing : 101
% 0.12/0.45 % Other redundant clauses eliminated : 0
% 0.12/0.45 % Clauses deleted for lack of memory : 0
% 0.12/0.45 % Backward-subsumed : 1
% 0.12/0.45 % Backward-rewritten : 70
% 0.12/0.45 % Generated clauses : 2498
% 0.12/0.45 % ...of the previous two non-redundant : 1855
% 0.12/0.45 % ...aggressively subsumed : 0
% 0.12/0.45 % Contextual simplify-reflections : 0
% 0.12/0.45 % Paramodulations : 2498
% 0.12/0.45 % Factorizations : 0
% 0.12/0.45 % NegExts : 0
% 0.12/0.45 % Equation resolutions : 0
% 0.12/0.45 % Disequality decompositions : 0
% 0.12/0.45 % Total rewrite steps : 2380
% 0.12/0.45 % ...of those cached : 1855
% 0.12/0.45 % Propositional unsat checks : 0
% 0.12/0.45 % Propositional check models : 0
% 0.12/0.45 % Propositional check unsatisfiable : 0
% 0.12/0.45 % Propositional clauses : 0
% 0.12/0.45 % Propositional clauses after purity: 0
% 0.12/0.45 % Propositional unsat core size : 0
% 0.12/0.45 % Propositional preprocessing time : 0.000
% 0.12/0.45 % Propositional encoding time : 0.000
% 0.12/0.45 % Propositional solver time : 0.000
% 0.12/0.45 % Success case prop preproc time : 0.000
% 0.12/0.45 % Success case prop encoding time : 0.000
% 0.12/0.45 % Success case prop solver time : 0.000
% 0.12/0.45 % Current number of processed clauses : 30
% 0.12/0.45 % Positive orientable unit clauses : 27
% 0.12/0.45 % Positive unorientable unit clauses: 3
% 0.12/0.45 % Negative unit clauses : 0
% 0.12/0.45 % Non-unit-clauses : 0
% 0.12/0.45 % Current number of unprocessed clauses: 1602
% 0.12/0.45 % ...number of literals in the above : 1602
% 0.12/0.45 % Current number of archived formulas : 0
% 0.12/0.45 % Current number of archived clauses : 72
% 0.12/0.45 % Clause-clause subsumption calls (NU) : 0
% 0.12/0.45 % Rec. Clause-clause subsumption calls : 0
% 0.12/0.45 % Non-unit clause-clause subsumptions : 0
% 0.12/0.45 % Unit Clause-clause subsumption calls : 24
% 0.12/0.45 % Rewrite failures with RHS unbound : 109
% 0.12/0.45 % BW rewrite match attempts : 372
% 0.12/0.45 % BW rewrite match successes : 142
% 0.12/0.45 % Condensation attempts : 0
% 0.12/0.45 % Condensation successes : 0
% 0.12/0.45 % Termbank termtop insertions : 33904
% 0.12/0.45 % Search garbage collected termcells : 2
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.033 s
% 0.12/0.45 % System time : 0.006 s
% 0.12/0.45 % Total time : 0.039 s
% 0.12/0.45 % Maximum resident set size: 3380 pages
% 0.12/0.45
% 0.12/0.45 % -------------------------------------------------
% 0.12/0.45 % User time : 0.136 s
% 0.12/0.45 % System time : 0.024 s
% 0.12/0.45 % Total time : 0.160 s
% 0.12/0.45 % Maximum resident set size: 4608 pages
% 0.12/0.45 % E exiting
%------------------------------------------------------------------------------