%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : BOO028-1 : 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 : 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 12:07:17 PM UTC 2026
% Result : Unsatisfiable 6.37s 6.47s
% Output : CNFRefutation 6.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 5 RR)
% Number of literals : 63 ( 62 equ; 4 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 36 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l2,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2) ).
cnf(l1,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiply) ).
cnf(b2,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
cnf(b1,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(l4,axiom,
multiply(multiply(add(X1,X2),add(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(l3,axiom,
add(add(multiply(X1,X2),multiply(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3) ).
cnf(prove_multiply_add_property,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_multiply_add_property) ).
cnf(c_0_11,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
l2 ).
cnf(c_0_12,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
l1 ).
cnf(c_0_13,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_14,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
b2 ).
cnf(c_0_16,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
b1 ).
cnf(c_0_18,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_19,axiom,
multiply(multiply(add(X1,X2),add(X2,X3)),X2) = X2,
l4 ).
cnf(c_0_20,plain,
multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_13]) ).
cnf(c_0_21,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_13]) ).
cnf(c_0_23,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_24,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_25,plain,
multiply(add(X1,X2),multiply(X2,add(X2,X3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_13]),c_0_18]) ).
cnf(c_0_26,plain,
add(X1,multiply(X2,multiply(X3,multiply(X1,X4)))) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_27,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(X1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_18]) ).
cnf(c_0_28,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
add(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_25]) ).
cnf(c_0_30,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_31,plain,
add(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_33,plain,
multiply(X1,add(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_29]) ).
cnf(c_0_34,plain,
add(multiply(X1,X2),multiply(inverse(X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_35,plain,
add(multiply(X1,inverse(X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_37,plain,
multiply(X1,multiply(X2,X1)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_15]),c_0_13]) ).
cnf(c_0_38,plain,
add(multiply(X1,X2),multiply(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_39,plain,
multiply(X1,inverse(inverse(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_18]) ).
cnf(c_0_40,plain,
add(X1,inverse(inverse(X1))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_31]) ).
cnf(c_0_41,plain,
add(X1,add(X2,multiply(X3,X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_17]),c_0_23]) ).
cnf(c_0_42,plain,
multiply(X1,add(X2,add(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_30]) ).
cnf(c_0_43,plain,
add(multiply(X1,X2),multiply(X2,X1)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_44,plain,
multiply(X1,multiply(add(X2,inverse(X1)),X3)) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_21]),c_0_13]) ).
cnf(c_0_45,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]),c_0_40]) ).
cnf(c_0_46,plain,
add(X1,add(X2,multiply(X1,X3))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_18]) ).
cnf(c_0_47,axiom,
add(add(multiply(X1,X2),multiply(X2,X3)),X2) = X2,
l3 ).
cnf(c_0_48,plain,
multiply(X1,multiply(X2,add(X3,multiply(X2,X1)))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_13]) ).
cnf(c_0_49,plain,
add(X1,multiply(add(X2,X1),X3)) = add(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_44]),c_0_36]),c_0_45]) ).
cnf(c_0_50,plain,
multiply(add(X1,X2),add(X2,multiply(X1,X3))) = add(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_46]),c_0_18]) ).
cnf(c_0_51,plain,
add(multiply(X1,X2),add(X2,multiply(X2,X3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_23]),c_0_30]) ).
cnf(c_0_52,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
inference(fof_simplification,[status(thm)],[prove_multiply_add_property]) ).
cnf(c_0_53,plain,
multiply(X1,add(X2,multiply(X3,X1))) = multiply(X1,add(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]) ).
cnf(c_0_54,plain,
add(X1,multiply(X2,add(X3,X1))) = add(X1,multiply(X3,X2)),
inference(spm,[status(thm)],[c_0_49,c_0_18]) ).
cnf(c_0_55,plain,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
c_0_52 ).
cnf(c_0_57,plain,
multiply(add(X1,X2),add(X3,X2)) = add(X2,multiply(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_50]) ).
cnf(c_0_58,plain,
add(X1,multiply(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_55]) ).
cnf(c_0_59,plain,
multiply(X1,add(X2,multiply(X1,X3))) = multiply(X1,add(X3,X2)),
inference(spm,[status(thm)],[c_0_53,c_0_18]) ).
cnf(c_0_60,negated_conjecture,
add(multiply(a,b),multiply(a,c)) != multiply(a,add(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_18]),c_0_18]) ).
cnf(c_0_61,plain,
add(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/5.49 % Computer : n002.cluster.edu
% 0.21/5.49 % Model : x86_64 x86_64
% 0.21/5.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/5.49 % Memory : 8046.5625MB
% 0.21/5.49 % OS : Linux 6.8.0-71-generic
% 0.21/5.49 % CPULimit : 300
% 0.21/5.49 % WCLimit : 300
% 0.21/5.49 % DateTime : Mon Sep 21 13:51:22 UTC 2026
% 0.21/5.49 % CPUTime :
% 0.21/5.49 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/5.57 Running first-order theorem proving
% 0.25/5.57 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
% 6.37/6.47 % Version: 3.5.1
% 6.37/6.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 6.37/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.37/6.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 6.37/6.47 % Starting new_bool_3 with 300s (1) cores
% 6.37/6.47 % Starting new_bool_1 with 300s (1) cores
% 6.37/6.47 % Starting sh5l with 300s (1) cores
% 6.37/6.47 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3444741 completed with status 0
% 6.37/6.47 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 6.37/6.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 6.37/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.37/6.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 6.37/6.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.37/6.47 % No SInE strategy applied
% 6.37/6.47 % Search class: FUUPM-FFSF21-MFFFFFNN
% 6.37/6.47 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 6.37/6.47 % Starting SubtermCWHack with 136s (1) cores
% 6.37/6.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 6.37/6.47 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 6.37/6.47 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 6.37/6.47 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 6.37/6.47 % G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with pid 3444751 completed with status 0
% 6.37/6.47 % Result found by G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y
% 6.37/6.47 % Preprocessing class: FSSSSMSSSSSNFFN.
% 6.37/6.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.37/6.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 6.37/6.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 6.37/6.47 % No SInE strategy applied
% 6.37/6.47 % Search class: FUUPM-FFSF21-MFFFFFNN
% 6.37/6.47 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 6.37/6.47 % Starting SubtermCWHack with 136s (1) cores
% 6.37/6.47 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 6.37/6.47 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 6.37/6.47 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 6.37/6.47 % Preprocessing time : 0.002 s
% 6.37/6.47
% 6.37/6.47 % Proof found!
% 6.37/6.47 % SZS status Unsatisfiable
% 6.37/6.47 % SZS output start CNFRefutation
% See solution above
% 6.37/6.47 % Parsed axioms : 11
% 6.37/6.47 % Removed by relevancy pruning/SinE : 0
% 6.37/6.47 % Initial clauses : 11
% 6.37/6.47 % Removed in clause preprocessing : 0
% 6.37/6.47 % Initial clauses in saturation : 11
% 6.37/6.47 % Processed clauses : 5107
% 6.37/6.47 % ...of these trivial : 1827
% 6.37/6.47 % ...subsumed : 3004
% 6.37/6.47 % ...remaining for further processing : 276
% 6.37/6.47 % Other redundant clauses eliminated : 0
% 6.37/6.47 % Clauses deleted for lack of memory : 0
% 6.37/6.47 % Backward-subsumed : 0
% 6.37/6.47 % Backward-rewritten : 73
% 6.37/6.47 % Generated clauses : 54480
% 6.37/6.47 % ...of the previous two non-redundant : 29827
% 6.37/6.47 % ...aggressively subsumed : 0
% 6.37/6.47 % Contextual simplify-reflections : 0
% 6.37/6.47 % Paramodulations : 54480
% 6.37/6.47 % Factorizations : 0
% 6.37/6.47 % NegExts : 0
% 6.37/6.47 % Equation resolutions : 0
% 6.37/6.47 % Disequality decompositions : 0
% 6.37/6.47 % Total rewrite steps : 86975
% 6.37/6.47 % ...of those cached : 69380
% 6.37/6.47 % Propositional unsat checks : 0
% 6.37/6.47 % Propositional check models : 0
% 6.37/6.47 % Propositional check unsatisfiable : 0
% 6.37/6.47 % Propositional clauses : 0
% 6.37/6.47 % Propositional clauses after purity: 0
% 6.37/6.47 % Propositional unsat core size : 0
% 6.37/6.47 % Propositional preprocessing time : 0.000
% 6.37/6.47 % Propositional encoding time : 0.000
% 6.37/6.47 % Propositional solver time : 0.000
% 6.37/6.47 % Success case prop preproc time : 0.000
% 6.37/6.47 % Success case prop encoding time : 0.000
% 6.37/6.47 % Success case prop solver time : 0.000
% 6.37/6.47 % Current number of processed clauses : 203
% 6.37/6.47 % Positive orientable unit clauses : 191
% 6.37/6.47 % Positive unorientable unit clauses: 12
% 6.37/6.47 % Negative unit clauses : 0
% 6.37/6.47 % Non-unit-clauses : 0
% 6.37/6.47 % Current number of unprocessed clauses: 24349
% 6.37/6.47 % ...number of literals in the above : 24349
% 6.37/6.47 % Current number of archived formulas : 0
% 6.37/6.47 % Current number of archived clauses : 73
% 6.37/6.47 % Clause-clause subsumption calls (NU) : 0
% 6.37/6.47 % Rec. Clause-clause subsumption calls : 0
% 6.37/6.47 % Non-unit clause-clause subsumptions : 0
% 6.37/6.47 % Unit Clause-clause subsumption calls : 63
% 6.37/6.47 % Rewrite failures with RHS unbound : 72
% 6.37/6.47 % BW rewrite match attempts : 1476
% 6.37/6.47 % BW rewrite match successes : 354
% 6.37/6.47 % Condensation attempts : 5107
% 6.37/6.47 % Condensation successes : 0
% 6.37/6.47 % Termbank termtop insertions : 482656
% 6.37/6.47 % Search garbage collected termcells : 2
% 6.37/6.47
% 6.37/6.47 % -------------------------------------------------
% 6.37/6.47 % User time : 0.782 s
% 6.37/6.47 % System time : 0.040 s
% 6.37/6.47 % Total time : 0.823 s
% 6.37/6.47 % Maximum resident set size: 3380 pages
% 6.37/6.47
% 6.37/6.47 % -------------------------------------------------
% 6.37/6.47 % User time : 3.660 s
% 6.37/6.47 % System time : 0.205 s
% 6.37/6.47 % Total time : 3.865 s
% 6.37/6.47 % Maximum resident set size: 4608 pages
% 6.37/6.47 % E exiting
%------------------------------------------------------------------------------