%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO028-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 2.84s 1.12s
% Output : CNFRefutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 4 RR)
% Number of literals : 43 ( 42 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(l2,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
cnf(l1,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
cnf(associativity_of_multiply,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_multiply) ).
cnf(b1,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(associativity_of_add,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_add) ).
cnf(b2,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
cnf(commutativity_of_multiply,axiom,
multiply(X1,X2) = multiply(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(prove_multiply_add_property,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_add_property) ).
cnf(c_0_9,axiom,
multiply(X1,add(X2,add(X1,X3))) = X1,
l2 ).
cnf(c_0_10,axiom,
add(X1,multiply(X2,multiply(X1,X3))) = X1,
l1 ).
cnf(c_0_11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity_of_multiply ).
cnf(c_0_12,plain,
multiply(X1,add(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
multiply(X1,multiply(add(X2,X1),X3)) = multiply(X1,X3),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
multiply(add(X1,X2),add(X1,inverse(X2))) = X1,
b1 ).
cnf(c_0_15,plain,
multiply(X1,add(X2,inverse(X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_17,axiom,
add(add(X1,X2),X3) = add(X1,add(X2,X3)),
associativity_of_add ).
cnf(c_0_18,plain,
add(X1,multiply(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_19,plain,
multiply(X1,add(inverse(X1),X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
add(X1,add(multiply(X2,X1),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
add(multiply(X1,X2),multiply(X1,inverse(X2))) = X1,
b2 ).
cnf(c_0_22,plain,
add(X1,add(X2,multiply(X3,X1))) = add(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_17]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(X2,inverse(X1))) = multiply(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_24,axiom,
multiply(X1,X2) = multiply(X2,X1),
commutativity_of_multiply ).
cnf(c_0_25,plain,
add(X1,multiply(X2,inverse(X1))) = add(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
add(inverse(X1),multiply(X2,X1)) = add(inverse(X1),X2),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,plain,
add(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_23]) ).
cnf(c_0_28,plain,
add(multiply(X1,X2),add(multiply(X1,inverse(X2)),X3)) = add(X1,X3),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_29,plain,
add(multiply(X1,X2),multiply(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_30,plain,
add(X1,multiply(inverse(X1),X2)) = add(X1,X2),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_31,plain,
add(X1,inverse(inverse(X1))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_16]) ).
cnf(c_0_32,plain,
multiply(X1,add(X2,add(X3,inverse(X1)))) = multiply(X1,add(X2,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_33,plain,
add(multiply(X1,X2),inverse(X2)) = add(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]) ).
cnf(c_0_34,plain,
multiply(X1,add(multiply(X2,inverse(X1)),X3)) = multiply(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_19]) ).
cnf(c_0_35,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_30]),c_0_31]) ).
cnf(c_0_36,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_37,plain,
multiply(add(X1,X2),add(multiply(X3,X1),X2)) = add(multiply(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_20]),c_0_24]) ).
cnf(c_0_38,plain,
multiply(X1,add(X2,multiply(X3,X1))) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]) ).
cnf(c_0_39,plain,
multiply(X1,add(multiply(X2,X1),X3)) = multiply(X1,add(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
multiply(a,add(b,c)) != add(multiply(b,a),multiply(c,a)),
c_0_36 ).
cnf(c_0_41,plain,
add(multiply(X1,X2),multiply(X3,X2)) = multiply(X2,add(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_18]),c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 % Computer : n014.cluster.edu
% 0.22/0.49 % Model : x86_64 x86_64
% 0.22/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.49 % Memory : 8046.5625MB
% 0.22/0.49 % OS : Linux 6.8.0-71-generic
% 0.22/0.49 % CPULimit : 300
% 0.22/0.49 % WCLimit : 300
% 0.22/0.49 % DateTime : Mon Sep 21 13:48:35 UTC 2026
% 0.22/0.50 % CPUTime :
% 0.22/0.50 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.59 Running first-order theorem proving
% 0.26/0.59 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 2.84/1.12 % Version: 3.5.1
% 2.84/1.12 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.84/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.84/1.12 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.84/1.12 % Starting new_bool_3 with 300s (1) cores
% 2.84/1.12 % Starting new_bool_1 with 300s (1) cores
% 2.84/1.12 % Starting sh5l with 300s (1) cores
% 2.84/1.12 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 28011 completed with status 0
% 2.84/1.12 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 2.84/1.12 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.84/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.84/1.12 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.84/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.84/1.12 % No SInE strategy applied
% 2.84/1.12 % Search class: FUUPM-FFSF21-MFFFFFNN
% 2.84/1.12 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 2.84/1.12 % Starting SubtermCWHack with 136s (1) cores
% 2.84/1.12 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.84/1.12 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 2.84/1.12 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 2.84/1.12 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 2.84/1.12 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 28018 completed with status 0
% 2.84/1.12 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 2.84/1.12 % Preprocessing class: FSSSSMSSSSSNFFN.
% 2.84/1.12 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.84/1.12 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 2.84/1.12 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.84/1.12 % No SInE strategy applied
% 2.84/1.12 % Search class: FUUPM-FFSF21-MFFFFFNN
% 2.84/1.12 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 2.84/1.12 % Starting SubtermCWHack with 136s (1) cores
% 2.84/1.12 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 2.84/1.12 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 2.84/1.12 % Preprocessing time : 0.002 s
% 2.84/1.12
% 2.84/1.12 % Proof found!
% 2.84/1.12 % SZS status Unsatisfiable
% 2.84/1.12 % SZS output start CNFRefutation
% See solution above
% 2.84/1.12 % Parsed axioms : 11
% 2.84/1.12 % Removed by relevancy pruning/SinE : 0
% 2.84/1.12 % Initial clauses : 11
% 2.84/1.12 % Removed in clause preprocessing : 0
% 2.84/1.12 % Initial clauses in saturation : 11
% 2.84/1.12 % Processed clauses : 3193
% 2.84/1.12 % ...of these trivial : 1077
% 2.84/1.12 % ...subsumed : 1861
% 2.84/1.12 % ...remaining for further processing : 255
% 2.84/1.12 % Other redundant clauses eliminated : 0
% 2.84/1.12 % Clauses deleted for lack of memory : 0
% 2.84/1.12 % Backward-subsumed : 0
% 2.84/1.12 % Backward-rewritten : 46
% 2.84/1.12 % Generated clauses : 42532
% 2.84/1.12 % ...of the previous two non-redundant : 24940
% 2.84/1.12 % ...aggressively subsumed : 0
% 2.84/1.12 % Contextual simplify-reflections : 0
% 2.84/1.12 % Paramodulations : 42532
% 2.84/1.12 % Factorizations : 0
% 2.84/1.12 % NegExts : 0
% 2.84/1.12 % Equation resolutions : 0
% 2.84/1.12 % Disequality decompositions : 0
% 2.84/1.12 % Total rewrite steps : 84492
% 2.84/1.12 % ...of those cached : 69356
% 2.84/1.12 % Propositional unsat checks : 0
% 2.84/1.12 % Propositional check models : 0
% 2.84/1.12 % Propositional check unsatisfiable : 0
% 2.84/1.12 % Propositional clauses : 0
% 2.84/1.12 % Propositional clauses after purity: 0
% 2.84/1.12 % Propositional unsat core size : 0
% 2.84/1.12 % Propositional preprocessing time : 0.000
% 2.84/1.12 % Propositional encoding time : 0.000
% 2.84/1.12 % Propositional solver time : 0.000
% 2.84/1.12 % Success case prop preproc time : 0.000
% 2.84/1.12 % Success case prop encoding time : 0.000
% 2.84/1.12 % Success case prop solver time : 0.000
% 2.84/1.12 % Current number of processed clauses : 209
% 2.84/1.12 % Positive orientable unit clauses : 196
% 2.84/1.12 % Positive unorientable unit clauses: 13
% 2.84/1.12 % Negative unit clauses : 0
% 2.84/1.12 % Non-unit-clauses : 0
% 2.84/1.12 % Current number of unprocessed clauses: 21263
% 2.84/1.12 % ...number of literals in the above : 21263
% 2.84/1.12 % Current number of archived formulas : 0
% 2.84/1.12 % Current number of archived clauses : 46
% 2.84/1.12 % Clause-clause subsumption calls (NU) : 0
% 2.84/1.12 % Rec. Clause-clause subsumption calls : 0
% 2.84/1.12 % Non-unit clause-clause subsumptions : 0
% 2.84/1.12 % Unit Clause-clause subsumption calls : 135
% 2.84/1.12 % Rewrite failures with RHS unbound : 176
% 2.84/1.12 % BW rewrite match attempts : 1018
% 2.84/1.12 % BW rewrite match successes : 472
% 2.84/1.12 % Condensation attempts : 0
% 2.84/1.12 % Condensation successes : 0
% 2.84/1.12 % Termbank termtop insertions : 445175
% 2.84/1.12 % Search garbage collected termcells : 2
% 2.84/1.12
% 2.84/1.12 % -------------------------------------------------
% 2.84/1.12 % User time : 0.433 s
% 2.84/1.12 % System time : 0.022 s
% 2.84/1.12 % Total time : 0.456 s
% 2.84/1.12 % Maximum resident set size: 3636 pages
% 2.84/1.12
% 2.84/1.12 % -------------------------------------------------
% 2.84/1.12 % User time : 1.676 s
% 2.84/1.12 % System time : 0.095 s
% 2.84/1.12 % Total time : 1.771 s
% 2.84/1.12 % Maximum resident set size: 4864 pages
% 2.84/1.12 % E exiting
%------------------------------------------------------------------------------