%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO022-1 : 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 : n006.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 0.61s 0.51s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 5 RR)
% Number of literals : 34 ( 33 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(add_multiply,axiom,
add(multiply(X1,X2),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply) ).
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(add_multiply_property,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X2,X1),add(X3,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_multiply_property) ).
cnf(prove_associativity_of_multiply,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
cnf(c_0_5,axiom,
add(multiply(X1,X2),X2) = X2,
add_multiply ).
cnf(c_0_6,axiom,
multiply(add(X1,X2),X2) = X2,
multiply_add ).
cnf(c_0_7,axiom,
multiply(X1,add(X2,X3)) = add(multiply(X2,X1),multiply(X3,X1)),
multiply_add_property ).
cnf(c_0_8,plain,
add(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,axiom,
add(X1,multiply(X2,X3)) = multiply(add(X2,X1),add(X3,X1)),
add_multiply_property ).
cnf(c_0_10,plain,
multiply(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_11,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
multiply(multiply(X1,add(X2,X3)),add(X4,multiply(X3,X1))) = add(multiply(X3,X1),multiply(multiply(X2,X1),X4)),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_13,plain,
add(X1,multiply(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_6]) ).
cnf(c_0_14,plain,
multiply(X1,add(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_10]),c_0_5]) ).
cnf(c_0_15,plain,
add(multiply(X1,X2),multiply(X3,X1)) = multiply(X1,add(X2,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_16,plain,
add(multiply(multiply(X1,X2),X3),multiply(multiply(X2,X3),X4)) = multiply(multiply(X3,X2),add(X4,multiply(multiply(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
add(X1,multiply(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_8]),c_0_14]) ).
cnf(c_0_18,plain,
multiply(multiply(X1,X2),multiply(X3,X2)) = multiply(multiply(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_13]) ).
cnf(c_0_19,plain,
multiply(multiply(X1,X2),multiply(X2,X3)) = multiply(multiply(X2,X3),X1),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_20,plain,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(multiply(X3,X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_21,plain,
add(X1,multiply(multiply(X2,X1),X3)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_14]),c_0_14]) ).
cnf(c_0_22,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
inference(fof_simplification,[status(thm)],[prove_associativity_of_multiply]) ).
cnf(c_0_23,plain,
multiply(multiply(X1,X2),multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_7]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,X2),X3) = multiply(multiply(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_19]),c_0_20]) ).
cnf(c_0_25,plain,
multiply(X1,multiply(multiply(X2,X1),X3)) = multiply(multiply(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_11]) ).
cnf(c_0_26,plain,
multiply(X1,multiply(X2,X1)) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_11]) ).
cnf(c_0_27,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
c_0_22 ).
cnf(c_0_28,plain,
multiply(X1,multiply(X2,add(X3,X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_19]),c_0_11]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_24]) ).
cnf(c_0_30,plain,
multiply(X1,multiply(X2,multiply(X3,X1))) = multiply(X2,multiply(X3,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
multiply(c,multiply(a,b)) != multiply(a,multiply(b,c)),
inference(rw,[status(thm)],[c_0_27,c_0_11]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_17]),c_0_29]),c_0_30]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO022-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 21 13:48:27 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.61/0.51 % Version: 3.5.1
% 0.61/0.51 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.61/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.61/0.51 % Starting new_bool_3 with 300s (1) cores
% 0.61/0.51 % Starting new_bool_1 with 300s (1) cores
% 0.61/0.51 % Starting sh5l with 300s (1) cores
% 0.61/0.51 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3003607 completed with status 0
% 0.61/0.51 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.61/0.51 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.61/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.61/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.51 % No SInE strategy applied
% 0.61/0.51 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.61/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.61/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.61/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.61/0.51 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.61/0.51 % Starting new_bool_3 with 136s (1) cores
% 0.61/0.51 % Starting new_bool_1 with 136s (1) cores
% 0.61/0.51 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3003612 completed with status 0
% 0.61/0.51 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 0.61/0.51 % Preprocessing class: FSSSSMSSSSSNFFN.
% 0.61/0.51 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.61/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.61/0.51 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.61/0.51 % No SInE strategy applied
% 0.61/0.51 % Search class: FUUPM-FFSF21-SFFFFFNN
% 0.61/0.51 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.61/0.51 % Starting SubtermCWHack with 136s (1) cores
% 0.61/0.51 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 0.61/0.51 % Preprocessing time : 0.001 s
% 0.61/0.51
% 0.61/0.51 % Proof found!
% 0.61/0.51 % SZS status Unsatisfiable
% 0.61/0.51 % SZS output start CNFRefutation
% See solution above
% 0.61/0.51 % Parsed axioms : 7
% 0.61/0.51 % Removed by relevancy pruning/SinE : 0
% 0.61/0.51 % Initial clauses : 7
% 0.61/0.51 % Removed in clause preprocessing : 0
% 0.61/0.51 % Initial clauses in saturation : 7
% 0.61/0.51 % Processed clauses : 441
% 0.61/0.51 % ...of these trivial : 178
% 0.61/0.51 % ...subsumed : 140
% 0.61/0.51 % ...remaining for further processing : 123
% 0.61/0.51 % Other redundant clauses eliminated : 0
% 0.61/0.51 % Clauses deleted for lack of memory : 0
% 0.61/0.51 % Backward-subsumed : 0
% 0.61/0.51 % Backward-rewritten : 58
% 0.61/0.51 % Generated clauses : 10023
% 0.61/0.51 % ...of the previous two non-redundant : 7398
% 0.61/0.51 % ...aggressively subsumed : 0
% 0.61/0.51 % Contextual simplify-reflections : 0
% 0.61/0.51 % Paramodulations : 10023
% 0.61/0.51 % Factorizations : 0
% 0.61/0.51 % NegExts : 0
% 0.61/0.51 % Equation resolutions : 0
% 0.61/0.51 % Disequality decompositions : 0
% 0.61/0.51 % Total rewrite steps : 9398
% 0.61/0.51 % ...of those cached : 7583
% 0.61/0.51 % Propositional unsat checks : 0
% 0.61/0.51 % Propositional check models : 0
% 0.61/0.51 % Propositional check unsatisfiable : 0
% 0.61/0.51 % Propositional clauses : 0
% 0.61/0.51 % Propositional clauses after purity: 0
% 0.61/0.51 % Propositional unsat core size : 0
% 0.61/0.51 % Propositional preprocessing time : 0.000
% 0.61/0.51 % Propositional encoding time : 0.000
% 0.61/0.51 % Propositional solver time : 0.000
% 0.61/0.51 % Success case prop preproc time : 0.000
% 0.61/0.51 % Success case prop encoding time : 0.000
% 0.61/0.51 % Success case prop solver time : 0.000
% 0.61/0.51 % Current number of processed clauses : 65
% 0.61/0.51 % Positive orientable unit clauses : 62
% 0.61/0.51 % Positive unorientable unit clauses: 3
% 0.61/0.51 % Negative unit clauses : 0
% 0.61/0.51 % Non-unit-clauses : 0
% 0.61/0.51 % Current number of unprocessed clauses: 6778
% 0.61/0.51 % ...number of literals in the above : 6778
% 0.61/0.51 % Current number of archived formulas : 0
% 0.61/0.51 % Current number of archived clauses : 58
% 0.61/0.51 % Clause-clause subsumption calls (NU) : 0
% 0.61/0.51 % Rec. Clause-clause subsumption calls : 0
% 0.61/0.51 % Non-unit clause-clause subsumptions : 0
% 0.61/0.51 % Unit Clause-clause subsumption calls : 48
% 0.61/0.51 % Rewrite failures with RHS unbound : 0
% 0.61/0.51 % BW rewrite match attempts : 373
% 0.61/0.51 % BW rewrite match successes : 215
% 0.61/0.51 % Condensation attempts : 0
% 0.61/0.51 % Condensation successes : 0
% 0.61/0.51 % Termbank termtop insertions : 97928
% 0.61/0.51 % Search garbage collected termcells : 2
% 0.61/0.51
% 0.61/0.51 % -------------------------------------------------
% 0.61/0.51 % User time : 0.070 s
% 0.61/0.51 % System time : 0.009 s
% 0.61/0.51 % Total time : 0.079 s
% 0.61/0.51 % Maximum resident set size: 3580 pages
% 0.61/0.51
% 0.61/0.51 % -------------------------------------------------
% 0.61/0.51 % User time : 0.324 s
% 0.61/0.51 % System time : 0.037 s
% 0.61/0.51 % Total time : 0.361 s
% 0.61/0.51 % Maximum resident set size: 4864 pages
% 0.61/0.51 % E exiting
%------------------------------------------------------------------------------