%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:06:53 PM UTC 2026
% Result : Unsatisfiable 0.57s 0.54s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 4 RR)
% Number of literals : 40 ( 39 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 88 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(distributivity5,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity5) ).
cnf(additive_inverse2,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse2) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(addition_is_well_defined,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
cnf(additive_identity1,axiom,
sum(additive_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(commutativity_of_addition,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_addition) ).
cnf(closure_of_addition,axiom,
sum(X1,X2,add(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
cnf(multiplicative_inverse1,axiom,
product(inverse(X1),X1,additive_identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_inverse1) ).
cnf(multiplication_is_well_defined,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
cnf(multiplicative_identity1,axiom,
product(multiplicative_identity,X1,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
cnf(closure_of_multiplication,axiom,
product(X1,X2,multiply(X1,X2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
cnf(prove_both_equalities,negated_conjecture,
sum(x,x,x) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_both_equalities) ).
cnf(c_0_13,axiom,
ifeq(product(X1,X2,X3),true,ifeq(sum(X4,X3,X5),true,ifeq(sum(X4,X2,X6),true,ifeq(sum(X4,X1,X7),true,product(X7,X6,X5),true),true),true),true) = true,
distributivity5 ).
cnf(c_0_14,axiom,
sum(X1,inverse(X1),multiplicative_identity) = true,
additive_inverse2 ).
cnf(c_0_15,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_16,axiom,
ifeq2(sum(X1,X2,X3),true,ifeq2(sum(X1,X2,X4),true,X4,X3),X3) = X3,
addition_is_well_defined ).
cnf(c_0_17,axiom,
sum(additive_identity,X1,X1) = true,
additive_identity1 ).
cnf(c_0_18,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_19,axiom,
ifeq(sum(X1,X2,X3),true,sum(X2,X1,X3),true) = true,
commutativity_of_addition ).
cnf(c_0_20,axiom,
sum(X1,X2,add(X1,X2)) = true,
closure_of_addition ).
cnf(c_0_21,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(sum(X1,X3,X4),true,ifeq(sum(X1,X2,X5),true,product(multiplicative_identity,X5,X4),true),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_22,axiom,
product(inverse(X1),X1,additive_identity) = true,
multiplicative_inverse1 ).
cnf(c_0_23,plain,
ifeq2(sum(additive_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,plain,
sum(X1,X2,add(X2,X1)) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_15]) ).
cnf(c_0_25,plain,
ifeq(sum(X1,additive_identity,X2),true,ifeq(sum(X1,X1,X3),true,product(multiplicative_identity,X3,X2),true),true) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15]) ).
cnf(c_0_26,plain,
add(X1,additive_identity) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_18]) ).
cnf(c_0_27,axiom,
ifeq2(product(X1,X2,X3),true,ifeq2(product(X1,X2,X4),true,X4,X3),X3) = X3,
multiplication_is_well_defined ).
cnf(c_0_28,axiom,
product(multiplicative_identity,X1,X1) = true,
multiplicative_identity1 ).
cnf(c_0_29,axiom,
product(X1,X2,multiply(X1,X2)) = true,
closure_of_multiplication ).
cnf(c_0_30,plain,
ifeq(sum(X1,X1,X2),true,product(multiplicative_identity,X2,X1),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_26]),c_0_15]) ).
cnf(c_0_31,plain,
ifeq2(product(multiplicative_identity,X1,X2),true,X1,X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_18]) ).
cnf(c_0_32,plain,
ifeq2(product(X1,X2,X3),true,multiply(X1,X2),X3) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_18]) ).
cnf(c_0_33,plain,
product(multiplicative_identity,add(X1,X1),X1) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_15]) ).
cnf(c_0_34,plain,
multiply(multiplicative_identity,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_18]) ).
cnf(c_0_35,negated_conjecture,
sum(x,x,x) != true,
inference(fof_simplification,[status(thm)],[prove_both_equalities]) ).
cnf(c_0_36,plain,
add(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_18]) ).
cnf(c_0_37,negated_conjecture,
sum(x,x,x) != true,
c_0_35 ).
cnf(c_0_38,plain,
sum(X1,X1,X1) = true,
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO004-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 13:46:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.43 Running first-order theorem proving
% 0.15/0.43 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
% 0.57/0.54 % Version: 3.5.1
% 0.57/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.57/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.57/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.57/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.57/0.54 % Starting sh5l with 300s (1) cores
% 0.57/0.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1139543 completed with status 0
% 0.57/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.57/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.57/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.57/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.54 % No SInE strategy applied
% 0.57/0.54 % Search class: FUUPM-FFMF32-MFFFFFNN
% 0.57/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.57/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.57/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.57/0.54 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 437s (1) cores
% 0.57/0.54 % Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.57/0.54 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 0.57/0.54 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with pid 1139550 completed with status 0
% 0.57/0.54 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN
% 0.57/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.57/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.57/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.57/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.57/0.54 % No SInE strategy applied
% 0.57/0.54 % Search class: FUUPM-FFMF32-MFFFFFNN
% 0.57/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.57/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.57/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.57/0.54 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 437s (1) cores
% 0.57/0.54 % Preprocessing time : 0.002 s
% 0.57/0.54 % Presaturation interreduction done
% 0.57/0.54
% 0.57/0.54 % Proof found!
% 0.57/0.54 % SZS status Unsatisfiable
% 0.57/0.54 % SZS output start CNFRefutation
% See solution above
% 0.57/0.54 % Parsed axioms : 25
% 0.57/0.54 % Removed by relevancy pruning/SinE : 0
% 0.57/0.54 % Initial clauses : 25
% 0.57/0.54 % Removed in clause preprocessing : 0
% 0.57/0.54 % Initial clauses in saturation : 25
% 0.57/0.54 % Processed clauses : 330
% 0.57/0.54 % ...of these trivial : 113
% 0.57/0.54 % ...subsumed : 6
% 0.57/0.54 % ...remaining for further processing : 211
% 0.57/0.54 % Other redundant clauses eliminated : 0
% 0.57/0.54 % Clauses deleted for lack of memory : 0
% 0.57/0.54 % Backward-subsumed : 0
% 0.57/0.54 % Backward-rewritten : 38
% 0.57/0.54 % Generated clauses : 2741
% 0.57/0.54 % ...of the previous two non-redundant : 1208
% 0.57/0.54 % ...aggressively subsumed : 0
% 0.57/0.54 % Contextual simplify-reflections : 0
% 0.57/0.54 % Paramodulations : 2741
% 0.57/0.54 % Factorizations : 0
% 0.57/0.54 % NegExts : 0
% 0.57/0.54 % Equation resolutions : 0
% 0.57/0.54 % Disequality decompositions : 0
% 0.57/0.54 % Total rewrite steps : 3573
% 0.57/0.54 % ...of those cached : 2471
% 0.57/0.54 % Propositional unsat checks : 0
% 0.57/0.54 % Propositional check models : 0
% 0.57/0.54 % Propositional check unsatisfiable : 0
% 0.57/0.54 % Propositional clauses : 0
% 0.57/0.54 % Propositional clauses after purity: 0
% 0.57/0.54 % Propositional unsat core size : 0
% 0.57/0.54 % Propositional preprocessing time : 0.000
% 0.57/0.54 % Propositional encoding time : 0.000
% 0.57/0.54 % Propositional solver time : 0.000
% 0.57/0.54 % Success case prop preproc time : 0.000
% 0.57/0.54 % Success case prop encoding time : 0.000
% 0.57/0.54 % Success case prop solver time : 0.000
% 0.57/0.54 % Current number of processed clauses : 148
% 0.57/0.54 % Positive orientable unit clauses : 146
% 0.57/0.54 % Positive unorientable unit clauses: 2
% 0.57/0.54 % Negative unit clauses : 0
% 0.57/0.54 % Non-unit-clauses : 0
% 0.57/0.54 % Current number of unprocessed clauses: 899
% 0.57/0.54 % ...number of literals in the above : 899
% 0.57/0.54 % Current number of archived formulas : 0
% 0.57/0.54 % Current number of archived clauses : 63
% 0.57/0.54 % Clause-clause subsumption calls (NU) : 0
% 0.57/0.54 % Rec. Clause-clause subsumption calls : 0
% 0.57/0.54 % Non-unit clause-clause subsumptions : 0
% 0.57/0.54 % Unit Clause-clause subsumption calls : 0
% 0.57/0.54 % Rewrite failures with RHS unbound : 0
% 0.57/0.54 % BW rewrite match attempts : 2278
% 0.57/0.54 % BW rewrite match successes : 60
% 0.57/0.54 % Condensation attempts : 0
% 0.57/0.54 % Condensation successes : 0
% 0.57/0.54 % Termbank termtop insertions : 41377
% 0.57/0.55 % Search garbage collected termcells : 2
% 0.57/0.55
% 0.57/0.55 % -------------------------------------------------
% 0.57/0.55 % User time : 0.071 s
% 0.57/0.55 % System time : 0.009 s
% 0.57/0.55 % Total time : 0.080 s
% 0.57/0.55 % Maximum resident set size: 3652 pages
% 0.57/0.55
% 0.57/0.55 % -------------------------------------------------
% 0.57/0.55 % User time : 0.315 s
% 0.57/0.55 % System time : 0.048 s
% 0.57/0.55 % Total time : 0.363 s
% 0.57/0.55 % Maximum resident set size: 4608 pages
% 0.57/0.55 % E exiting
%------------------------------------------------------------------------------