%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : KLE084-10 : TPTP v9.3.1. Released v7.5.0.
% 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 12:59:18 PM UTC 2026
% Result : Unsatisfiable 13.68s 2.45s
% Output : CNFRefutation 13.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 7 RR)
% Number of literals : 58 ( 57 equ; 4 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(domain3,axiom,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
cnf(additive_commutativity,axiom,
addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
cnf(additive_identity,axiom,
addition(X1,zero) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
cnf(additive_associativity,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
cnf(left_distributivity,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
cnf(domain1,axiom,
multiplication(antidomain(X1),X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
cnf(right_distributivity,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
cnf(multiplicative_right_identity,axiom,
multiplication(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
cnf(additive_idempotence,axiom,
addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
cnf(multiplicative_left_identity,axiom,
multiplication(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
cnf(multiplicative_associativity,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
cnf(left_annihilation,axiom,
multiplication(zero,X1) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
cnf(domain2,axiom,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
cnf(goals,negated_conjecture,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(domain4,axiom,
domain(X1) = antidomain(antidomain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
cnf(c_0_15,axiom,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
domain3 ).
cnf(c_0_16,axiom,
addition(X1,X2) = addition(X2,X1),
additive_commutativity ).
cnf(c_0_17,axiom,
addition(X1,zero) = X1,
additive_identity ).
cnf(c_0_18,axiom,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
additive_associativity ).
cnf(c_0_19,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
left_distributivity ).
cnf(c_0_21,axiom,
multiplication(antidomain(X1),X1) = zero,
domain1 ).
cnf(c_0_22,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,axiom,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
right_distributivity ).
cnf(c_0_24,axiom,
multiplication(X1,one) = X1,
multiplicative_right_identity ).
cnf(c_0_25,plain,
addition(antidomain(X1),addition(antidomain(antidomain(X1)),X2)) = addition(one,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,axiom,
addition(X1,X1) = X1,
additive_idempotence ).
cnf(c_0_27,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,axiom,
multiplication(one,X1) = X1,
multiplicative_left_identity ).
cnf(c_0_29,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_17]) ).
cnf(c_0_30,axiom,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
multiplicative_associativity ).
cnf(c_0_31,axiom,
multiplication(zero,X1) = zero,
left_annihilation ).
cnf(c_0_32,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_33,plain,
addition(one,antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_19]) ).
cnf(c_0_34,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_28]) ).
cnf(c_0_35,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,addition(X3,X2))) = multiplication(antidomain(multiplication(X1,X2)),multiplication(X1,X3)),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_36,axiom,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
domain2 ).
cnf(c_0_37,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_31]) ).
cnf(c_0_38,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_32]),c_0_22]) ).
cnf(c_0_39,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_19]),c_0_33]),c_0_16]) ).
cnf(c_0_40,plain,
multiplication(antidomain(antidomain(X1)),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_34]) ).
cnf(c_0_41,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),multiplication(X1,antidomain(X2))) = multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_19]),c_0_24]) ).
cnf(c_0_42,plain,
antidomain(multiplication(antidomain(X1),antidomain(antidomain(multiplication(X1,X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]) ).
cnf(c_0_43,plain,
multiplication(antidomain(antidomain(multiplication(X1,X2))),multiplication(X1,multiplication(X2,X3))) = multiplication(X1,multiplication(X2,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_30]) ).
cnf(c_0_44,plain,
multiplication(antidomain(antidomain(antidomain(X1))),antidomain(X1)) = antidomain(antidomain(antidomain(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_24]) ).
cnf(c_0_45,negated_conjecture,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_46,plain,
multiplication(antidomain(multiplication(X1,X2)),multiplication(addition(X3,X1),X2)) = multiplication(antidomain(multiplication(X1,X2)),multiplication(X3,X2)),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_47,plain,
multiplication(antidomain(X1),antidomain(multiplication(X1,X2))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_28]),c_0_28]) ).
cnf(c_0_48,plain,
multiplication(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),multiplication(X1,X2)) = multiplication(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_34]) ).
cnf(c_0_49,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[c_0_44,c_0_34]) ).
cnf(c_0_50,negated_conjecture,
domain(multiplication(sK2_goals_X0,sK1_goals_X1)) != domain(multiplication(sK2_goals_X0,domain(sK1_goals_X1))),
c_0_45 ).
cnf(c_0_51,axiom,
domain(X1) = antidomain(antidomain(X1)),
domain4 ).
cnf(c_0_52,plain,
multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X2)),multiplication(antidomain(X1),X2)) = multiplication(antidomain(multiplication(antidomain(antidomain(X1)),X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_19]),c_0_28]) ).
cnf(c_0_53,plain,
multiplication(antidomain(multiplication(X1,antidomain(antidomain(X2)))),antidomain(multiplication(X1,X2))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_49]) ).
cnf(c_0_54,plain,
multiplication(antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),antidomain(multiplication(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_36]),c_0_21]) ).
cnf(c_0_55,negated_conjecture,
antidomain(antidomain(multiplication(sK2_goals_X0,sK1_goals_X1))) != antidomain(antidomain(multiplication(sK2_goals_X0,antidomain(antidomain(sK1_goals_X1))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_51]),c_0_51]) ).
cnf(c_0_56,plain,
antidomain(multiplication(X1,antidomain(antidomain(X2)))) = antidomain(multiplication(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]),c_0_38]),c_0_28]),c_0_54]),c_0_38]),c_0_28]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE084-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 22:44:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 13.68/2.45 % Version: 3.5.1
% 13.68/2.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.68/2.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.68/2.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.68/2.45 % Starting new_bool_3 with 300s (1) cores
% 13.68/2.45 % Starting new_bool_1 with 300s (1) cores
% 13.68/2.45 % Starting sh5l with 300s (1) cores
% 13.68/2.45 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1865122 completed with status 0
% 13.68/2.45 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 13.68/2.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.68/2.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.68/2.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.68/2.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.68/2.45 % No SInE strategy applied
% 13.68/2.45 % Search class: FUUPM-FFSF32-MFFFFFNN
% 13.68/2.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.68/2.45 % Starting SubtermCWHack with 136s (1) cores
% 13.68/2.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.68/2.45 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 13.68/2.45 % Starting G-E--_208_B02_F1_AE_CS_SP_PS_S0Y with 136s (1) cores
% 13.68/2.45 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 13.68/2.45 % G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with pid 1865130 completed with status 0
% 13.68/2.45 % Result found by G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN
% 13.68/2.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 13.68/2.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 13.68/2.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 13.68/2.45 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 13.68/2.45 % No SInE strategy applied
% 13.68/2.45 % Search class: FUUPM-FFSF32-MFFFFFNN
% 13.68/2.45 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 13.68/2.45 % Starting SubtermCWHack with 136s (1) cores
% 13.68/2.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 13.68/2.45 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 13.68/2.45 % Preprocessing time : 0.002 s
% 13.68/2.45
% 13.68/2.45 % Proof found!
% 13.68/2.45 % SZS status Unsatisfiable
% 13.68/2.45 % SZS output start CNFRefutation
% See solution above
% 13.68/2.45 % Parsed axioms : 24
% 13.68/2.45 % Removed by relevancy pruning/SinE : 0
% 13.68/2.45 % Initial clauses : 24
% 13.68/2.45 % Removed in clause preprocessing : 2
% 13.68/2.45 % Initial clauses in saturation : 22
% 13.68/2.45 % Processed clauses : 1258
% 13.68/2.45 % ...of these trivial : 576
% 13.68/2.45 % ...subsumed : 315
% 13.68/2.45 % ...remaining for further processing : 367
% 13.68/2.45 % Other redundant clauses eliminated : 0
% 13.68/2.45 % Clauses deleted for lack of memory : 0
% 13.68/2.45 % Backward-subsumed : 0
% 13.68/2.45 % Backward-rewritten : 34
% 13.68/2.45 % Generated clauses : 78399
% 13.68/2.45 % ...of the previous two non-redundant : 47825
% 13.68/2.45 % ...aggressively subsumed : 0
% 13.68/2.45 % Contextual simplify-reflections : 0
% 13.68/2.45 % Paramodulations : 78399
% 13.68/2.45 % Factorizations : 0
% 13.68/2.45 % NegExts : 0
% 13.68/2.45 % Equation resolutions : 0
% 13.68/2.45 % Disequality decompositions : 0
% 13.68/2.45 % Total rewrite steps : 160738
% 13.68/2.45 % ...of those cached : 143296
% 13.68/2.45 % Propositional unsat checks : 0
% 13.68/2.45 % Propositional check models : 0
% 13.68/2.45 % Propositional check unsatisfiable : 0
% 13.68/2.45 % Propositional clauses : 0
% 13.68/2.45 % Propositional clauses after purity: 0
% 13.68/2.45 % Propositional unsat core size : 0
% 13.68/2.45 % Propositional preprocessing time : 0.000
% 13.68/2.45 % Propositional encoding time : 0.000
% 13.68/2.45 % Propositional solver time : 0.000
% 13.68/2.45 % Success case prop preproc time : 0.000
% 13.68/2.45 % Success case prop encoding time : 0.000
% 13.68/2.45 % Success case prop solver time : 0.000
% 13.68/2.45 % Current number of processed clauses : 333
% 13.68/2.45 % Positive orientable unit clauses : 322
% 13.68/2.45 % Positive unorientable unit clauses: 11
% 13.68/2.45 % Negative unit clauses : 0
% 13.68/2.45 % Non-unit-clauses : 0
% 13.68/2.45 % Current number of unprocessed clauses: 46477
% 13.68/2.45 % ...number of literals in the above : 46477
% 13.68/2.45 % Current number of archived formulas : 0
% 13.68/2.45 % Current number of archived clauses : 36
% 13.68/2.45 % Clause-clause subsumption calls (NU) : 0
% 13.68/2.45 % Rec. Clause-clause subsumption calls : 0
% 13.68/2.45 % Non-unit clause-clause subsumptions : 0
% 13.68/2.45 % Unit Clause-clause subsumption calls : 20
% 13.68/2.45 % Rewrite failures with RHS unbound : 0
% 13.68/2.45 % BW rewrite match attempts : 1725
% 13.68/2.45 % BW rewrite match successes : 72
% 13.68/2.45 % Condensation attempts : 0
% 13.68/2.45 % Condensation successes : 0
% 13.68/2.45 % Termbank termtop insertions : 1582028
% 13.68/2.45 % Search garbage collected termcells : 2
% 13.68/2.45
% 13.68/2.45 % -------------------------------------------------
% 13.68/2.45 % User time : 1.860 s
% 13.68/2.45 % System time : 0.081 s
% 13.68/2.45 % Total time : 1.940 s
% 13.68/2.45 % Maximum resident set size: 3388 pages
% 13.68/2.45
% 13.68/2.45 % -------------------------------------------------
% 13.68/2.45 % User time : 9.240 s
% 13.68/2.45 % System time : 0.400 s
% 13.68/2.45 % Total time : 9.641 s
% 13.68/2.45 % Maximum resident set size: 4608 pages
% 13.68/2.45 % E exiting
%------------------------------------------------------------------------------