%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWX197+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 03:14:13 PM UTC 2026
% Result : Theorem 156.85s 23.77s
% Output : CNFRefutation 156.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 65 ( 57 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 19 ~; 6 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 4 con; 0-3 aty)
% Number of variables : 167 ( 37 sgn 71 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_060,axiom,
! [X1,X18,X19] :
( eval(X1,X18) = eval(X1,X19)
=> eval(X1,eq(X18,X19)) = suc(zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_060) ).
fof(axiom_047,axiom,
! [X11,X12,X13] : opti2(if(X11,X12,X13)) = if(add(n(suc(zero)),X11),X13,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_047) ).
fof(axiom_073,axiom,
! [X14] : apply1(lam,X14) = opti2(X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_073) ).
fof(axiom_058,axiom,
! [X1,X15,X16] : eval(X1,add(X15,X16)) = addNat(eval(X1,X15),eval(X1,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_058) ).
fof(axiom_026,axiom,
! [X1,X2,X3] : proj1If(if(X1,X2,X3)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_026) ).
fof(axiom_037,axiom,
! [X1,X2] : nil != cons(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_037) ).
fof(goal_074,conjecture,
? [X10] : run(nil,cons2(X10,nil2)) != run(nil,cons2(opti2(X10),nil2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal_074) ).
fof(axiom_057,axiom,
! [X1,X7] : eval(X1,n(X7)) = X7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_057) ).
fof(axiom_053,axiom,
! [X6,X2] : addNat(suc(X6),suc(X2)) = suc(addNat(X6,suc(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_053) ).
fof(axiom_051,axiom,
! [X14] : addNat(zero,X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
fof(axiom_064,axiom,
! [X1,X13,X9] : run(X1,cons2(print(X9),X13)) = cons(eval(X1,X9),run(X1,X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_064) ).
fof(axiom_068,axiom,
! [X1,X13,X22,X12,X23,X3] :
( eval(X1,X22) = suc(X3)
=> run(X1,cons2(if(X22,X12,X23),X13)) = run(X1,append(X12,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_068) ).
fof(axiom_072,axiom,
! [X14,X6,X25] : append(cons2(X6,X25),X14) = cons2(X6,append(X25,X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_072) ).
fof(axiom_071,axiom,
! [X14] : append(nil2,X14) = X14,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_071) ).
fof(axiom_063,axiom,
! [X1] : run(X1,nil2) = nil,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_063) ).
fof(c_0_15,plain,
! [X166,X167,X168] :
( eval(X166,eq(X167,X168)) = suc(zero)
| eval(X166,X167) != eval(X166,X168) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_060])])]) ).
fof(c_0_16,plain,
! [X141,X142,X143] : opti2(if(X141,X142,X143)) = if(add(n(suc(zero)),X141),X143,X142),
inference(variable_rename,[status(thm)],[axiom_047]) ).
fof(c_0_17,plain,
! [X205] : apply1(lam,X205) = opti2(X205),
inference(variable_rename,[status(thm)],[axiom_073]) ).
fof(c_0_18,plain,
! [X160,X161,X162] : eval(X160,add(X161,X162)) = addNat(eval(X160,X161),eval(X160,X162)),
inference(variable_rename,[status(thm)],[axiom_058]) ).
cnf(c_0_19,plain,
( eval(X1,X2) != eval(X1,X3)
| eval(X1,eq(X2,X3)) = suc(zero) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,plain,
! [X83,X84,X85] : proj1If(if(X83,X84,X85)) = X83,
inference(variable_rename,[status(thm)],[axiom_026]) ).
cnf(c_0_21,plain,
opti2(if(X1,X2,X3)) = if(add(n(suc(zero)),X1),X3,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
apply1(lam,X1) = opti2(X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X1,X2] : nil != cons(X1,X2),
inference(fof_simplification,[status(thm)],[axiom_037]) ).
fof(c_0_24,negated_conjecture,
~ ? [X10] : run(nil,cons2(X10,nil2)) != run(nil,cons2(opti2(X10),nil2)),
inference(assume_negation,[status(cth)],[goal_074]) ).
cnf(c_0_25,plain,
eval(X1,add(X2,X3)) = addNat(eval(X1,X2),eval(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
eval(X1,eq(X2,X2)) = suc(zero),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
proj1If(if(X1,X2,X3)) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
apply1(lam,if(X1,X2,X3)) = if(add(n(suc(zero)),X1),X3,X2),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_29,plain,
! [X158,X159] : eval(X158,n(X159)) = X159,
inference(variable_rename,[status(thm)],[axiom_057]) ).
fof(c_0_30,plain,
! [X152,X153] : addNat(suc(X152),suc(X153)) = suc(addNat(X152,suc(X153))),
inference(variable_rename,[status(thm)],[axiom_053]) ).
fof(c_0_31,plain,
! [X150] : addNat(zero,X150) = X150,
inference(variable_rename,[status(thm)],[axiom_051]) ).
fof(c_0_32,plain,
! [X120,X121] : nil != cons(X120,X121),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
fof(c_0_33,plain,
! [X175,X176,X177] : run(X175,cons2(print(X177),X176)) = cons(eval(X175,X177),run(X175,X176)),
inference(variable_rename,[status(thm)],[axiom_064]) ).
fof(c_0_34,negated_conjecture,
~ ? [X10] : run(nil,cons2(X10,nil2)) != run(nil,cons2(opti2(X10),nil2)),
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_35,plain,
! [X191,X192,X193,X194,X195,X196] :
( run(X191,cons2(if(X193,X194,X195),X192)) = run(X191,append(X194,X192))
| eval(X191,X193) != suc(X196) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_068])])]) ).
cnf(c_0_36,plain,
addNat(eval(X1,X2),suc(zero)) = eval(X1,add(X2,eq(X3,X3))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_37,plain,
proj1If(apply1(lam,if(X1,X2,X3))) = add(n(suc(zero)),X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_38,plain,
eval(X1,n(X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
addNat(suc(X1),suc(X2)) = suc(addNat(X1,suc(X2))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_40,plain,
addNat(zero,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,plain,
nil != cons(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
run(X1,cons2(print(X2),X3)) = cons(eval(X1,X2),run(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_43,plain,
! [X202,X203,X204] : append(cons2(X203,X204),X202) = cons2(X203,append(X204,X202)),
inference(variable_rename,[status(thm)],[axiom_072]) ).
fof(c_0_44,negated_conjecture,
! [X206] : run(nil,cons2(X206,nil2)) = run(nil,cons2(opti2(X206),nil2)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])]) ).
cnf(c_0_45,plain,
( eval(X1,X2) != suc(X3)
| run(X1,cons2(if(X2,X4,X5),X6)) = run(X1,append(X4,X6)) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_46,plain,
eval(X1,proj1If(apply1(lam,if(eq(X2,X2),X3,X4)))) = suc(suc(zero)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_47,plain,
if(proj1If(apply1(lam,if(X1,X2,X3))),X4,X5) = apply1(lam,if(X1,X5,X4)),
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_48,plain,
run(X1,cons2(print(X2),X3)) != nil,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
append(cons2(X1,X2),X3) = cons2(X1,append(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,negated_conjecture,
run(nil,cons2(X1,nil2)) = run(nil,cons2(opti2(X1),nil2)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,plain,
( suc(suc(zero)) != suc(X6)
| run(X1,cons2(apply1(lam,if(eq(X2,X2),X3,X4)),X5)) = run(X1,append(X4,X5)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_52,plain,
( suc(zero) != suc(X6)
| run(X1,cons2(if(eq(X2,X2),X3,X4),X5)) = run(X1,append(X3,X5)) ),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_53,plain,
run(X1,append(cons2(print(X2),X3),X4)) != nil,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
run(nil,cons2(X1,nil2)) = run(nil,cons2(apply1(lam,X1),nil2)),
inference(rw,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_55,plain,
run(X1,cons2(apply1(lam,if(eq(X2,X2),X3,X4)),X5)) = run(X1,append(X4,X5)),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_56,plain,
run(X1,cons2(if(eq(X2,X2),X3,X4),X5)) = run(X1,append(X3,X5)),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
run(X1,append(append(cons2(print(X2),X3),X4),X5)) != nil,
inference(spm,[status(thm)],[c_0_53,c_0_49]) ).
cnf(c_0_58,negated_conjecture,
run(nil,append(X1,nil2)) = run(nil,append(X2,nil2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
fof(c_0_59,plain,
! [X201] : append(nil2,X201) = X201,
inference(variable_rename,[status(thm)],[axiom_071]) ).
fof(c_0_60,plain,
! [X174] : run(X174,nil2) = nil,
inference(variable_rename,[status(thm)],[axiom_063]) ).
cnf(c_0_61,negated_conjecture,
run(nil,append(X1,nil2)) != nil,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
append(nil2,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_63,plain,
run(X1,nil2) = nil,
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX197+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.56 % Computer : n017.cluster.edu
% 0.11/0.56 % Model : x86_64 x86_64
% 0.11/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.56 % Memory : 8046.5625MB
% 0.11/0.56 % OS : Linux 6.8.0-71-generic
% 0.11/0.56 % CPULimit : 300
% 0.11/0.56 % WCLimit : 300
% 0.11/0.56 % DateTime : Mon Sep 21 10:28:13 UTC 2026
% 0.11/0.56 % CPUTime :
% 0.11/0.56 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.60 Running first-order theorem proving
% 0.15/0.60 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
% 156.85/23.77 % Version: 3.5.1
% 156.85/23.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 156.85/23.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 156.85/23.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 156.85/23.77 % Starting new_bool_3 with 300s (1) cores
% 156.85/23.77 % Starting new_bool_1 with 300s (1) cores
% 156.85/23.77 % Starting sh5l with 300s (1) cores
% 156.85/23.77 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2098887 completed with status 0
% 156.85/23.77 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 156.85/23.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 156.85/23.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 156.85/23.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 156.85/23.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 156.85/23.77 % No SInE strategy applied
% 156.85/23.77 % Search class: FGUPM-FFMF31-DFFFFFNN
% 156.85/23.77 % partial match(2): FUUPM-FFMF21-DFFFFFNN
% 156.85/23.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 156.85/23.77 % Starting SubtermCWHack with 136s (1) cores
% 156.85/23.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 156.85/23.77 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 156.85/23.77 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 156.85/23.77 % Starting new_bool_3 with 136s (1) cores
% 156.85/23.77 % H----_047_C09_12_F1_AE_ND_CS_SP_S2S with pid 2098897 completed with status 0
% 156.85/23.77 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S2S
% 156.85/23.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 156.85/23.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 156.85/23.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 156.85/23.77 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 156.85/23.77 % No SInE strategy applied
% 156.85/23.77 % Search class: FGUPM-FFMF31-DFFFFFNN
% 156.85/23.77 % partial match(2): FUUPM-FFMF21-DFFFFFNN
% 156.85/23.77 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 156.85/23.77 % Starting SubtermCWHack with 136s (1) cores
% 156.85/23.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 156.85/23.77 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 156.85/23.77 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 156.85/23.77 % Preprocessing time : 0.002 s
% 156.85/23.77 % Presaturation interreduction done
% 156.85/23.77
% 156.85/23.77 % Proof found!
% 156.85/23.77 % SZS status Theorem
% 156.85/23.77 % SZS output start CNFRefutation
% See solution above
% 156.85/23.77 % Parsed axioms : 74
% 156.85/23.77 % Removed by relevancy pruning/SinE : 0
% 156.85/23.77 % Initial clauses : 74
% 156.85/23.77 % Removed in clause preprocessing : 2
% 156.85/23.77 % Initial clauses in saturation : 72
% 156.85/23.77 % Processed clauses : 8889
% 156.85/23.77 % ...of these trivial : 652
% 156.85/23.77 % ...subsumed : 5190
% 156.85/23.77 % ...remaining for further processing : 3047
% 156.85/23.77 % Other redundant clauses eliminated : 439
% 156.85/23.77 % Clauses deleted for lack of memory : 0
% 156.85/23.77 % Backward-subsumed : 57
% 156.85/23.77 % Backward-rewritten : 19
% 156.85/23.77 % Generated clauses : 831619
% 156.85/23.77 % ...of the previous two non-redundant : 794470
% 156.85/23.77 % ...aggressively subsumed : 0
% 156.85/23.77 % Contextual simplify-reflections : 0
% 156.85/23.77 % Paramodulations : 830627
% 156.85/23.77 % Factorizations : 0
% 156.85/23.77 % NegExts : 0
% 156.85/23.77 % Equation resolutions : 992
% 156.85/23.77 % Disequality decompositions : 0
% 156.85/23.77 % Total rewrite steps : 209258
% 156.85/23.77 % ...of those cached : 113559
% 156.85/23.77 % Propositional unsat checks : 0
% 156.85/23.77 % Propositional check models : 0
% 156.85/23.77 % Propositional check unsatisfiable : 0
% 156.85/23.77 % Propositional clauses : 0
% 156.85/23.77 % Propositional clauses after purity: 0
% 156.85/23.77 % Propositional unsat core size : 0
% 156.85/23.77 % Propositional preprocessing time : 0.000
% 156.85/23.77 % Propositional encoding time : 0.000
% 156.85/23.77 % Propositional solver time : 0.000
% 156.85/23.77 % Success case prop preproc time : 0.000
% 156.85/23.77 % Success case prop encoding time : 0.000
% 156.85/23.77 % Success case prop solver time : 0.000
% 156.85/23.77 % Current number of processed clauses : 2899
% 156.85/23.77 % Positive orientable unit clauses : 939
% 156.85/23.77 % Positive unorientable unit clauses: 33
% 156.85/23.77 % Negative unit clauses : 624
% 156.85/23.77 % Non-unit-clauses : 1303
% 156.85/23.77 % Current number of unprocessed clauses: 785372
% 156.85/23.77 % ...number of literals in the above : 1362504
% 156.85/23.77 % Current number of archived formulas : 0
% 156.85/23.77 % Current number of archived clauses : 150
% 156.85/23.77 % Clause-clause subsumption calls (NU) : 142226
% 156.85/23.77 % Rec. Clause-clause subsumption calls : 124957
% 156.85/23.77 % Non-unit clause-clause subsumptions : 1808
% 156.85/23.77 % Unit Clause-clause subsumption calls : 353375
% 156.85/23.77 % Rewrite failures with RHS unbound : 181
% 156.85/23.77 % BW rewrite match attempts : 20997
% 156.85/23.77 % BW rewrite match successes : 57
% 156.85/23.77 % Condensation attempts : 0
% 156.85/23.77 % Condensation successes : 0
% 156.85/23.77 % Termbank termtop insertions : 17033729
% 156.85/23.77 % Search garbage collected termcells : 281
% 156.85/23.77
% 156.85/23.77 % -------------------------------------------------
% 156.85/23.77 % User time : 21.174 s
% 156.85/23.77 % System time : 1.034 s
% 156.85/23.77 % Total time : 22.208 s
% 156.85/23.77 % Maximum resident set size: 3712 pages
% 156.85/23.77
% 156.85/23.77 % -------------------------------------------------
% 156.85/23.77 % User time : 106.231 s
% 156.85/23.77 % System time : 4.599 s
% 156.85/23.77 % Total time : 110.829 s
% 156.85/23.77 % Maximum resident set size: 4864 pages
% 156.85/23.77 % E exiting
%------------------------------------------------------------------------------