%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:00:57 PM UTC 2026
% Result : Unsatisfiable 1.45s 1.77s
% Output : CNFRefutation 1.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 4 RR)
% Number of literals : 57 ( 56 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 121 ( 15 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule12,axiom,
f(s(X1),zero,X2,X3) = f(X1,X3,minus(X2,s(X1)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule12) ).
cnf(rule2,axiom,
minus(s(X1),s(X2)) = minus(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule2) ).
cnf(rule13,axiom,
f(s(X1),s(X2),X3,X4) = if('<='(X1,X2),f(s(X1),minus(X2,X1),X3,X4),f(X1,X4,X3,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule13) ).
cnf(rule4,axiom,
'<='(s(X1),zero) = false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule4) ).
cnf(rule7,axiom,
if(false,X1,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule7) ).
cnf(rule1,axiom,
minus(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule1) ).
cnf(rule3,axiom,
'<='(zero,X1) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule3) ).
cnf(rule6,axiom,
if(true,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule6) ).
cnf(rule5,axiom,
'<='(s(X1),s(X2)) = '<='(X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule5) ).
cnf(rule9,axiom,
perfectp(s(X1)) = f(X1,s(zero),s(X1),s(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule9) ).
cnf(rule10,axiom,
f(zero,X1,zero,X2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule10) ).
cnf(goal,negated_conjecture,
perfectp(X1) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c_0_12,axiom,
f(s(X1),zero,X2,X3) = f(X1,X3,minus(X2,s(X1)),X3),
rule12 ).
cnf(c_0_13,axiom,
minus(s(X1),s(X2)) = minus(X1,X2),
rule2 ).
cnf(c_0_14,plain,
f(X1,X2,minus(X3,X1),X2) = f(s(X1),zero,s(X3),X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,axiom,
f(s(X1),s(X2),X3,X4) = if('<='(X1,X2),f(s(X1),minus(X2,X1),X3,X4),f(X1,X4,X3,X4)),
rule13 ).
cnf(c_0_16,axiom,
'<='(s(X1),zero) = false,
rule4 ).
cnf(c_0_17,axiom,
if(false,X1,X2) = X2,
rule7 ).
cnf(c_0_18,plain,
f(s(X1),X2,minus(X3,X1),X2) = f(s(s(X1)),zero,s(s(X3)),X2),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_19,axiom,
minus(X1,zero) = X1,
rule1 ).
cnf(c_0_20,axiom,
'<='(zero,X1) = true,
rule3 ).
cnf(c_0_21,axiom,
if(true,X1,X2) = X1,
rule6 ).
cnf(c_0_22,plain,
f(s(X1),X2,X3,X2) = f(s(s(X1)),s(zero),X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
f(s(zero),X1,X2,X1) = f(s(s(zero)),zero,s(s(X2)),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
'<='(s(X1),s(X2)) = '<='(X1,X2),
rule5 ).
cnf(c_0_25,plain,
f(s(zero),s(X1),X2,X3) = f(s(zero),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
f(s(s(zero)),zero,s(s(X1)),X2) = f(s(s(zero)),s(zero),X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
if('<='(X1,X2),f(s(s(X1)),minus(X2,X1),X3,X4),f(s(X1),X4,X3,X4)) = f(s(s(X1)),s(s(X2)),X3,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_24]) ).
cnf(c_0_28,plain,
f(s(s(zero)),s(zero),X1,s(X2)) = f(s(zero),X2,X1,s(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_19]),c_0_26]) ).
cnf(c_0_29,plain,
if('<='(X1,X2),f(s(s(s(X1))),minus(X2,X1),X3,X4),f(s(s(X1)),X4,X3,X4)) = f(s(s(s(X1))),s(s(s(X2))),X3,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_24]) ).
cnf(c_0_30,plain,
f(s(s(zero)),s(zero),X1,s(s(X2))) = f(s(zero),X2,X1,s(s(X2))),
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_31,plain,
if('<='(X1,X2),f(s(s(s(s(X1)))),minus(X2,X1),X3,X4),f(s(s(s(X1))),X4,X3,X4)) = f(s(s(s(s(X1)))),s(s(s(s(X2)))),X3,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_13]),c_0_24]) ).
cnf(c_0_32,plain,
f(s(s(zero)),s(s(X1)),X2,X3) = f(s(s(zero)),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_33,plain,
f(s(s(zero)),s(zero),X1,s(s(s(X2)))) = f(s(zero),X2,X1,s(s(s(X2)))),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_34,plain,
f(s(s(s(s(zero)))),s(s(s(s(X1)))),X2,X3) = f(s(s(s(s(zero)))),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_35,plain,
f(s(s(X1)),X2,X3,X2) = f(s(s(s(X1))),s(s(zero)),X3,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_16]),c_0_17]) ).
cnf(c_0_36,plain,
f(s(s(s(zero))),s(s(s(X1))),X2,X3) = f(s(s(s(zero))),X1,X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_37,plain,
f(s(s(X1)),X2,minus(X3,X1),X2) = f(s(s(s(X1))),zero,s(s(s(X3))),X2),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_38,plain,
f(s(s(zero)),X1,X2,s(s(X1))) = f(s(s(s(zero))),s(zero),X2,s(s(X1))),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_39,plain,
f(s(s(zero)),s(zero),X1,s(s(s(s(X2))))) = f(s(zero),X2,X1,s(s(s(s(X2))))),
inference(spm,[status(thm)],[c_0_25,c_0_33]) ).
cnf(c_0_40,axiom,
perfectp(s(X1)) = f(X1,s(zero),s(X1),s(X1)),
rule9 ).
cnf(c_0_41,plain,
f(s(s(s(s(zero)))),X1,X2,s(s(s(s(X1))))) = f(s(s(s(s(s(zero))))),s(zero),X2,s(s(s(s(X1))))),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_42,plain,
f(s(s(s(X1))),s(s(zero)),X2,X3) = f(s(s(s(X1))),s(zero),X2,X3),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_43,plain,
f(s(s(s(zero))),X1,X2,s(s(s(X1)))) = f(s(s(s(s(zero)))),s(zero),X2,s(s(s(X1)))),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_44,plain,
f(s(s(zero)),X1,X2,X1) = f(s(s(s(zero))),zero,s(s(s(X2))),X1),
inference(spm,[status(thm)],[c_0_37,c_0_19]) ).
cnf(c_0_45,plain,
f(s(s(s(zero))),s(zero),X1,s(s(s(s(X2))))) = f(s(s(zero)),X2,X1,s(s(s(s(X2))))),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_46,plain,
f(s(s(zero)),s(zero),X1,s(s(s(s(s(X2)))))) = f(s(zero),X2,X1,s(s(s(s(s(X2)))))),
inference(spm,[status(thm)],[c_0_25,c_0_39]) ).
cnf(c_0_47,axiom,
f(zero,X1,zero,X2) = true,
rule10 ).
cnf(c_0_48,plain,
f(zero,X1,X2,X1) = f(s(zero),zero,s(X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_19]) ).
cnf(c_0_49,plain,
f(s(s(s(s(zero)))),s(zero),s(s(s(s(s(s(zero)))))),s(s(s(s(s(s(zero))))))) = perfectp(s(s(s(s(s(s(zero))))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_50,plain,
f(s(s(s(s(zero)))),s(zero),X1,s(s(s(s(s(s(X2))))))) = f(s(s(s(zero))),X2,X1,s(s(s(s(s(s(X2))))))),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_51,plain,
f(s(s(s(zero))),zero,s(s(s(X1))),X2) = f(s(s(s(zero))),s(zero),X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_44]) ).
cnf(c_0_52,plain,
f(s(s(s(zero))),s(zero),X1,s(s(s(s(s(s(X2))))))) = f(s(s(zero)),X2,X1,s(s(s(s(s(s(X2))))))),
inference(spm,[status(thm)],[c_0_32,c_0_45]) ).
cnf(c_0_53,plain,
f(s(s(zero)),s(zero),X1,s(s(s(s(s(s(X2))))))) = f(s(zero),X2,X1,s(s(s(s(s(s(X2))))))),
inference(spm,[status(thm)],[c_0_25,c_0_46]) ).
cnf(c_0_54,plain,
f(s(zero),zero,s(zero),X1) = true,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
perfectp(X1) != true,
goal ).
cnf(c_0_56,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_52]),c_0_26]),c_0_53]),c_0_54]),c_0_55]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN135-1.006 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:24:35 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.45/1.77 % Version : CSE_E---1.7
% 1.45/1.77 % Problem : theBenchmark.p
% 1.45/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.45/1.77 % SZS output start CNFRefutation
% See solution above
% 1.45/1.77 % Total time : 1.372s
%------------------------------------------------------------------------------