%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW350+1 : TPTP v9.2.1. Released v5.2.0.
% 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 : n025.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 05:32:05 PM UTC 2026
% Result : Theorem 31.30s 19.11s
% Output : CNFRefutation 31.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 16 unt; 0 def)
% Number of atoms : 52 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 17 ~; 16 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 70 ( 7 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_com__det,axiom,
! [X4,X5,X6,X7] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X7),X6),X5))
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(X7),X6),X4))
=> X4 = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).
fof(conj_1,hypothesis,
! [X333] :
( ! [X30] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),X30))
=> X333 = X30 )
=> X333 = v_s_H ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_self__append__conv2,axiom,
! [X275,X51,X276] :
( X276 = hAPP(hAPP(c_List_Oappend(X51),X275),X276)
<=> X275 = c_List_Olist_ONil(X51) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).
fof(fact_append__Cons,axiom,
! [X282,X281,X81,X51] : hAPP(hAPP(c_List_Oappend(X51),hAPP(hAPP(c_List_Olist_OCons(X51),X81),X281)),X282) = hAPP(hAPP(c_List_Olist_OCons(X51),X81),hAPP(hAPP(c_List_Oappend(X51),X281),X282)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).
fof(fact_list_Osimps_I2_J,axiom,
! [X299,X83,X51] : c_List_Olist_ONil(X51) != hAPP(hAPP(c_List_Olist_OCons(X51),X83),X299),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(fact_rev__append,axiom,
! [X282,X281,X51] : hAPP(c_List_Orev(X51),hAPP(hAPP(c_List_Oappend(X51),X281),X282)) = hAPP(hAPP(c_List_Oappend(X51),hAPP(c_List_Orev(X51),X282)),hAPP(c_List_Orev(X51),X281)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__append) ).
fof(conj_3,conjecture,
hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
fof(c_0_7,plain,
! [X17187,X17188,X17189,X17190] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17190),X17189),X17188))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17190),X17189),X17187))
| X17187 = X17188 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com__det])]) ).
fof(c_0_8,hypothesis,
! [X34734] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),esk522_1(X34734)))
| X34734 = v_s_H )
& ( X34734 != esk522_1(X34734)
| X34734 = v_s_H ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_1])])])]) ).
cnf(c_0_9,plain,
( X4 = X3
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X2),X4)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,hypothesis,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),esk522_1(X1)))
| X1 = v_s_H ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X31165,X31166,X31167] :
( ( X31167 != hAPP(hAPP(c_List_Oappend(X31166),X31165),X31167)
| X31165 = c_List_Olist_ONil(X31166) )
& ( X31165 != c_List_Olist_ONil(X31166)
| X31167 = hAPP(hAPP(c_List_Oappend(X31166),X31165),X31167) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).
fof(c_0_12,plain,
! [X31265,X31266,X31267,X31268] : hAPP(hAPP(c_List_Oappend(X31268),hAPP(hAPP(c_List_Olist_OCons(X31268),X31267),X31266)),X31265) = hAPP(hAPP(c_List_Olist_OCons(X31268),X31267),hAPP(hAPP(c_List_Oappend(X31268),X31266),X31265)),
inference(variable_rename,[status(thm)],[fact_append__Cons]) ).
fof(c_0_13,plain,
! [X30933,X30934,X30935] : c_List_Olist_ONil(X30935) != hAPP(hAPP(c_List_Olist_OCons(X30935),X30934),X30933),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
cnf(c_0_14,hypothesis,
( X1 = esk522_1(X2)
| X2 = v_s_H
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( X3 = c_List_Olist_ONil(X2)
| X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
hAPP(hAPP(c_List_Oappend(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X32545,X32546,X32547] : hAPP(c_List_Orev(X32547),hAPP(hAPP(c_List_Oappend(X32547),X32546),X32545)) = hAPP(hAPP(c_List_Oappend(X32547),hAPP(c_List_Orev(X32547),X32545)),hAPP(c_List_Orev(X32547),X32546)),
inference(variable_rename,[status(thm)],[fact_rev__append]) ).
cnf(c_0_19,hypothesis,
( X1 = v_s_H
| X1 != esk522_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,hypothesis,
( esk522_1(X1) = esk522_1(X2)
| X1 = v_s_H
| X2 = v_s_H ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
fof(c_0_21,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_3])]) ).
cnf(c_0_22,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)) != X4,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X2),X3)) = hAPP(hAPP(c_List_Oappend(X1),hAPP(c_List_Orev(X1),X3)),hAPP(c_List_Orev(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,hypothesis,
( esk522_1(X1) = v_s_H
| X1 = v_s_H ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_25,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),v_Z),v_s_H)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(c_List_Orev(X1),hAPP(hAPP(c_List_Oappend(X1),X3),X4))) != hAPP(c_List_Orev(X1),X3),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,hypothesis,
X1 = v_s_H,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW350+1 : TPTP v9.2.1. Released v5.2.0.
% 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
% 0.16/0.33 % Computer : n025.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 06:39:43 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 31.30/19.11 % Version : CSE_E---1.7
% 31.30/19.11 % Problem : theBenchmark.p
% 31.30/19.11 % SZS status Theorem for theBenchmark.p
% 31.30/19.11 % SZS output start CNFRefutation
% See solution above
% 31.46/19.20 % Total time : 15.246s
%------------------------------------------------------------------------------