%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW348+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n001.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 05:32:04 PM UTC 2026
% Result : Theorem 31.26s 18.98s
% Output : CNFRefutation 31.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 14 unt; 0 def)
% Number of atoms : 56 ( 40 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 46 ( 18 ~; 16 |; 3 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 76 ( 7 sgn 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_1,conjecture,
! [X106,X107] :
( ! [X333] :
( ! [X30] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X106),X30))
=> X333 = X30 )
=> X333 = X107 )
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X106),X107)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
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/sandbox/benchmark/theBenchmark.p',fact_com__det) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',fact_rev__append) ).
fof(c_0_6,negated_conjecture,
~ ! [X106,X107] :
( ! [X333] :
( ! [X30] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X106),X30))
=> X333 = X30 )
=> X333 = X107 )
=> hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),X106),X107)) ),
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(c_0_7,plain,
! [X17188,X17189,X17190,X17191] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17191),X17190),X17189))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X17191),X17190),X17188))
| X17188 = X17189 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_com__det])]) ).
fof(c_0_8,negated_conjecture,
! [X34737] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),esk522_0),esk524_1(X34737)))
| X34737 = esk523_0 )
& ( X34737 != esk524_1(X34737)
| X34737 = esk523_0 )
& ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),esk522_0),esk523_0)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
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,negated_conjecture,
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),esk522_0),esk524_1(X1)))
| X1 = esk523_0 ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X31166,X31167,X31168] :
( ( X31168 != hAPP(hAPP(c_List_Oappend(X31167),X31166),X31168)
| X31166 = c_List_Olist_ONil(X31167) )
& ( X31166 != c_List_Olist_ONil(X31167)
| X31168 = hAPP(hAPP(c_List_Oappend(X31167),X31166),X31168) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).
fof(c_0_12,plain,
! [X31266,X31267,X31268,X31269] : hAPP(hAPP(c_List_Oappend(X31269),hAPP(hAPP(c_List_Olist_OCons(X31269),X31268),X31267)),X31266) = hAPP(hAPP(c_List_Olist_OCons(X31269),X31268),hAPP(hAPP(c_List_Oappend(X31269),X31267),X31266)),
inference(variable_rename,[status(thm)],[fact_append__Cons]) ).
fof(c_0_13,plain,
! [X30934,X30935,X30936] : c_List_Olist_ONil(X30936) != hAPP(hAPP(c_List_Olist_OCons(X30936),X30935),X30934),
inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).
cnf(c_0_14,negated_conjecture,
( X1 = esk524_1(X2)
| X2 = esk523_0
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),esk522_0),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,
! [X32546,X32547,X32548] : hAPP(c_List_Orev(X32548),hAPP(hAPP(c_List_Oappend(X32548),X32547),X32546)) = hAPP(hAPP(c_List_Oappend(X32548),hAPP(c_List_Orev(X32548),X32546)),hAPP(c_List_Orev(X32548),X32547)),
inference(variable_rename,[status(thm)],[fact_rev__append]) ).
cnf(c_0_19,negated_conjecture,
( X1 = esk523_0
| X1 != esk524_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( esk524_1(X1) = esk524_1(X2)
| X1 = esk523_0
| X2 = esk523_0 ),
inference(spm,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_21,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_22,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_23,negated_conjecture,
( esk524_1(X1) = esk523_0
| X1 = esk523_0 ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(v_c),esk522_0),esk523_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,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_21,c_0_22]) ).
cnf(c_0_26,negated_conjecture,
X1 = esk523_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW348+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 06:40:33 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.35 % start to proof: theBenchmark
% 31.26/18.98 % Version : CSE_E---1.7
% 31.26/18.98 % Problem : theBenchmark.p
% 31.26/18.98 % SZS status Theorem for theBenchmark.p
% 31.26/18.98 % SZS output start CNFRefutation
% See solution above
% 31.38/19.07 % Total time : 15.144s
%------------------------------------------------------------------------------