%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW209+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 : n013.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 05:30:03 PM UTC 2026
% Result : Theorem 1.99s 2.10s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 def)
% Number of atoms : 26 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 4 |; 1 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 34 ( 3 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X4),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_o__apply,axiom,
! [X11,X1,X2,X10,X8,X9] : hAPP(hAPP(c_Fun_Ocomp(X9,X8,X10,X2),X1),X11) = hAPP(X2,hAPP(X1,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__apply) ).
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X4),hAPP(v_f____,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096) ).
fof(fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X4),hAPP(v_ga____,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096) ).
fof(c_0_4,negated_conjecture,
~ ! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X4),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),X5)) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_5,negated_conjecture,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk49_0,esk50_0)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk49_0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk50_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X2751,X2752,X2753,X2754,X2755,X2756] : hAPP(hAPP(c_Fun_Ocomp(X2756,X2755,X2754,X2753),X2752),X2751) = hAPP(X2753,hAPP(X2752,X2751)),
inference(variable_rename,[status(thm)],[fact_o__apply]) ).
cnf(c_0_7,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk49_0),hAPP(hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____),v_ga____),esk50_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X2740,X2741] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2740,X2741)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X2740),hAPP(v_f____,X2741)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Af_Am_A_060_Af_An_096])]) ).
cnf(c_0_10,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,hAPP(v_ga____,esk49_0)),hAPP(v_f____,hAPP(v_ga____,esk50_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
cnf(c_0_11,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_f____,X1),hAPP(v_f____,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X2742,X2743] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2742,X2743)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X2742),hAPP(v_ga____,X2743)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096ALL_Am_An_O_Am_A_060_An_A_N_N_062_Ag_Am_A_060_Ag_An_096])]) ).
cnf(c_0_13,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,esk49_0),hAPP(v_ga____,esk50_0)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(v_ga____,X1),hAPP(v_ga____,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk49_0,esk50_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW209+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n013.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 06:27:11 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.99/2.10 % Version : CSE_E---1.7
% 1.99/2.10 % Problem : theBenchmark.p
% 1.99/2.10 % SZS status Theorem for theBenchmark.p
% 1.99/2.10 % SZS output start CNFRefutation
% See solution above
% 1.99/2.10 % Total time : 1.590s
%------------------------------------------------------------------------------