%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL784-1 : TPTP v9.2.1. Released v4.1.0.
% 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 04:45:01 PM UTC 2026
% Result : Unsatisfiable 1.34s 1.78s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 9 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-5 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_True_0,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
cnf(cls_Var__eq__apps__conv_2,axiom,
c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
cnf(cls_Nil_0,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nil_0) ).
cnf(cls_subst__eq_0,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
cnf(cls_uIT_0,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
cnf(c_0_6,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))),
cls_conjecture_0 ).
cnf(c_0_7,axiom,
v_n____ = v_i____,
cls_True_0 ).
cnf(c_0_8,axiom,
c_Lambda_OdB_OVar(X1) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
cls_Var__eq__apps__conv_2 ).
cnf(c_0_9,axiom,
v_rs____ = c_List_Olist_ONil(tc_Lambda_OdB),
cls_Nil_0 ).
cnf(c_0_10,negated_conjecture,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_n____))),
inference(rw,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X1),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_OdB_OVar(X1),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X1)),X2),X1) = X2,
cls_subst__eq_0 ).
cnf(c_0_13,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
cls_uIT_0 ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL784-1 : TPTP v9.2.1. Released v4.1.0.
% 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
% 0.16/0.33 % Computer : n001.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
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 23:07:33 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.34/1.78 % Version : CSE_E---1.7
% 1.34/1.78 % Problem : theBenchmark.p
% 1.34/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 1.34/1.78 % SZS output start CNFRefutation
% See solution above
% 1.34/1.78 % Total time : 1.422s
%------------------------------------------------------------------------------