%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV858-1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n026.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 05:27:33 PM UTC 2026
% Result : Unsatisfiable 2.04s 1.96s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 8 unt; 4 nHn; 19 RR)
% Number of literals : 48 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 35 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_subset__iff_0,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
cnf(cls_conjecture_2,negated_conjecture,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_6,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,v_n(X1),t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_4,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(v_x,X1,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_Ga)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_mem__def_1,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,t_a)
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(X1)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts_H)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_mem__def_0,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
cnf(c_0_9,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_in(X1),X2),X4))
| ~ c_lessequals(X4,X3,tc_fun(X1,tc_bool)) ),
cls_subset__iff_0 ).
cnf(c_0_10,negated_conjecture,
hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)),
cls_conjecture_2 ).
cnf(c_0_11,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts_H))
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,v_n(X1),t_a) ),
cls_conjecture_6 ).
cnf(c_0_12,negated_conjecture,
( hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),X1))
| ~ c_lessequals(v_tsa,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),
cls_conjecture_1 ).
cnf(c_0_14,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(v_x,X1,t_a)
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),X1),v_Ga)) ),
cls_conjecture_4 ).
cnf(c_0_15,axiom,
( hBOOL(hAPP(hAPP(c_in(X1),X2),X3))
| ~ hBOOL(hAPP(X3,X2)) ),
cls_mem__def_1 ).
cnf(c_0_16,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(X1,X2,t_a)
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(X1)),v_Ga))
| ~ hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts_H)) ),
cls_conjecture_5 ).
cnf(c_0_17,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(X1,v_xa,t_a)
| ~ c_Hoare__Mirabelle_Otriple__valid(X1,v_n(X1),t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_18,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(v_x,X1,t_a)
| ~ hBOOL(hAPP(v_Ga,X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
~ c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a),
cls_conjecture_3 ).
cnf(c_0_20,axiom,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(c_in(X3),X2),X1)) ),
cls_mem__def_0 ).
cnf(c_0_21,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(X1,v_xa,t_a)
| hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(X1)),v_Ga)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_13])]) ).
cnf(c_0_22,negated_conjecture,
~ hBOOL(hAPP(v_Ga,v_n(v_x))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( c_Hoare__Mirabelle_Otriple__valid(X1,v_xa,t_a)
| hBOOL(hAPP(v_Ga,v_n(X1))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV858-1 : TPTP v9.2.1. Released v4.1.0.
% 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
% 0.14/0.33 % Computer : n026.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 06:04:23 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 2.04/1.96 % Version : CSE_E---1.7
% 2.04/1.96 % Problem : theBenchmark.p
% 2.04/1.96 % SZS status Unsatisfiable for theBenchmark.p
% 2.04/1.96 % SZS output start CNFRefutation
% See solution above
% 2.04/1.96 % Total time : 1.428s
%------------------------------------------------------------------------------