%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET839-2 : TPTP v9.2.1. Released v3.2.0.
% 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 05:08:40 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.73s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 6 unt; 7 nHn; 10 RR)
% Number of literals : 40 ( 3 equ; 14 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 41 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
( c_lessequals(X1,X2,tc_set(t_a))
| ~ c_in(X2,v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,negated_conjecture,
( c_lessequals(X1,X2,tc_set(t_a))
| ~ c_in(X2,v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
cls_conjecture_1 ).
cnf(c_0_7,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_8,negated_conjecture,
( c_lessequals(X1,c_Main_OsubsetI__1(v_S,X2,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X2,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
cls_Set_Osubset__antisym_0 ).
cnf(c_0_10,negated_conjecture,
( c_lessequals(c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),c_Main_OsubsetI__1(v_S,X2,tc_set(t_a)),tc_set(t_a))
| c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X2,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_11,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
cls_Set_OsubsetI_1 ).
cnf(c_0_12,negated_conjecture,
( c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)) = c_Main_OsubsetI__1(v_S,X2,tc_set(t_a))
| c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X2,tc_set(tc_set(t_a))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( c_lessequals(v_S,X1,tc_set(tc_set(t_a)))
| c_lessequals(v_S,X2,tc_set(tc_set(t_a)))
| ~ c_in(c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_15,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_a)),tc_set(tc_set(t_a))),
cls_conjecture_0 ).
cnf(c_0_16,negated_conjecture,
( c_lessequals(v_S,c_insert(c_Main_OsubsetI__1(v_S,X1,tc_set(t_a)),X2,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(v_S,X1,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
c_lessequals(v_S,X1,tc_set(tc_set(t_a))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET839-2 : TPTP v9.2.1. Released v3.2.0.
% 0.11/0.13 % 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
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 02:38:18 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.25/1.73 % Version : CSE_E---1.7
% 1.25/1.73 % Problem : theBenchmark.p
% 1.25/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.73 % SZS output start CNFRefutation
% See solution above
% 1.25/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------