%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET840-2 : TPTP v9.2.1. Released v3.2.0.
% 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 : n007.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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 8 unt; 7 nHn; 21 RR)
% Number of literals : 68 ( 10 equ; 28 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 91 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OinsertE_0,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OUnionI_0,axiom,
( c_in(X1,c_Union(X4,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionI_0) ).
cnf(cls_Set_OinsertCI_1,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(cls_Set_OinsertCI_0,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_lessequals(c_Union(v_S,t_b),X1,tc_set(t_b))
| ~ c_in(X1,v_S,tc_set(t_b)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_9,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
cls_Set_OinsertE_0 ).
cnf(c_0_10,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_11,axiom,
( c_in(X1,c_Union(X4,X3),X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X2,X4,tc_set(X3)) ),
cls_Set_OUnionI_0 ).
cnf(c_0_12,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_13,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_14,plain,
( c_Main_OsubsetI__1(c_insert(X1,X2,X3),X4,X3) = X1
| c_in(c_Main_OsubsetI__1(c_insert(X1,X2,X3),X4,X3),X2,X3)
| c_lessequals(c_insert(X1,X2,X3),X4,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,axiom,
( c_in(X1,c_insert(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OinsertCI_0 ).
cnf(c_0_16,plain,
( c_in(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),X4)
| ~ c_in(X1,X2,X4) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( c_Main_OsubsetI__1(c_insert(X1,X2,X3),X2,X3) = X1
| c_lessequals(c_insert(X1,X2,X3),X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( c_lessequals(X1,c_insert(X2,X3,X4),tc_set(X4))
| ~ c_in(c_Main_OsubsetI__1(X1,c_insert(X2,X3,X4),X4),X3,X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_19,plain,
( c_lessequals(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),tc_set(X4))
| ~ c_in(c_Main_OsubsetI__1(X1,c_Union(c_insert(X2,X3,tc_set(X4)),X4),X4),X2,X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_20,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_21,plain,
( c_lessequals(c_insert(X1,X2,X3),X2,tc_set(X3))
| ~ c_in(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_22,plain,
c_lessequals(X1,c_insert(X2,X1,X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( c_lessequals(c_Union(v_S,t_b),X1,tc_set(t_b))
| ~ c_in(X1,v_S,tc_set(t_b)) ),
cls_conjecture_1 ).
cnf(c_0_24,plain,
c_lessequals(X1,c_Union(c_insert(X1,X2,tc_set(X3)),X3),tc_set(X3)),
inference(spm,[status(thm)],[c_0_19,c_0_10]) ).
cnf(c_0_25,plain,
( c_insert(X1,X2,X3) = X2
| ~ c_in(X1,X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
( X1 = c_Union(v_S,t_b)
| ~ c_in(X1,v_S,tc_set(t_b))
| ~ c_lessequals(X1,c_Union(v_S,t_b),tc_set(t_b)) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_27,plain,
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( X1 = c_Union(v_S,t_b)
| ~ c_in(X1,v_S,tc_set(t_b)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( c_Main_OsubsetI__1(v_S,X1,tc_set(t_b)) = c_Union(v_S,t_b)
| c_lessequals(v_S,X1,tc_set(tc_set(t_b))) ),
inference(spm,[status(thm)],[c_0_28,c_0_10]) ).
cnf(c_0_30,negated_conjecture,
( c_lessequals(v_S,X1,tc_set(tc_set(t_b)))
| ~ c_in(c_Union(v_S,t_b),X1,tc_set(t_b)) ),
inference(spm,[status(thm)],[c_0_13,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
~ c_lessequals(v_S,c_insert(X1,c_emptyset,tc_set(t_b)),tc_set(tc_set(t_b))),
cls_conjecture_0 ).
cnf(c_0_32,negated_conjecture,
c_lessequals(v_S,c_insert(c_Union(v_S,t_b),X1,tc_set(t_b)),tc_set(tc_set(t_b))),
inference(spm,[status(thm)],[c_0_30,c_0_12]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET840-2 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:36:54 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------