%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET820-2 : 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 : n010.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 05:08:33 PM UTC 2026
% Result : Unsatisfiable 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 18 ( 10 unt; 3 nHn; 13 RR)
% Number of literals : 28 ( 4 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
( c_in(v_x(X2),X2,tc_IntDef_Oint)
| ~ c_in(X1,X2,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
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_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_OemptyE_0,axiom,
~ c_in(X1,c_emptyset,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OemptyE_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( ~ c_in(X1,X2,tc_IntDef_Oint)
| ~ v_P(v_x(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_0,negated_conjecture,
v_P(v_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(c_0_6,negated_conjecture,
( c_in(v_x(X2),X2,tc_IntDef_Oint)
| ~ c_in(X1,X2,tc_IntDef_Oint) ),
cls_conjecture_1 ).
cnf(c_0_7,axiom,
c_in(X1,c_insert(X1,X2,X3),X3),
cls_Set_OinsertCI_1 ).
cnf(c_0_8,axiom,
( c_in(X1,X3,X4)
| X1 = X2
| ~ c_in(X1,c_insert(X2,X3,X4),X4) ),
cls_Set_OinsertE_0 ).
cnf(c_0_9,negated_conjecture,
c_in(v_x(c_insert(X1,X2,tc_IntDef_Oint)),c_insert(X1,X2,tc_IntDef_Oint),tc_IntDef_Oint),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,axiom,
~ c_in(X1,c_emptyset,X2),
cls_Set_OemptyE_0 ).
cnf(c_0_11,negated_conjecture,
( v_x(c_insert(X1,X2,tc_IntDef_Oint)) = X1
| c_in(v_x(c_insert(X1,X2,tc_IntDef_Oint)),X2,tc_IntDef_Oint) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( ~ c_in(X1,X2,tc_IntDef_Oint)
| ~ v_P(v_x(X2)) ),
cls_conjecture_2 ).
cnf(c_0_13,negated_conjecture,
v_x(c_insert(X1,c_emptyset,tc_IntDef_Oint)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
( ~ v_P(X1)
| ~ c_in(X2,c_insert(X1,c_emptyset,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,negated_conjecture,
v_P(v_a),
cls_conjecture_0 ).
cnf(c_0_16,negated_conjecture,
~ v_P(X1),
inference(spm,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_15,c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET820-2 : 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
% 0.16/0.33 % Computer : n010.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 : Tue May 5 02:36:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.368s
%------------------------------------------------------------------------------