%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV276-2 : 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 : n012.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 05:21:24 PM UTC 2026
% Result : Unsatisfiable 1.16s 1.62s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of clauses : 61 ( 25 unt; 14 nHn; 38 RR)
% Number of literals : 111 ( 14 equ; 42 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 105 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_Message_OkeysFor__mono_0,axiom,
( c_lessequals(c_Message_OkeysFor(X1),c_Message_OkeysFor(X2),tc_set(tc_nat))
| ~ c_lessequals(X1,X2,tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__mono_0) ).
cnf(cls_Message_Oparts__insert__subset__Un_0,axiom,
( c_lessequals(c_Message_Oparts(c_insert(X1,X3,tc_Message_Omsg)),c_union(c_Message_Oparts(X2),c_Message_Oparts(X3),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X1,X2,tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__subset__Un_0) ).
cnf(cls_Message_Oparts__Un_0,axiom,
c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
cnf(cls_Set_OUn__iff_1,axiom,
( c_in(X1,c_union(X2,X4,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
cnf(cls_Message_OkeysFor__Un_0,axiom,
c_Message_OkeysFor(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X1),c_Message_OkeysFor(X2),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
cnf(cls_Set_OUn__iff_0,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg))),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg))),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Set_OUn__iff_2,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
cnf(cls_Message_Oparts__synth_0,axiom,
c_Message_Oparts(c_Message_Osynth(X1)) = c_union(c_Message_Oparts(X1),c_Message_Osynth(X1),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Message_Oparts__analz_0,axiom,
c_Message_Oparts(c_Message_Oanalz(X1)) = c_Message_Oparts(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
cnf(cls_Event_OkeysFor__synth_H_1,axiom,
( c_in(X1,c_Message_OkeysFor(X2),tc_nat)
| X1 = c_Message_OinvKey(v_sko__uhi(X2,X1))
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
cnf(cls_Event_OkeysFor__synth_H_0,axiom,
( c_in(X1,c_Message_OkeysFor(X2),tc_nat)
| c_in(c_Message_Omsg_OKey(v_sko__uhi(X2,X1)),X2,tc_Message_Omsg)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
cnf(cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0,axiom,
c_Message_OinvKey(c_Message_OinvKey(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
cnf(cls_Message_Oanalz__subset__parts_0,axiom,
c_lessequals(c_Message_Oanalz(X1),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__parts_0) ).
cnf(cls_Message_Oanalz__conj__parts_0,axiom,
( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
| ~ c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oparts(v_H),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(c_0_19,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0 ).
cnf(c_0_20,axiom,
( c_lessequals(c_Message_OkeysFor(X1),c_Message_OkeysFor(X2),tc_set(tc_nat))
| ~ c_lessequals(X1,X2,tc_set(tc_Message_Omsg)) ),
cls_Message_OkeysFor__mono_0 ).
cnf(c_0_21,axiom,
( c_lessequals(c_Message_Oparts(c_insert(X1,X3,tc_Message_Omsg)),c_union(c_Message_Oparts(X2),c_Message_Oparts(X3),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ c_in(X1,X2,tc_Message_Omsg) ),
cls_Message_Oparts__insert__subset__Un_0 ).
cnf(c_0_22,axiom,
c_Message_Oparts(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_Oparts(X1),c_Message_Oparts(X2),tc_Message_Omsg),
cls_Message_Oparts__Un_0 ).
cnf(c_0_23,axiom,
( c_in(X1,c_union(X2,X4,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OUn__iff_1 ).
cnf(c_0_24,axiom,
c_Message_OkeysFor(c_union(X1,X2,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X1),c_Message_OkeysFor(X2),tc_nat),
cls_Message_OkeysFor__Un_0 ).
cnf(c_0_25,axiom,
( c_in(X1,X3,X4)
| c_in(X1,X2,X4)
| ~ c_in(X1,c_union(X2,X3,X4),X4) ),
cls_Set_OUn__iff_0 ).
cnf(c_0_26,plain,
( c_in(X1,c_Message_OkeysFor(X2),tc_nat)
| ~ c_lessequals(X3,X2,tc_set(tc_Message_Omsg))
| ~ c_in(X1,c_Message_OkeysFor(X3),tc_nat) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( c_lessequals(c_Message_Oparts(c_insert(X1,X2,tc_Message_Omsg)),c_Message_Oparts(c_union(X3,X2,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_in(X1,X3,tc_Message_Omsg) ),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
( c_in(X1,c_Message_OkeysFor(c_union(X2,X3,tc_Message_Omsg)),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(X2),tc_nat) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( c_in(X1,c_Message_OkeysFor(X2),tc_nat)
| c_in(X1,c_Message_OkeysFor(X3),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(c_union(X2,X3,tc_Message_Omsg)),tc_nat) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,plain,
( c_in(X1,c_Message_OkeysFor(c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg))),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Oparts(c_insert(X4,X3,tc_Message_Omsg))),tc_nat)
| ~ c_in(X4,X2,tc_Message_Omsg) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_insert(v_X,v_G,tc_Message_Omsg))),tc_nat),
cls_conjecture_0 ).
cnf(c_0_32,negated_conjecture,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(v_G,v_H,tc_Message_Omsg))),tc_nat),
cls_conjecture_2 ).
cnf(c_0_33,plain,
( c_in(X1,c_Message_OkeysFor(c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg))),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Oparts(X2)),tc_nat) ),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_34,axiom,
( c_in(X1,c_union(X4,X2,X3),X3)
| ~ c_in(X1,X2,X3) ),
cls_Set_OUn__iff_2 ).
cnf(c_0_35,axiom,
c_Message_Oparts(c_Message_Osynth(X1)) = c_union(c_Message_Oparts(X1),c_Message_Osynth(X1),tc_Message_Omsg),
cls_Message_Oparts__synth_0 ).
cnf(c_0_36,plain,
( c_in(X1,c_Message_OkeysFor(c_Message_Oparts(X2)),tc_nat)
| c_in(X1,c_Message_OkeysFor(c_Message_Oparts(X3)),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Oparts(c_union(X3,X2,tc_Message_Omsg))),tc_nat) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_37,negated_conjecture,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_union(X1,v_G,tc_Message_Omsg))),tc_nat)
| ~ c_in(v_X,X1,tc_Message_Omsg) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_G)),tc_nat),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( c_in(X1,c_Message_OkeysFor(c_union(X2,X3,tc_Message_Omsg)),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(X3),tc_nat) ),
inference(spm,[status(thm)],[c_0_34,c_0_24]) ).
cnf(c_0_40,plain,
( c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat)
| c_in(X1,c_Message_OkeysFor(c_Message_Oparts(X2)),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Oparts(c_Message_Osynth(X2))),tc_nat) ),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(X1)),tc_nat)
| ~ c_in(v_X,X1,tc_Message_Omsg) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_42,plain,
( c_in(X1,c_Message_OkeysFor(c_Message_Oparts(c_union(X2,X3,tc_Message_Omsg))),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Oparts(X3)),tc_nat) ),
inference(spm,[status(thm)],[c_0_39,c_0_22]) ).
cnf(c_0_43,negated_conjecture,
( c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(X1)),tc_nat)
| c_in(v_K,c_Message_OkeysFor(c_Message_Osynth(X1)),tc_nat)
| ~ c_in(v_X,c_Message_Osynth(X1),tc_Message_Omsg) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
c_in(v_X,c_Message_Osynth(c_Message_Oanalz(v_H)),tc_Message_Omsg),
cls_conjecture_1 ).
cnf(c_0_45,axiom,
c_Message_Oparts(c_Message_Oanalz(X1)) = c_Message_Oparts(X1),
cls_Message_Oparts__analz_0 ).
cnf(c_0_46,negated_conjecture,
~ c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(v_H)),tc_nat),
inference(spm,[status(thm)],[c_0_32,c_0_42]) ).
cnf(c_0_47,axiom,
( c_in(X1,c_Message_OkeysFor(X2),tc_nat)
| X1 = c_Message_OinvKey(v_sko__uhi(X2,X1))
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
cls_Event_OkeysFor__synth_H_1 ).
cnf(c_0_48,negated_conjecture,
c_in(v_K,c_Message_OkeysFor(c_Message_Osynth(c_Message_Oanalz(v_H))),tc_nat),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_49,axiom,
( c_in(X1,c_Message_OkeysFor(X2),tc_nat)
| c_in(c_Message_Omsg_OKey(v_sko__uhi(X2,X1)),X2,tc_Message_Omsg)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Osynth(X2)),tc_nat) ),
cls_Event_OkeysFor__synth_H_0 ).
cnf(c_0_50,axiom,
c_Message_OinvKey(c_Message_OinvKey(X1)) = X1,
cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0 ).
cnf(c_0_51,negated_conjecture,
( c_Message_OinvKey(v_sko__uhi(c_Message_Oanalz(v_H),v_K)) = v_K
| c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( c_in(c_Message_Omsg_OKey(v_sko__uhi(c_Message_Oanalz(v_H),v_K)),c_Message_Oanalz(v_H),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( v_sko__uhi(c_Message_Oanalz(v_H),v_K) = c_Message_OinvKey(v_K)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,axiom,
c_lessequals(c_Message_Oanalz(X1),c_Message_Oparts(X1),tc_set(tc_Message_Omsg)),
cls_Message_Oanalz__subset__parts_0 ).
cnf(c_0_55,axiom,
( c_in(X1,c_Message_Oparts(X2),tc_Message_Omsg)
| ~ c_in(X1,c_Message_Oanalz(X2),tc_Message_Omsg) ),
cls_Message_Oanalz__conj__parts_0 ).
cnf(c_0_56,negated_conjecture,
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oanalz(v_H),tc_Message_Omsg)
| c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(v_K)),c_Message_Oparts(v_H),tc_Message_Omsg),
cls_conjecture_3 ).
cnf(c_0_58,plain,
( c_in(X1,c_Message_OkeysFor(c_Message_Oparts(X2)),tc_nat)
| ~ c_in(X1,c_Message_OkeysFor(c_Message_Oanalz(X2)),tc_nat) ),
inference(spm,[status(thm)],[c_0_26,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
c_in(v_K,c_Message_OkeysFor(c_Message_Oanalz(v_H)),tc_nat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWV276-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue May 5 04:59:31 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.16/1.62 % Version : CSE_E---1.7
% 1.16/1.62 % Problem : theBenchmark.p
% 1.16/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 1.16/1.62 % SZS output start CNFRefutation
% See solution above
% 1.16/1.63 % Total time : 1.361s
%------------------------------------------------------------------------------