%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV281-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:12:44 PM UTC 2026
% Result : Unsatisfiable 4.23s 1.01s
% Output : Proof 4.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 78 unt; 0 def)
% Number of atoms : 106 ( 85 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 19 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-4 aty)
% Number of variables : 131 ( 27 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( V_m = V_n
| c_plus(V_m,V_k,tc_nat) != c_plus(V_n,V_k,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f3_nnf,plain,
! [V_m,V_k,V_n] :
( V_m = V_n
| c_plus(V_m,V_k,tc_nat) != c_plus(V_n,V_k,tc_nat) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_m,V_k,V_n] :
( V_m = V_n
| c_plus(V_m,V_k,tc_nat) != c_plus(V_n,V_k,tc_nat) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X0 = X2
| c_plus(X0,X1,tc_nat) != c_plus(X2,X1,tc_nat) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t14,plain,
ifeq(c_plus(X1,X2,tc_nat),c_plus(X3,X2,tc_nat),X1,X3) = X3,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t22,plain,
ifeq(c_plus(X1,X2,tc_nat),c_plus(X3,X2,tc_nat),X1,X3) = X3,
inference(orient,[status(thm)],[t14]) ).
cnf(f4,axiom,
c_plus(c_0,V_y,tc_nat) = V_y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f4_nnf,plain,
! [V_y] : c_plus(c_0,V_y,tc_nat) = V_y,
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_y] : c_plus(c_0,V_y,tc_nat) = V_y,
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
c_plus(c_0,X0,tc_nat) = X0,
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t7,plain,
c_plus(c_0,X1,tc_nat) = X1,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t23,plain,
c_plus(c_0,X1,tc_nat) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t25,plain,
c_0 = ifeq(c_plus(X1,X2,tc_nat),X2,X1,c_0),
inference(cp,[status(thm)],[t22,t23]) ).
cnf(t49,plain,
ifeq(c_plus(X1,X2,tc_nat),X2,X1,c_0) = c_0,
inference(orient,[status(thm)],[t25]) ).
cnf(t12,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t21,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(f0,negated_conjecture,
( c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| V_U = V_V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
! [V_U,V_V] :
( c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| V_U = V_V ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_U,V_V] :
( c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(V_V),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| V_U = V_V ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(v_evs),tc_Message_Omsg)
| c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t16,plain,
or(eq(X1,X2),or(c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg),c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg))) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t29,plain,
or(eq(X1,X2),or(c_in(c_Message_Omsg_ONonce(X2),c_Event_Oused(v_evs_H),tc_Message_Omsg),c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg))) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t10,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t38,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t10]) ).
cnf(f5,axiom,
( ~ c_lessequals(v_sko__urX(V_evs),V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(V_evs),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).
fof(f5_nnf,plain,
! [V_U,V_evs] :
( ~ c_lessequals(v_sko__urX(V_evs),V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(V_evs),tc_Message_Omsg) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_U,V_evs] :
( ~ c_lessequals(v_sko__urX(V_evs),V_U,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(V_U),c_Event_Oused(V_evs),tc_Message_Omsg) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ c_lessequals(v_sko__urX(X1),X0,tc_nat)
| ~ c_in(c_Message_Omsg_ONonce(X0),c_Event_Oused(X1),tc_Message_Omsg) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t15,plain,
or(not(c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(X2),tc_Message_Omsg)),not(c_lessequals(v_sko__urX(X2),X1,tc_nat))) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t28,plain,
or(not(c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(X2),tc_Message_Omsg)),not(c_lessequals(v_sko__urX(X2),X1,tc_nat))) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(f2,axiom,
c_lessequals(V_n,c_plus(V_m,V_n,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add2_0) ).
fof(f2_nnf,plain,
! [V_n,V_m] : c_lessequals(V_n,c_plus(V_m,V_n,tc_nat),tc_nat),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_n,V_m] : c_lessequals(V_n,c_plus(V_m,V_n,tc_nat),tc_nat),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_lessequals(X0,c_plus(X1,X0,tc_nat),tc_nat),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t11,plain,
c_lessequals(X1,c_plus(X2,X1,tc_nat),tc_nat) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t34,plain,
c_lessequals(X1,c_plus(X2,X1,tc_nat),tc_nat) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t35,plain,
true = c_lessequals(X1,X1,tc_nat),
inference(cp,[status(thm)],[t34,t23]) ).
cnf(t44,plain,
c_lessequals(X1,X1,tc_nat) = true,
inference(orient,[status(thm)],[t35]) ).
cnf(t45,plain,
true = or(not(c_in(c_Message_Omsg_ONonce(v_sko__urX(X1)),c_Event_Oused(X1),tc_Message_Omsg)),not(true)),
inference(cp,[status(thm)],[t28,t44]) ).
cnf(t1,plain,
not(true) = false,
introduced(definition) ).
cnf(t39,plain,
not(true) = false,
inference(orient,[status(thm)],[t1]) ).
cnf(t119,plain,
true = or(not(c_in(c_Message_Omsg_ONonce(v_sko__urX(X1)),c_Event_Oused(X1),tc_Message_Omsg)),false),
inference(step,[status(thm)],[t45,t39]) ).
cnf(t3,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t18,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t120,plain,
true = not(c_in(c_Message_Omsg_ONonce(v_sko__urX(X1)),c_Event_Oused(X1),tc_Message_Omsg)),
inference(step,[status(thm)],[t119,t18]) ).
cnf(t50,plain,
not(c_in(c_Message_Omsg_ONonce(v_sko__urX(X1)),c_Event_Oused(X1),tc_Message_Omsg)) = true,
inference(orient,[status(thm)],[t120]) ).
cnf(t51,plain,
false = ifeq(true,true,c_in(c_Message_Omsg_ONonce(v_sko__urX(X1)),c_Event_Oused(X1),tc_Message_Omsg),false),
inference(cp,[status(thm)],[t38,t50]) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t20,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t8]) ).
cnf(t121,plain,
false = c_in(c_Message_Omsg_ONonce(v_sko__urX(X1)),c_Event_Oused(X1),tc_Message_Omsg),
inference(step,[status(thm)],[t51,t20]) ).
cnf(t52,plain,
c_in(c_Message_Omsg_ONonce(v_sko__urX(X1)),c_Event_Oused(X1),tc_Message_Omsg) = false,
inference(orient,[status(thm)],[t121]) ).
cnf(t55,plain,
true = or(eq(v_sko__urX(v_evs),X1),or(c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg),false)),
inference(cp,[status(thm)],[t29,t52]) ).
cnf(t54,plain,
true = or(eq(X1,v_sko__urX(v_evs_H)),or(false,c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg))),
inference(cp,[status(thm)],[t29,t52]) ).
cnf(t5,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t19,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t124,plain,
true = or(eq(X1,v_sko__urX(v_evs_H)),c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg)),
inference(step,[status(thm)],[t54,t19]) ).
cnf(t58,plain,
or(eq(X1,v_sko__urX(v_evs_H)),c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs),tc_Message_Omsg)) = true,
inference(orient,[status(thm)],[t124]) ).
cnf(t59,plain,
true = or(eq(v_sko__urX(v_evs),v_sko__urX(v_evs_H)),false),
inference(cp,[status(thm)],[t58,t52]) ).
cnf(t125,plain,
true = eq(v_sko__urX(v_evs),v_sko__urX(v_evs_H)),
inference(step,[status(thm)],[t59,t18]) ).
cnf(t60,plain,
eq(v_sko__urX(v_evs),v_sko__urX(v_evs_H)) = true,
inference(orient,[status(thm)],[t125]) ).
cnf(t61,plain,
v_sko__urX(v_evs_H) = ifeq(true,true,v_sko__urX(v_evs),v_sko__urX(v_evs_H)),
inference(cp,[status(thm)],[t21,t60]) ).
cnf(t126,plain,
v_sko__urX(v_evs_H) = v_sko__urX(v_evs),
inference(step,[status(thm)],[t61,t20]) ).
cnf(t62,plain,
v_sko__urX(v_evs) = v_sko__urX(v_evs_H),
inference(orient,[status(thm)],[t126]) ).
cnf(t127,plain,
true = or(eq(v_sko__urX(v_evs_H),X1),or(c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg),false)),
inference(step,[status(thm)],[t55,t62]) ).
cnf(t128,plain,
true = or(eq(v_sko__urX(v_evs_H),X1),c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg)),
inference(step,[status(thm)],[t127,t18]) ).
cnf(t68,plain,
or(eq(v_sko__urX(v_evs_H),X1),c_in(c_Message_Omsg_ONonce(X1),c_Event_Oused(v_evs_H),tc_Message_Omsg)) = true,
inference(orient,[status(thm)],[t128]) ).
cnf(t36,plain,
true = or(not(c_in(c_Message_Omsg_ONonce(c_plus(X1,v_sko__urX(X2),tc_nat)),c_Event_Oused(X2),tc_Message_Omsg)),not(true)),
inference(cp,[status(thm)],[t28,t34]) ).
cnf(t129,plain,
true = or(not(c_in(c_Message_Omsg_ONonce(c_plus(X1,v_sko__urX(X2),tc_nat)),c_Event_Oused(X2),tc_Message_Omsg)),false),
inference(step,[status(thm)],[t36,t39]) ).
cnf(t130,plain,
true = not(c_in(c_Message_Omsg_ONonce(c_plus(X1,v_sko__urX(X2),tc_nat)),c_Event_Oused(X2),tc_Message_Omsg)),
inference(step,[status(thm)],[t129,t18]) ).
cnf(t69,plain,
not(c_in(c_Message_Omsg_ONonce(c_plus(X1,v_sko__urX(X2),tc_nat)),c_Event_Oused(X2),tc_Message_Omsg)) = true,
inference(orient,[status(thm)],[t130]) ).
cnf(t71,plain,
false = ifeq(true,true,c_in(c_Message_Omsg_ONonce(c_plus(X1,v_sko__urX(X2),tc_nat)),c_Event_Oused(X2),tc_Message_Omsg),false),
inference(cp,[status(thm)],[t38,t69]) ).
cnf(t131,plain,
false = c_in(c_Message_Omsg_ONonce(c_plus(X1,v_sko__urX(X2),tc_nat)),c_Event_Oused(X2),tc_Message_Omsg),
inference(step,[status(thm)],[t71,t20]) ).
cnf(t72,plain,
c_in(c_Message_Omsg_ONonce(c_plus(X1,v_sko__urX(X2),tc_nat)),c_Event_Oused(X2),tc_Message_Omsg) = false,
inference(orient,[status(thm)],[t131]) ).
cnf(t74,plain,
true = or(eq(v_sko__urX(v_evs_H),c_plus(X1,v_sko__urX(v_evs_H),tc_nat)),false),
inference(cp,[status(thm)],[t68,t72]) ).
cnf(t132,plain,
true = eq(v_sko__urX(v_evs_H),c_plus(X1,v_sko__urX(v_evs_H),tc_nat)),
inference(step,[status(thm)],[t74,t18]) ).
cnf(t78,plain,
eq(v_sko__urX(v_evs_H),c_plus(X1,v_sko__urX(v_evs_H),tc_nat)) = true,
inference(orient,[status(thm)],[t132]) ).
cnf(t79,plain,
c_plus(X1,v_sko__urX(v_evs_H),tc_nat) = ifeq(true,true,v_sko__urX(v_evs_H),c_plus(X1,v_sko__urX(v_evs_H),tc_nat)),
inference(cp,[status(thm)],[t21,t78]) ).
cnf(t133,plain,
c_plus(X1,v_sko__urX(v_evs_H),tc_nat) = v_sko__urX(v_evs_H),
inference(step,[status(thm)],[t79,t20]) ).
cnf(t80,plain,
c_plus(X1,v_sko__urX(v_evs_H),tc_nat) = v_sko__urX(v_evs_H),
inference(orient,[status(thm)],[t133]) ).
cnf(t81,plain,
c_0 = ifeq(v_sko__urX(v_evs_H),v_sko__urX(v_evs_H),X1,c_0),
inference(cp,[status(thm)],[t49,t80]) ).
cnf(t134,plain,
c_0 = X1,
inference(step,[status(thm)],[t81,t20]) ).
cnf(t85,plain,
c_0 = X1,
inference(orient,[status(thm)],[t134]) ).
cnf(f1,axiom,
c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
fof(f1_nnf,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_a_H,V_list_H,T_a] : c_List_Olist_ONil != c_List_Olist_OCons(V_a_H,V_list_H,T_a),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
c_List_Olist_ONil != c_List_Olist_OCons(X0,X1,X2),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c1,c5]) ).
cnf(g0_0,plain,
c_0 != false,
inference(rw,[status(thm)],[goal_0,t85]) ).
cnf(g0_1,plain,
c_0 != c_0,
inference(rw,[status(thm)],[g0_0,t85]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV281-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 19:03:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.23/1.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.23/1.01 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------