%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV242-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 03:12:34 PM UTC 2026
% Result : Unsatisfiable 7.19s 1.43s
% Output : Proof 7.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 37 unt; 0 def)
% Number of atoms : 65 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 74 ( 14 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,negated_conjecture,
( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2_nnf,plain,
( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t22,plain,
ifeq(c_lessequals(v_H,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),true,ifeq(c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f3,axiom,
( c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
fof(f3_nnf,plain,
! [V_G,V_H] :
( c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_G,V_H] :
( c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(V_G,V_H,tc_set(tc_Message_Omsg)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(c_Message_Oanalz(X0),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X0,X1,tc_set(tc_Message_Omsg)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(c_lessequals(X0,X1,tc_set(tc_Message_Omsg)),true,c_lessequals(c_Message_Oanalz(X0),c_Message_Oanalz(X1),tc_set(tc_Message_Omsg)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f5,axiom,
c_lessequals(V_B,c_union(V_A,V_B,T_a),tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__upper2_0) ).
fof(f5_nnf,plain,
! [V_B,V_A,T_a] : c_lessequals(V_B,c_union(V_A,V_B,T_a),tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_B,V_A,T_a] : c_lessequals(V_B,c_union(V_A,V_B,T_a),tc_set(T_a)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
c_lessequals(X0,c_union(X1,X0,X2),tc_set(X2)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h7,plain,
c_lessequals(c_Message_Oanalz(V0),c_Message_Oanalz(c_union(V1,V0,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi4]) ).
cnf(f6,axiom,
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
fof(f6_nnf,plain,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_B,V_C,T_a,V_A] :
( c_lessequals(V_A,V_C,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_C,tc_set(T_a)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(c_lessequals(X0,X1,tc_set(X2)),true,ifeq(c_lessequals(X3,X0,tc_set(X2)),true,c_lessequals(X3,X1,tc_set(X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f1,negated_conjecture,
c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,negated_conjecture,
c_lessequals(v_H,c_Message_Oanalz(v_H_H),tc_set(tc_Message_Omsg)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t12,plain,
c_lessequals(v_H,c_Message_Oanalz(c_union(X1,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h7,hi1]) ).
cnf(t32,plain,
c_lessequals(v_H,c_Message_Oanalz(c_union(X1,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t111,plain,
ifeq(true,true,ifeq(c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),true,false,true),true) = true,
inference(step,[status(thm)],[t22,t32]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t112,plain,
ifeq(c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,v_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),true,false,true) = true,
inference(step,[status(thm)],[t111,t23]) ).
cnf(f4,axiom,
c_lessequals(V_A,c_union(V_A,V_B,T_a),tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__upper1_0) ).
fof(f4_nnf,plain,
! [V_A,V_B,T_a] : c_lessequals(V_A,c_union(V_A,V_B,T_a),tc_set(T_a)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_A,V_B,T_a] : c_lessequals(V_A,c_union(V_A,V_B,T_a),tc_set(T_a)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
c_lessequals(X0,c_union(X0,X1,X2),tc_set(X2)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h4,plain,
c_lessequals(c_Message_Oanalz(V0),c_Message_Oanalz(c_union(V0,V1,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi3]) ).
cnf(f0,negated_conjecture,
c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,negated_conjecture,
c_lessequals(v_G,c_Message_Oanalz(v_G_H),tc_set(tc_Message_Omsg)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t9,plain,
c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h4,hi0]) ).
cnf(t38,plain,
c_lessequals(v_G,c_Message_Oanalz(c_union(v_G_H,X1,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t113,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t112,t38]) ).
cnf(t114,plain,
false = true,
inference(step,[status(thm)],[t113,t23]) ).
cnf(t110,plain,
false = true,
inference(orient,[status(thm)],[t114]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t110]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV242-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 18:45:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.19/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.19/1.43 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------