%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 02:02:00 PM UTC 2026
% Result : Unsatisfiable 5.17s 1.38s
% Output : Proof 5.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 27 unt; 0 def)
% Number of atoms : 71 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 99 ( 8 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
( c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a)
| ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Osat__imp_0) ).
fof(f3_nnf,plain,
! [V_p,V_H,T_a,V_q] :
( c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a)
| ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_p,V_H,T_a,V_q] :
( c_PropLog_Osat(V_H,c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),T_a)
| ~ c_PropLog_Osat(c_insert(V_p,V_H,tc_PropLog_Opl(T_a)),V_q,T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_PropLog_Osat(X1,c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),X2)
| ~ c_PropLog_Osat(c_insert(X0,X1,tc_PropLog_Opl(X2)),X3,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(c_PropLog_Osat(c_insert(X0,X1,tc_PropLog_Opl(X2)),X3,X2),true,c_PropLog_Osat(X1,c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),X2),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f0,negated_conjecture,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f0_nnf,plain,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
inference(nnf_transformation,[status(thm)],[f0]) ).
cnf(c0,plain,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a),
inference(cnf_transformation,[status(esa)],[f0_nnf]) ).
cnf(hi0,negated_conjecture,
c_PropLog_Osat(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),v_xa,t_a) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h1,plain,
c_PropLog_Osat(v_F,c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),t_a) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi0]) ).
cnf(f2,negated_conjecture,
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f2_nnf,plain,
! [V_U] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_U] :
( ~ c_PropLog_Osat(v_F,V_U,t_a)
| c_in(V_U,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ c_PropLog_Osat(v_F,X0,t_a)
| c_in(X0,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(c_PropLog_Osat(v_F,X0,t_a),true,c_in(X0,c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h4,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(v_F,t_a),tc_PropLog_Opl(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi1,h1]) ).
cnf(f6,axiom,
( c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
fof(f6_nnf,plain,
! [V_p,V_G,T_a,V_a] :
( c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [V_p,V_G,T_a,V_a] :
( c_in(V_p,c_PropLog_Othms(c_insert(V_a,V_G,tc_PropLog_Opl(T_a)),T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_G,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(c_insert(X3,X1,tc_PropLog_Opl(X2)),X2),tc_PropLog_Opl(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h5,plain,
c_in(c_PropLog_Opl_Oop_A_N_62(v_x,v_xa,t_a),c_PropLog_Othms(c_insert(V0,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi5,h4]) ).
cnf(f4,axiom,
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
fof(f4_nnf,plain,
! [V_p,V_H,T_a] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_p,V_H,T_a] :
( c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,V_H,tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,X1,tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(c_in(X0,X1,tc_PropLog_Opl(X2)),true,c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f7,axiom,
c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
fof(f7_nnf,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,axiom,
c_in(X0,c_insert(X0,X1,X2),X2) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h0,plain,
c_in(V0,c_PropLog_Othms(c_insert(V0,V1,tc_PropLog_Opl(V2)),V2),tc_PropLog_Opl(V2)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi6]) ).
cnf(f5,axiom,
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
fof(f5_nnf,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_p,V_H,T_a,V_q] :
( c_in(V_q,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(V_p,V_q,T_a),c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a))
| ~ c_in(V_p,c_PropLog_Othms(V_H,T_a),tc_PropLog_Opl(T_a)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2))
| ~ c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(c_in(X0,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,ifeq(c_in(c_PropLog_Opl_Oop_A_N_62(X0,X3,X2),c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true,c_in(X3,c_PropLog_Othms(X1,X2),tc_PropLog_Opl(X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t6,plain,
c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0,h5]) ).
cnf(t38,plain,
c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f1,negated_conjecture,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1_nnf,plain,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
c_in(v_xa,c_PropLog_Othms(c_insert(v_x,v_F,tc_PropLog_Opl(t_a)),t_a),tc_PropLog_Opl(t_a)) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t38]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL433-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.53 % Computer : n010.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.53 % WCLimit : 300
% 0.11/0.53 % DateTime : Wed Sep 23 23:20:27 UTC 2026
% 0.11/0.54 % CPUTime :
% 0.11/0.54 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.17/1.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.17/1.38 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------