%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL443-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Wed Oct 7 10:29:07 AM UTC 2026
% Result : Unsatisfiable 138.56s 27.95s
% Output : CNFRefutation 138.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 235 ( 63 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 849 ( 46 ~; 48 |; 0 &; 755 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 158 ( 0 ^; 158 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_PropLog_Opl_Ofalse,type,
c_PropLog_Opl_Ofalse: $i ).
thf(tp_c_PropLog_Opl_Oop_A_N_62,type,
c_PropLog_Opl_Oop_A_N_62: $i > $i > $i > $i ).
thf(tp_c_PropLog_Othms,type,
c_PropLog_Othms: $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_PropLog_Opl,type,
tc_PropLog_Opl: $i > $i ).
thf(tp_v_H,type,
v_H: $i ).
thf(tp_v_p,type,
v_p: $i ).
thf(tp_v_q,type,
v_q: $i ).
thf(1,axiom,
! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(2,axiom,
! [V_p: $i,V_G: $i,T_a: $i,V_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Oweaken__left__insert_0) ).
thf(3,axiom,
! [V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OH_0) ).
thf(4,axiom,
! [V_q: $i,V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ 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 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Odeduction_0) ).
thf(5,axiom,
! [V_p: $i,V_H: $i,T_a: $i,V_q: $i] :
( ~ ( c_in @ V_p @ ( 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_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PropLog_Othms_OMP_0) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_q @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(9,negated_conjecture,
c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_q @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(10,negated_conjecture,
c_in @ v_p @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(11,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(12,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(13,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i,V_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(14,plain,
( ( ! [V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [V_q: $i,V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(16,plain,
( ( ! [V_p: $i,V_H: $i,T_a: $i,V_q: $i] :
( ~ ( c_in @ V_p @ ( 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_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(17,plain,
( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_q @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(18,plain,
( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_q @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(19,plain,
( ( c_in @ v_p @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(21,plain,
( ( c_in @ v_p @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(22,plain,
( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ v_q @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(23,plain,
( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_q @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [V_p: $i,V_H: $i,T_a: $i,V_q: $i] :
( ~ ( c_in @ V_p @ ( 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_q @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
( ( ! [V_q: $i,V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_q @ ( c_PropLog_Othms @ ( c_insert @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) ) @ 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(26,plain,
( ( ! [V_p: $i,V_H: $i,T_a: $i] :
( ~ ( c_in @ V_p @ V_H @ ( tc_PropLog_Opl @ T_a ) )
| ( c_in @ V_p @ ( c_PropLog_Othms @ V_H @ T_a ) @ ( tc_PropLog_Opl @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [V_p: $i,V_G: $i,T_a: $i,V_a: $i] :
( ~ ( c_in @ V_p @ ( c_PropLog_Othms @ V_G @ T_a ) @ ( tc_PropLog_Opl @ T_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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(28,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( c_in @ V_x @ ( c_insert @ V_x @ V_B @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(29,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ ( c_PropLog_Opl_Oop_A_N_62 @ v_p @ v_q @ t_a ) @ c_PropLog_Opl_Ofalse @ t_a ) @ ( c_PropLog_Othms @ v_H @ t_a ) @ ( tc_PropLog_Opl @ t_a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV1: $i] :
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ~ ( c_in @ SV1 @ ( c_PropLog_Othms @ SY18 @ SY19 ) @ ( tc_PropLog_Opl @ SY19 ) )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY20 @ SY19 ) @ ( c_PropLog_Othms @ SY18 @ SY19 ) @ ( tc_PropLog_Opl @ SY19 ) )
| ( c_in @ SY20 @ ( c_PropLog_Othms @ SY18 @ SY19 ) @ ( tc_PropLog_Opl @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV2: $i] :
( ( ! [SY21: $i,SY22: $i,SY23: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_insert @ SY21 @ SY22 @ ( tc_PropLog_Opl @ SY23 ) ) @ SY23 ) @ ( tc_PropLog_Opl @ SY23 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SY21 @ SV2 @ SY23 ) @ ( c_PropLog_Othms @ SY22 @ SY23 ) @ ( tc_PropLog_Opl @ SY23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV3: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( c_in @ SV3 @ SY24 @ ( tc_PropLog_Opl @ SY25 ) )
| ( c_in @ SV3 @ ( c_PropLog_Othms @ SY24 @ SY25 ) @ ( tc_PropLog_Opl @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV4: $i] :
( ( ! [SY26: $i,SY27: $i,SY28: $i] :
( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SY26 @ SY27 ) @ ( tc_PropLog_Opl @ SY27 ) )
| ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_insert @ SY28 @ SY26 @ ( tc_PropLog_Opl @ SY27 ) ) @ SY27 ) @ ( tc_PropLog_Opl @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV5: $i] :
( ( ! [SY29: $i,SY30: $i] : ( c_in @ SV5 @ ( c_insert @ SV5 @ SY29 @ SY30 ) @ SY30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( c_in @ SV1 @ ( c_PropLog_Othms @ SV6 @ SY31 ) @ ( tc_PropLog_Opl @ SY31 ) )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY32 @ SY31 ) @ ( c_PropLog_Othms @ SV6 @ SY31 ) @ ( tc_PropLog_Opl @ SY31 ) )
| ( c_in @ SY32 @ ( c_PropLog_Othms @ SV6 @ SY31 ) @ ( tc_PropLog_Opl @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_insert @ SV7 @ SY33 @ ( tc_PropLog_Opl @ SY34 ) ) @ SY34 ) @ ( tc_PropLog_Opl @ SY34 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV7 @ SV2 @ SY34 ) @ ( c_PropLog_Othms @ SY33 @ SY34 ) @ ( tc_PropLog_Opl @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY35: $i] :
( ~ ( c_in @ SV3 @ SV8 @ ( tc_PropLog_Opl @ SY35 ) )
| ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SY35 ) @ ( tc_PropLog_Opl @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(40,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SY36 ) @ ( tc_PropLog_Opl @ SY36 ) )
| ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_insert @ SY37 @ SV9 @ ( tc_PropLog_Opl @ SY36 ) ) @ SY36 ) @ ( tc_PropLog_Opl @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY38: $i] : ( c_in @ SV5 @ ( c_insert @ SV5 @ SV10 @ SY38 ) @ SY38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ! [SY39: $i] :
( ~ ( c_in @ SV1 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SY39 @ SV11 ) @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
| ( c_in @ SY39 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ! [SY40: $i] :
( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_insert @ SV7 @ SV12 @ ( tc_PropLog_Opl @ SY40 ) ) @ SY40 ) @ ( tc_PropLog_Opl @ SY40 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV7 @ SV2 @ SY40 ) @ ( c_PropLog_Othms @ SV12 @ SY40 ) @ ( tc_PropLog_Opl @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ SV8 @ ( tc_PropLog_Opl @ SV13 ) )
| ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV14: $i,SV9: $i,SV4: $i] :
( ( ! [SY41: $i] :
( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
| ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_insert @ SY41 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( c_in @ SV5 @ ( c_insert @ SV5 @ SV10 @ SV15 ) @ SV15 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
| ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SV16 @ SV11 ) @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
| ( c_in @ SV16 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV17: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_insert @ SV7 @ SV12 @ ( tc_PropLog_Opl @ SV17 ) ) @ SV17 ) @ ( tc_PropLog_Opl @ SV17 ) )
| ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV7 @ SV2 @ SV17 ) @ ( c_PropLog_Othms @ SV12 @ SV17 ) @ ( tc_PropLog_Opl @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ SV8 @ ( tc_PropLog_Opl @ SV13 ) ) )
= $true )
| ( ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV18: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
| ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_insert @ SV18 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SV16 @ SV11 ) @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
| ( c_in @ SV16 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV17: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_insert @ SV7 @ SV12 @ ( tc_PropLog_Opl @ SV17 ) ) @ SV17 ) @ ( tc_PropLog_Opl @ SV17 ) ) )
= $true )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV7 @ SV2 @ SV17 ) @ ( c_PropLog_Othms @ SV12 @ SV17 ) @ ( tc_PropLog_Opl @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV13: $i,SV8: $i,SV3: $i] :
( ( ( c_in @ SV3 @ SV8 @ ( tc_PropLog_Opl @ SV13 ) )
= $false )
| ( ( c_in @ SV3 @ ( c_PropLog_Othms @ SV8 @ SV13 ) @ ( tc_PropLog_Opl @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV18: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) ) )
= $true )
| ( ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_insert @ SV18 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV16: $i,SV11: $i,SV6: $i,SV1: $i] :
( ( ( c_in @ SV1 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
= $false )
| ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SV16 @ SV11 ) @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
| ( c_in @ SV16 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV17: $i,SV12: $i,SV7: $i,SV2: $i] :
( ( ( c_in @ SV2 @ ( c_PropLog_Othms @ ( c_insert @ SV7 @ SV12 @ ( tc_PropLog_Opl @ SV17 ) ) @ SV17 ) @ ( tc_PropLog_Opl @ SV17 ) )
= $false )
| ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV7 @ SV2 @ SV17 ) @ ( c_PropLog_Othms @ SV12 @ SV17 ) @ ( tc_PropLog_Opl @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV18: $i,SV14: $i,SV9: $i,SV4: $i] :
( ( ( c_in @ SV4 @ ( c_PropLog_Othms @ SV9 @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
= $false )
| ( ( c_in @ SV4 @ ( c_PropLog_Othms @ ( c_insert @ SV18 @ SV9 @ ( tc_PropLog_Opl @ SV14 ) ) @ SV14 ) @ ( tc_PropLog_Opl @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV6: $i,SV11: $i,SV16: $i,SV1: $i] :
( ( ( ~ ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SV16 @ SV11 ) @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) ) )
= $true )
| ( ( c_in @ SV16 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
= $true )
| ( ( c_in @ SV1 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV6: $i,SV11: $i,SV16: $i,SV1: $i] :
( ( ( c_in @ ( c_PropLog_Opl_Oop_A_N_62 @ SV1 @ SV16 @ SV11 ) @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
= $false )
| ( ( c_in @ SV16 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
= $true )
| ( ( c_in @ SV1 @ ( c_PropLog_Othms @ SV6 @ SV11 ) @ ( tc_PropLog_Opl @ SV11 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(60,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,59,57,56,53,46,36,30,22]) ).
thf(61,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL443-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 12:21:40 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 138.56/27.95
% 138.56/27.95 No.of.Axioms: 8
% 138.56/27.95
% 138.56/27.95 Length.of.Defs: 0
% 138.56/27.95
% 138.56/27.95 Contains.Choice.Funs: false
% 138.56/27.95 .
% 138.56/27.95
% 138.56/27.95 ********************************
% 138.56/27.95 * All subproblems solved! *
% 138.56/27.95 ********************************
% 138.56/27.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
% 138.56/27.95
% 138.56/27.95 %**** Beginning of derivation protocol ****
% 138.56/27.95 % SZS output start CNFRefutation
% See solution above
% 138.56/27.95
% 138.56/27.95 %**** End of derivation protocol ****
% 138.56/27.95 %**** no. of clauses in derivation: 61 ****
% 138.56/27.95 %**** clause counter: 60 ****
% 138.56/27.95
% 138.56/27.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:60,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------