%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : COL109-2 : 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 10:11:21 AM UTC 2026
% Result : Unsatisfiable 0.27s 0.28s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 45 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 851 ( 31 ~; 31 |; 0 &; 789 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-4 aty)
% Number of variables : 73 ( 0 ^; 73 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Comb_Ocomb_OS,type,
c_Comb_Ocomb_OS: $i ).
thf(tp_c_Comb_Ocomb_Oop_A_D_D,type,
c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).
thf(tp_c_Comb_Oparcontract,type,
c_Comb_Oparcontract: $i ).
thf(tp_c_Pair,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_tc_Comb_Ocomb,type,
tc_Comb_Ocomb: $i ).
thf(tp_tc_prod,type,
tc_prod: $i > $i > $i ).
thf(tp_v_w,type,
v_w: $i ).
thf(tp_v_x_H,type,
v_x_H: $i ).
thf(tp_v_xb,type,
v_xb: $i ).
thf(tp_v_y_Ha,type,
v_y_Ha: $i ).
thf(tp_v_yb,type,
v_yb: $i ).
thf(tp_v_z,type,
v_z: $i ).
thf(1,axiom,
! [V_z: $i,V_w: $i,V_x: $i,V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_z @ V_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
thf(2,axiom,
! [V_x: $i,V_y: $i,V_z: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ V_x ) @ V_y ) @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_z ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__3_0) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ V_U @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ V_U @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(6,negated_conjecture,
c_in @ ( c_Pair @ v_yb @ v_y_Ha @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(7,negated_conjecture,
c_in @ ( c_Pair @ v_xb @ v_x_H @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,negated_conjecture,
c_in @ ( c_Pair @ v_z @ v_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(10,plain,
( ( ! [V_z: $i,V_w: $i,V_x: $i,V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_z @ V_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ V_x ) @ V_y ) @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_z ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ V_U @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ V_U @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(13,plain,
( ( c_in @ ( c_Pair @ v_yb @ v_y_Ha @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( c_in @ ( c_Pair @ v_xb @ v_x_H @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(15,plain,
( ( c_in @ ( c_Pair @ v_z @ v_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_z: $i,V_w: $i] :
( ~ ( c_in @ ( c_Pair @ V_z @ V_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(18,plain,
( ( c_in @ ( c_Pair @ v_z @ v_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(19,plain,
( ( c_in @ ( c_Pair @ v_xb @ v_x_H @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(20,plain,
( ( c_in @ ( c_Pair @ v_yb @ v_y_Ha @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(21,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ V_U @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ V_U @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(22,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ V_x ) @ V_y ) @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_z ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(23,plain,
( ( ! [V_z: $i,V_w: $i] :
( ~ ( c_in @ ( c_Pair @ V_z @ V_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_in @ ( c_Pair @ V_x @ V_y @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ V_x @ V_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ V_y @ V_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(25,plain,
! [SV1: $i] :
( ( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY8: $i,SY9: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ SV2 ) @ SY8 ) @ SY9 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ SV2 @ SY9 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SY8 @ SY9 ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY10: $i] :
( ~ ( c_in @ ( c_Pair @ SV3 @ SY10 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [SY11: $i,SY12: $i] :
( ~ ( c_in @ ( c_Pair @ SY11 @ SY12 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SY11 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SY12 @ SY10 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY13: $i] : ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ SV2 ) @ SV4 ) @ SY13 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ SV2 @ SY13 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV4 @ SY13 ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV5: $i,SV3: $i] :
( ( ~ ( c_in @ ( c_Pair @ SV3 @ SV5 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ! [SY14: $i,SY15: $i] :
( ~ ( c_in @ ( c_Pair @ SY14 @ SY15 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SY14 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SY15 @ SV5 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false )
| ( ( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(33,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ SV2 ) @ SV4 ) @ SV6 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ SV2 @ SV6 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV4 @ SV6 ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV5: $i,SV3: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV3 @ SV5 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true )
| ( ( ! [SY14: $i,SY15: $i] :
( ~ ( c_in @ ( c_Pair @ SY14 @ SY15 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SY14 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SY15 @ SV5 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(35,plain,
! [SV1: $i] :
( ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ SV1 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: $i,SV3: $i] :
( ( ( c_in @ ( c_Pair @ SV3 @ SV5 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false )
| ( ( ! [SY14: $i,SY15: $i] :
( ~ ( c_in @ ( c_Pair @ SY14 @ SY15 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SY14 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SY15 @ SV5 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV5: $i,SV3: $i,SV7: $i] :
( ( ( ! [SY16: $i] :
( ~ ( c_in @ ( c_Pair @ SV7 @ SY16 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV7 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SY16 @ SV5 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV5 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV5: $i,SV3: $i,SV8: $i,SV7: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV7 @ SV8 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV7 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV8 @ SV5 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV5 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV5: $i,SV3: $i,SV8: $i,SV7: $i] :
( ( ( ~ ( c_in @ ( c_Pair @ SV7 @ SV8 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) )
= $true )
| ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV7 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV8 @ SV5 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV5 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV5: $i,SV3: $i,SV8: $i,SV7: $i] :
( ( ( c_in @ ( c_Pair @ SV7 @ SV8 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false )
| ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ SV7 @ SV3 ) @ ( c_Comb_Ocomb_Oop_A_D_D @ SV8 @ SV5 ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $true )
| ( ( c_in @ ( c_Pair @ SV3 @ SV5 @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,40,35,33,28,20,19]) ).
thf(42,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL109-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.21 % Computer : n009.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Oct 6 18:35:17 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.28
% 0.27/0.28 No.of.Axioms: 6
% 0.27/0.28
% 0.27/0.28 Length.of.Defs: 0
% 0.27/0.28
% 0.27/0.28 Contains.Choice.Funs: false
% 0.27/0.28 .
% 0.27/0.28
% 0.27/0.28 ********************************
% 0.27/0.28 * All subproblems solved! *
% 0.27/0.28 ********************************
% 0.27/0.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.27/0.28
% 0.27/0.28 %**** Beginning of derivation protocol ****
% 0.27/0.28 % SZS output start CNFRefutation
% See solution above
% 0.27/0.28
% 0.27/0.28 %**** End of derivation protocol ****
% 0.27/0.28 %**** no. of clauses in derivation: 42 ****
% 0.27/0.28 %**** clause counter: 41 ****
% 0.27/0.28
% 0.27/0.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:6,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:41,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------