%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 : Sun Sep 27 06:56:30 AM UTC 2026
% Result : Unsatisfiable 10.41s 3.03s
% Output : Refutation 10.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 117 ( 48 unt; 0 typ; 2 def)
% Number of atoms : 304 ( 179 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2128 ( 161 ~; 131 |; 0 &;1836 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 201 ( 0 ^; 197 !; 2 ?; 201 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Comb_Ocomb_Oop_A_D_D_decl,type,
c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).
thf(c_Comb_Ocomb_OK_decl,type,
c_Comb_Ocomb_OK: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_ya_decl,type,
v_ya: $i ).
thf(v_xb_decl,type,
v_xb: $i ).
thf(tc_Comb_Ocomb_decl,type,
tc_Comb_Ocomb: $i ).
thf(c_Comb_Oparcontract_decl,type,
c_Comb_Oparcontract: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Comb_Ocomb_OS_decl,type,
c_Comb_Ocomb_OS: $i ).
thf(v_sko__uTF_decl,type,
v_sko__uTF: $i > $i > $i > $i ).
thf(v_sko__uTG_decl,type,
v_sko__uTG: $i > $i > $i > $i ).
thf(v_sko__uTI_decl,type,
v_sko__uTI: $i > $i > $i > $i ).
thf(v_sko__uTH_decl,type,
v_sko__uTH: $i > $i > $i > $i ).
thf(v_sko__uTE_decl,type,
v_sko__uTE: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) @ ( B @ A ) )
= C ) ) ) ).
thf(1,negated_conjecture,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(13,plain,
tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(10,axiom,
! [A: $i] : ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__1_0) ).
thf(40,plain,
! [A: $i] : ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(14,plain,
! [A: $i] :
( ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [A: $i] :
( ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,15]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( v_xb )),bind(B,$thf( v_xb ))]]) ).
thf(63,plain,
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,51]) ).
thf(64,plain,
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(67,plain,
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(69,plain,
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,15]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(54,plain,
~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( v_x )),bind(B,$thf( v_x ))]]) ).
thf(72,plain,
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,54]) ).
thf(73,plain,
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(76,plain,
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(78,plain,
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_0) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( B @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
= B ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ( ( C @ ( B @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[40,37]) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) )
| ( ( C @ ( B @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
= C ) ),
inference(simp,[status(thm)],[930]) ).
thf(932,plain,
! [A: $i] :
( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
= ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) ),
inference(pattern_uni,[status(thm)],[931:[bind(A,$thf( G @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )),bind(B,$thf( G )),bind(C,$thf( G @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ))]]) ).
thf(1064,plain,
! [A: $i] :
( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
= ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) ),
inference(simp,[status(thm)],[932]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_1) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(33,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ sk2 ) )
= B ),
inference(cnf,[status(esa)],[33]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ sk2 ) )
= B ),
inference(lifteq,[status(thm)],[34]) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( B @ sk2 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[1064,71]) ).
thf(1183,plain,
! [A: $i] :
( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( c_Comb_Ocomb_OK @ sk2 ) )
= ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ v_sko__uTE ) ) ),
inference(pattern_uni,[status(thm)],[1182:[bind(A,$thf( G )),bind(B,$thf( c_Comb_Ocomb_OK )),bind(C,$thf( G @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( G @ v_sko__uTE ) ))]]) ).
thf(1270,plain,
! [A: $i] :
( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( c_Comb_Ocomb_OK @ sk2 ) )
= ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ v_sko__uTE ) ) ),
inference(simp,[status(thm)],[1183]) ).
thf(1423,plain,
! [A: $i] :
( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ v_sko__uTE ) )
= A ),
inference(rewrite,[status(thm)],[1270,71]) ).
thf(55,plain,
! [A: $i] :
( ~ $true
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[15]) ).
thf(59,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[55]) ).
thf(62,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(893,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_xb @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,62]) ).
thf(894,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_xb @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( v_x @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[893]) ).
thf(895,plain,
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_x @ c_Pair ) ) ) ) ),
inference(pattern_uni,[status(thm)],[894:[bind(A,$thf( v_x )),bind(B,$thf( v_x ))]]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ v_sko__uTH ) ) @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_0) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ v_sko__uTH ) ) @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( A @ v_sko__uTH ) ) @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ v_sko__uTH ) ) @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= C )
| ( ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= A )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( D @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__4_0) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( D @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( c_Comb_Ocomb_OK
!= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Odistinct__3__iff1_0) ).
thf(22,plain,
! [B: $i,A: $i] :
( c_Comb_Ocomb_OK
!= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,plain,
! [B: $i,A: $i] :
( c_Comb_Ocomb_OK
!= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= c_Comb_Ocomb_OK ),
inference(lifteq,[status(thm)],[23]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Ocomb_Oinject__iff1_0) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [B: $i,A: $i] : ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_Oparcontract_Ointros__2_0) ).
thf(41,plain,
! [B: $i,A: $i] : ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,54]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( A != v_x )
| ( ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
!= v_xb ) ),
inference(simp,[status(thm)],[246]) ).
thf(452,plain,
! [A: $i] :
( ( A @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
!= v_xb ),
inference(simp,[status(thm)],[409]) ).
thf(45,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,15]) ).
thf(46,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(56,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(60,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_xb @ c_Pair ) ) ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(933,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( B != c_Comb_Ocomb_OK )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,24]) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( B != c_Comb_Ocomb_OK )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( c_Comb_Ocomb_OK )),bind(D,$thf( F @ ( E @ v_sko__uTE ) ))]]) ).
thf(1065,plain,
! [A: $i] :
~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( c_Comb_Ocomb_OK @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ),
inference(simp,[status(thm)],[934]) ).
thf(1109,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( c_Comb_Ocomb_OK @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,1065]) ).
thf(1110,plain,
! [A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( c_Comb_Ocomb_OK @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[1109]) ).
thf(1120,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( c_Comb_Ocomb_OK @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[1110]) ).
thf(1123,plain,
! [A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( c_Comb_Ocomb_OK @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[1120]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ v_sko__uTE ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OK1__parcontractD__dest_1) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ v_sko__uTE ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(65,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,51]) ).
thf(66,plain,
! [A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(68,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(70,plain,
! [A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comb_OAp__parcontractE_2) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= A )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( D @ ( C @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(28,plain,
? [A: $i > $i > $i] :
! [B: $i,C: $i] :
( ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ ( B @ sk1 ) )
= A ),
inference(cnf,[status(esa)],[28]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ ( B @ sk1 ) )
= A ),
inference(lifteq,[status(thm)],[29]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true
| ( ( C @ ( B @ ( A @ v_sko__uTH ) ) @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= C )
| ( ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= A )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,18]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( C @ ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) )
| ( ( C @ ( B @ ( A @ v_sko__uTH ) ) @ ( C @ ( B @ ( A @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= C )
| ( ( C @ ( B @ ( A @ v_sko__uTG ) ) @ ( C @ ( B @ ( A @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= A )
| ( A
= ( C @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( C
= ( B @ ( A @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
( ( ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTH ) ) @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= v_xb )
| ( ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTG ) ) @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( ( v_xb @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
= ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= v_xb ) ),
inference(pattern_uni,[status(thm)],[91:[bind(A,$thf( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )),bind(B,$thf( v_ya )),bind(C,$thf( v_xb ))]]) ).
thf(572,plain,
( ( ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTH ) ) @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTI ) ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= v_xb )
| ( ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTG ) ) @ ( v_xb @ ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ v_sko__uTF ) ) @ ( c_Comb_Ocomb_OS @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
= ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( ( v_xb @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
= ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) ) ) ),
inference(simplifyReflect,[status(thm)],[92,452]) ).
thf(150,plain,
( ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( v_xb != v_xb )
| ( ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
!= v_x ) ),
inference(simp,[status(thm)],[69]) ).
thf(172,plain,
( ( v_ya @ ( v_x @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
!= v_x ),
inference(simp,[status(thm)],[150]) ).
thf(80,plain,
! [A: $i] :
( ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( A != v_xb )
| ( A != v_x ) ),
inference(simp,[status(thm)],[70]) ).
thf(81,plain,
v_xb != v_x,
inference(simp,[status(thm)],[80]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ v_sko__uTE ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( A @ v_sko__uTE ) @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
!= ( C @ ( B @ c_Comb_Ocomb_Oop_A_D_D ) ) )
| ( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
!= c_Comb_Ocomb_OK ) ),
inference(paramod_ordered,[status(thm)],[1064,24]) ).
thf(1152,plain,
! [A: $i] :
( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
!= c_Comb_Ocomb_OK ),
inference(pattern_uni,[status(thm)],[1151:[bind(A,$thf( G )),bind(B,$thf( c_Comb_Ocomb_OK )),bind(C,$thf( G @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ ( G @ v_sko__uTE ) ))]]) ).
thf(1262,plain,
! [A: $i] :
( ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) )
!= c_Comb_Ocomb_OK ),
inference(simp,[status(thm)],[1152]) ).
thf(223,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,51]) ).
thf(224,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[223]) ).
thf(234,plain,
! [B: $i,A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_xb @ ( v_x @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( tc_Comb_Ocomb != tc_Comb_Ocomb )
| ( A != v_xb )
| ( ( B @ ( A @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
!= v_x ) ),
inference(simp,[status(thm)],[242]) ).
thf(272,plain,
! [A: $i] :
( ( A @ ( v_xb @ ( c_Comb_Ocomb_OK @ c_Comb_Ocomb_Oop_A_D_D ) @ c_Comb_Ocomb_Oop_A_D_D ) )
!= v_x ),
inference(simp,[status(thm)],[247]) ).
thf(74,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,54]) ).
thf(75,plain,
! [A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) @ ( c_Comb_Oparcontract @ ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(77,plain,
! [A: $i] :
( ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ tc_prod ) ) )
| ( c_Comb_Oparcontract != c_Comb_Oparcontract )
| ( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(79,plain,
! [A: $i] :
( ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( A @ ( A @ c_Pair ) ) ) )
!= ( tc_Comb_Ocomb @ ( tc_Comb_Ocomb @ ( v_x @ ( v_xb @ c_Pair ) ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(1859,plain,
$false,
inference(e,[status(thm)],[69,14,78,1423,32,895,35,18,40,42,24,37,25,452,60,1123,38,70,21,13,41,22,44,27,71,54,572,172,81,39,16,1262,246,272,30,51,19,242,79,1065,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL106-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.06/0.32 % Computer : n012.cluster.edu
% 0.06/0.32 % Model : x86_64 x86_64
% 0.06/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.32 % Memory : 8046.5625MB
% 0.06/0.32 % OS : Linux 6.8.0-71-generic
% 0.06/0.32 % CPULimit : 300
% 0.06/0.32 % WCLimit : 300
% 0.06/0.33 % DateTime : Sat Sep 26 23:15:34 UTC 2026
% 0.06/0.33 % CPUTime :
% 0.06/0.33 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.52/0.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.65/0.74 % [INFO] Parsing done (103ms).
% 0.65/0.75 % [INFO] Running in sequential loop mode.
% 1.04/0.95 % [INFO] eprover registered as external prover.
% 1.04/0.96 % [INFO] Scanning for conjecture ...
% 1.29/1.02 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.29/1.04 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.29/1.05 % [INFO] Problem is propositional (TPTP CNF).
% 1.29/1.06 % [INFO] Type checking passed.
% 1.29/1.06 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 10.41/3.03 % External prover 'e' found a proof!
% 10.41/3.03 % [INFO] Killing All external provers ...
% 10.41/3.03 % Time passed: 2627ms (effective reasoning time: 2282ms)
% 10.41/3.03 % Axioms used in derivation (10): cls_Comb_Oparcontract_Ointros__4_0, cls_Comb_OAp__parcontractE_0, cls_Comb_Ocomb_Oinject__iff1_0, cls_Comb_OK1__parcontractD__dest_1, cls_Comb_Oparcontract_Ointros__1_0, cls_Comb_Ocomb_Odistinct__3__iff1_0, cls_Comb_Oparcontract_Ointros__2_0, cls_Comb_OK1__parcontractD__dest_0, cls_Comb_OAp__parcontractE_2, cls_Comb_Ocomb_Oinject__iff1_1
% 10.41/3.03 % No. of inferences in proof: 115
% 10.41/3.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2627 ms resp. 2282 ms w/o parsing
% 10.41/3.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.41/3.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------