TSTP Solution File: COL109-2 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : COL109-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 10:27:57 EDT 2024
% Result : Unsatisfiable 29.55s 5.32s
% Output : Refutation 29.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 43 ( 14 unt; 13 typ; 0 def)
% Number of atoms : 64 ( 6 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 723 ( 34 ~; 22 |; 0 &; 667 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-4 aty)
% Number of variables : 45 ( 0 ^ 45 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_z_type,type,
v_z: $i ).
thf(v_w_type,type,
v_w: $i ).
thf(tc_Comb_Ocomb_type,type,
tc_Comb_Ocomb: $i ).
thf(c_Comb_Oparcontract_type,type,
c_Comb_Oparcontract: $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(v_xb_type,type,
v_xb: $i ).
thf(v_x_H_type,type,
v_x_H: $i ).
thf(v_yb_type,type,
v_yb: $i ).
thf(v_y_Ha_type,type,
v_y_Ha: $i ).
thf(c_Comb_Ocomb_Oop_A_D_D_type,type,
c_Comb_Ocomb_Oop_A_D_D: $i > $i > $i ).
thf(c_Comb_Ocomb_OS_type,type,
c_Comb_Ocomb_OS: $i ).
thf(2,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,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 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ C @ D @ 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 @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ 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(13,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ C @ D @ 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 @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ C @ D @ 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 @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ 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 @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( ( 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 ) )
!= ( c_in @ ( c_Pair @ C @ D @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ),
inference(paramod_ordered,[status(thm)],[8,14]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( v_xb )),bind(D,$thf( v_x_H ))]]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $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 @ A ) @ B ) @ C ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ A @ C ) @ ( c_Comb_Ocomb_Oop_A_D_D @ B @ C ) ) @ 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(12,plain,
! [C: $i,B: $i,A: $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 @ A ) @ B ) @ C ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ A @ C ) @ ( c_Comb_Ocomb_Oop_A_D_D @ B @ C ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,negated_conjecture,
! [A: $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 ) ) @ A @ 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 ) @ A @ 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(10,plain,
! [A: $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 ) ) @ A @ 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 ) @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,plain,
! [A: $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 ) ) @ A @ 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 ) @ A @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(cnf,[status(esa)],[10]) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ D @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ A ) @ B ) @ C ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ A @ C ) @ ( c_Comb_Ocomb_Oop_A_D_D @ B @ C ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
!= ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ c_Comb_Ocomb_OS @ v_x_H ) @ v_y_Ha ) @ v_w ) @ D @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,11]) ).
thf(19,plain,
~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ v_w ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
inference(pattern_uni,[status(thm)],[18:[bind(A,$thf( v_x_H )),bind(B,$thf( v_y_Ha )),bind(C,$thf( v_w )),bind(D,$thf( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ v_w ) ))]]) ).
thf(78,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ C @ D @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ C @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
!= ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) ) @ ( c_Comb_Ocomb_Oop_A_D_D @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ v_w ) ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,19]) ).
thf(79,plain,
( ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ v_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z )),bind(B,$thf( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ v_w )),bind(C,$thf( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z )),bind(D,$thf( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ))]]) ).
thf(1,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(7,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 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(3,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(9,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 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ 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 @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ D @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( ( 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 ) )
!= ( c_in @ ( c_Pair @ C @ D @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ),
inference(paramod_ordered,[status(thm)],[9,14]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( v_yb )),bind(D,$thf( v_y_Ha ))]]) ).
thf(183,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( ( c_in @ ( c_Pair @ v_z @ v_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
!= ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,61]) ).
thf(184,plain,
c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_yb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_y_Ha @ v_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( v_z )),bind(B,$thf( v_w ))]]) ).
thf(224,plain,
( ~ $true
| ~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ),
inference(rewrite,[status(thm)],[79,184]) ).
thf(225,plain,
~ ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
inference(simp,[status(thm)],[224]) ).
thf(2755,plain,
! [B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
| ( ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ A ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ B ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) )
!= ( c_in @ ( c_Pair @ ( c_Comb_Ocomb_Oop_A_D_D @ v_xb @ v_z ) @ ( c_Comb_Ocomb_Oop_A_D_D @ v_x_H @ v_w ) @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,225]) ).
thf(2756,plain,
~ ( c_in @ ( c_Pair @ v_z @ v_w @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) @ c_Comb_Oparcontract @ ( tc_prod @ tc_Comb_Ocomb @ tc_Comb_Ocomb ) ),
inference(pattern_uni,[status(thm)],[2755:[bind(A,$thf( v_z )),bind(B,$thf( v_w ))]]) ).
thf(2869,plain,
~ $true,
inference(rewrite,[status(thm)],[2756,7]) ).
thf(2870,plain,
$false,
inference(simp,[status(thm)],[2869]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL109-2 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 6 21:36:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (109ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.65/1.17 % [INFO] nitpick registered as external prover.
% 1.65/1.17 % [INFO] Scanning for conjecture ...
% 1.75/1.24 % [INFO] Found a conjecture and 2 axioms. Running axiom selection ...
% 1.92/1.26 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.92/1.27 % [INFO] Problem is propositional (TPTP CNF).
% 1.92/1.27 % [INFO] Type checking passed.
% 1.92/1.27 % [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 ...
% 29.55/5.31 % [INFO] Killing All external provers ...
% 29.55/5.32 % Time passed: 4781ms (effective reasoning time: 4339ms)
% 29.55/5.32 % Solved by 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)>
% 29.55/5.32 % Axioms used in derivation (2): cls_Comb_Oparcontract_Ointros__4_0, cls_Comb_Oparcontract_Ointros__3_0
% 29.55/5.32 % No. of inferences in proof: 30
% 29.55/5.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4781 ms resp. 4339 ms w/o parsing
% 29.55/5.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.55/5.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------