TSTP Solution File: ITP387_1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : ITP387_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 : Fri May 3 02:30:47 EDT 2024
% Result : Theorem 117.13s 16.31s
% Output : CNFRefutation 117.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 64 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 374 ( 113 equ)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 105 ( 55 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 260 ( 260 fml; 0 var)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 42 ( 40 usr; 21 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 90 ( 0 sgn 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
tff(f10,conjecture,
'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture9) ).
tff(f11,negated_conjecture,
( ~ 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) ),
inference(negated_conjecture,[],[f10]) ).
tff(f37,axiom,
! [X0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X2: 'A_c_prod_ell2$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b',X0),X1)),X2) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$',X0),X2),'fun_app$k'('fun_app$l'('cblinfun_apply$',X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom35) ).
tff(f42,axiom,
! [X0: 'C_ell2_d_ell2_cblinfun$',X1: 'C_ell2_d_ell2_cblinfun$',X2: 'C_ell2$'] : ( 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a',X0),X1)),X2) = 'plus$i'('fun_app$u'('cblinfun_apply$b'(X0),X2),'fun_app$u'('cblinfun_apply$b'(X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).
tff(f83,axiom,
! [X0: 'A$',X1: 'C$'] : ( 'tensor_ell2$b'('ket$a'(X0),'ket$b'(X1)) = 'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).
tff(f97,axiom,
! [X0: 'B_ell2$',X1: 'D_ell2$',X2: 'D_ell2$'] : ( 'tensor_ell2$'(X0,'plus$i'(X1,X2)) = 'plus$u'('tensor_ell2$'(X0,X1),'tensor_ell2$'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).
tff(f157,axiom,
! [X0: 'C_ell2_d_ell2_cblinfun$',X1: 'C_ell2_d_ell2_cblinfun$'] : ( 'fun_app$m'('fun_app$n'('plus$a',X0),X1) = 'fun_app$m'('fun_app$n'('plus$a',X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).
tff(f158,axiom,
! [X0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : ( 'fun_app$r'('fun_app$s'('plus$b',X0),X1) = 'fun_app$r'('fun_app$s'('plus$b',X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).
tff(f212,axiom,
! [X0: 'A_ell2_b_ell2_cblinfun$',X1: 'C_ell2_d_ell2_cblinfun$',X2: 'A_ell2$',X3: 'C_ell2$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'(X0,X1)),'tensor_ell2$b'(X2,X3)) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X0),X2),'fun_app$u'('cblinfun_apply$b'(X1),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).
tff(f645,plain,
'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
inference(flattening,[],[f11]) ).
tff(f1393,plain,
'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
inference(cnf_transformation,[],[f645]) ).
tff(f1419,plain,
! [X2: 'A_c_prod_ell2$',X0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b',X0),X1)),X2) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$',X0),X2),'fun_app$k'('fun_app$l'('cblinfun_apply$',X1),X2)) ),
inference(cnf_transformation,[],[f37]) ).
tff(f1424,plain,
! [X2: 'C_ell2$',X0: 'C_ell2_d_ell2_cblinfun$',X1: 'C_ell2_d_ell2_cblinfun$'] : ( 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a',X0),X1)),X2) = 'plus$i'('fun_app$u'('cblinfun_apply$b'(X0),X2),'fun_app$u'('cblinfun_apply$b'(X1),X2)) ),
inference(cnf_transformation,[],[f42]) ).
tff(f1503,plain,
! [X0: 'A$',X1: 'C$'] : ( 'tensor_ell2$b'('ket$a'(X0),'ket$b'(X1)) = 'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X0),X1)) ),
inference(cnf_transformation,[],[f83]) ).
tff(f1517,plain,
! [X2: 'D_ell2$',X0: 'B_ell2$',X1: 'D_ell2$'] : ( 'tensor_ell2$'(X0,'plus$i'(X1,X2)) = 'plus$u'('tensor_ell2$'(X0,X1),'tensor_ell2$'(X0,X2)) ),
inference(cnf_transformation,[],[f97]) ).
tff(f1599,plain,
! [X0: 'C_ell2_d_ell2_cblinfun$',X1: 'C_ell2_d_ell2_cblinfun$'] : ( 'fun_app$m'('fun_app$n'('plus$a',X0),X1) = 'fun_app$m'('fun_app$n'('plus$a',X1),X0) ),
inference(cnf_transformation,[],[f157]) ).
tff(f1600,plain,
! [X0: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$',X1: 'A_c_prod_ell2_b_d_prod_ell2_cblinfun$'] : ( 'fun_app$r'('fun_app$s'('plus$b',X0),X1) = 'fun_app$r'('fun_app$s'('plus$b',X1),X0) ),
inference(cnf_transformation,[],[f158]) ).
tff(f1670,plain,
! [X2: 'A_ell2$',X3: 'C_ell2$',X0: 'A_ell2_b_ell2_cblinfun$',X1: 'C_ell2_d_ell2_cblinfun$'] : ( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'(X0,X1)),'tensor_ell2$b'(X2,X3)) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X0),X2),'fun_app$u'('cblinfun_apply$b'(X1),X3)) ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_68,negated_conjecture,
'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b1$')),'tensor_op$'('a$','b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b1$'),'b2$'))),'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$','i$'),'j$'))),
inference(cnf_transformation,[],[f1393]) ).
cnf(c_94,plain,
'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$',X0_92),X0_38),'fun_app$k'('fun_app$l'('cblinfun_apply$',X1_92),X0_38)) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b',X0_92),X1_92)),X0_38),
inference(cnf_transformation,[],[f1419]) ).
cnf(c_99,plain,
'plus$i'('fun_app$u'('cblinfun_apply$b'(X0_36),X0_83),'fun_app$u'('cblinfun_apply$b'(X1_36),X0_83)) = 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a',X0_36),X1_36)),X0_83),
inference(cnf_transformation,[],[f1424]) ).
cnf(c_152,plain,
'fun_app$o'('ket$','fun_app$p'('fun_app$q'('pair$',X0_119),X0_75)) = 'tensor_ell2$b'('ket$a'(X0_119),'ket$b'(X0_75)),
inference(cnf_transformation,[],[f1503]) ).
cnf(c_166,plain,
'plus$u'('tensor_ell2$'(X0_155,X0_49),'tensor_ell2$'(X0_155,X1_49)) = 'tensor_ell2$'(X0_155,'plus$i'(X0_49,X1_49)),
inference(cnf_transformation,[],[f1517]) ).
cnf(c_248,plain,
'fun_app$m'('fun_app$n'('plus$a',X0_36),X1_36) = 'fun_app$m'('fun_app$n'('plus$a',X1_36),X0_36),
inference(cnf_transformation,[],[f1599]) ).
cnf(c_249,plain,
'fun_app$r'('fun_app$s'('plus$b',X0_92),X1_92) = 'fun_app$r'('fun_app$s'('plus$b',X1_92),X0_92),
inference(cnf_transformation,[],[f1600]) ).
cnf(c_300,plain,
'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'(X0_151),X0_115),'fun_app$u'('cblinfun_apply$b'(X0_36),X0_83)) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'(X0_151,X0_36)),'tensor_ell2$b'(X0_115,X0_83)),
inference(cnf_transformation,[],[f1670]) ).
cnf(c_3897,plain,
'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),
inference(demodulation,[status(thm)],[c_68,c_152,c_248,c_249]) ).
cnf(c_7733,plain,
X0_155 = X0_155,
theory(equality) ).
cnf(c_7734,plain,
X0_156 = X0_156,
theory(equality) ).
cnf(c_7776,plain,
( X0_156 != X1_156
| X2_156 != X1_156
| X2_156 = X0_156 ),
theory(equality) ).
cnf(c_7797,plain,
( X0_49 != X1_49
| X0_155 != X1_155
| 'tensor_ell2$'(X0_155,X0_49) = 'tensor_ell2$'(X1_155,X1_49) ),
theory(equality) ).
cnf(c_7811,plain,
( X0_156 != X1_156
| X2_156 != X3_156
| 'plus$u'(X0_156,X2_156) = 'plus$u'(X1_156,X3_156) ),
theory(equality) ).
cnf(c_14701,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != X0_156
| X1_156 != X0_156
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = X1_156 ),
inference(instantiation,[status(thm)],[c_7776]) ).
cnf(c_14918,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| X0_156 != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = X0_156 ),
inference(instantiation,[status(thm)],[c_14701]) ).
cnf(c_14919,plain,
'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),
inference(instantiation,[status(thm)],[c_7734]) ).
cnf(c_15953,plain,
( 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))) ),
inference(instantiation,[status(thm)],[c_14918]) ).
cnf(c_15954,plain,
'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),
inference(instantiation,[status(thm)],[c_300]) ).
cnf(c_18887,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$')))
| X0_156 != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = X0_156 ),
inference(instantiation,[status(thm)],[c_14701]) ).
cnf(c_25656,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$')))
| 'tensor_ell2$'(X0_155,X0_49) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'tensor_ell2$'(X0_155,X0_49) ),
inference(instantiation,[status(thm)],[c_18887]) ).
cnf(c_25657,plain,
( X0_49 != 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))
| X0_155 != 'fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$'))
| 'tensor_ell2$'(X0_155,X0_49) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))) ),
inference(instantiation,[status(thm)],[c_7797]) ).
cnf(c_27272,plain,
'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),
inference(instantiation,[status(thm)],[c_7734]) ).
cnf(c_31037,plain,
( 'fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')) != 'fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$'))
| X0_49 != 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))
| 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),X0_49) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))) ),
inference(instantiation,[status(thm)],[c_25657]) ).
cnf(c_31038,plain,
'fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')) = 'fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),
inference(instantiation,[status(thm)],[c_7733]) ).
cnf(c_38880,plain,
( 'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))) != 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))
| 'fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')) != 'fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$'))
| 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$'))) ),
inference(instantiation,[status(thm)],[c_31037]) ).
cnf(c_38881,plain,
'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))) = 'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$')),
inference(instantiation,[status(thm)],[c_99]) ).
cnf(c_48572,plain,
( 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$')),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) ),
inference(instantiation,[status(thm)],[c_25656]) ).
cnf(c_55375,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))))
| X0_156 != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = X0_156 ),
inference(instantiation,[status(thm)],[c_14701]) ).
cnf(c_63066,plain,
( 'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) ),
inference(instantiation,[status(thm)],[c_55375]) ).
cnf(c_63067,plain,
'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) = 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'plus$i'('fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))),
inference(instantiation,[status(thm)],[c_166]) ).
cnf(c_65263,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != X0_156
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != X0_156
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) ),
inference(instantiation,[status(thm)],[c_7776]) ).
cnf(c_65399,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != X0_156
| X1_156 != X0_156
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = X1_156 ),
inference(instantiation,[status(thm)],[c_7776]) ).
cnf(c_65662,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| X0_156 != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = X0_156 ),
inference(instantiation,[status(thm)],[c_65399]) ).
cnf(c_66466,plain,
( 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))) ),
inference(instantiation,[status(thm)],[c_65662]) ).
cnf(c_66467,plain,
'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),
inference(instantiation,[status(thm)],[c_94]) ).
cnf(c_69490,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))))
| X0_156 != 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = X0_156 ),
inference(instantiation,[status(thm)],[c_65399]) ).
cnf(c_73635,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))))
| 'plus$u'(X0_156,X1_156) != 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'plus$u'(X0_156,X1_156) ),
inference(instantiation,[status(thm)],[c_69490]) ).
cnf(c_73636,plain,
( X0_156 != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| X1_156 != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'plus$u'(X0_156,X1_156) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))) ),
inference(instantiation,[status(thm)],[c_7811]) ).
cnf(c_79136,plain,
( 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| X0_156 != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'plus$u'(X0_156,'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))) ),
inference(instantiation,[status(thm)],[c_73636]) ).
cnf(c_79137,plain,
'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),
inference(instantiation,[status(thm)],[c_300]) ).
cnf(c_84986,plain,
( 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))) != 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))
| 'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) = 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$')))) ),
inference(instantiation,[status(thm)],[c_79136]) ).
cnf(c_84987,plain,
'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),
inference(instantiation,[status(thm)],[c_300]) ).
cnf(c_94598,plain,
( 'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) != 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'plus$u'('fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b2$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))),'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','b1$')),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$')))) ),
inference(instantiation,[status(thm)],[c_73635]) ).
cnf(c_97547,plain,
( 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) != 'plus$u'('tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b2$'),'ket$b'('j$'))),'tensor_ell2$'('fun_app$t'('cblinfun_apply$a'('a$'),'ket$a'('i$')),'fun_app$u'('cblinfun_apply$b'('b1$'),'ket$b'('j$'))))
| 'fun_app$k'('fun_app$l'('cblinfun_apply$','fun_app$r'('fun_app$s'('plus$b','tensor_op$'('a$','b2$')),'tensor_op$'('a$','b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) = 'fun_app$k'('fun_app$l'('cblinfun_apply$','tensor_op$'('a$','fun_app$m'('fun_app$n'('plus$a','b2$'),'b1$'))),'tensor_ell2$b'('ket$a'('i$'),'ket$b'('j$'))) ),
inference(instantiation,[status(thm)],[c_65263]) ).
cnf(c_97548,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_97547,c_94598,c_84987,c_84986,c_79137,c_66467,c_66466,c_63067,c_63066,c_48572,c_38881,c_38880,c_31038,c_27272,c_15954,c_15953,c_14919,c_3897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP387_1 : TPTP v8.1.2. Released v8.0.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n003.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 2 22:02:50 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 117.13/16.31 % SZS status Started for theBenchmark.p
% 117.13/16.31 % SZS status Theorem for theBenchmark.p
% 117.13/16.31
% 117.13/16.31 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 117.13/16.31
% 117.13/16.31 ------ iProver source info
% 117.13/16.31
% 117.13/16.31 git: date: 2024-05-02 19:28:25 +0000
% 117.13/16.31 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 117.13/16.31 git: non_committed_changes: false
% 117.13/16.31
% 117.13/16.31 ------ Parsing...
% 117.13/16.31 ------ Clausification by vclausify_rel & Parsing by iProver...
% 117.13/16.31
% 117.13/16.31 ------ Preprocessing... sup_sim: 38 sf_s rm: 200 0s sf_e pe_s pe_e sup_sim: 1 sf_s rm: 88 0s sf_e pe_s pe_e
% 117.13/16.31
% 117.13/16.31 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 117.13/16.31
% 117.13/16.31 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 117.13/16.31 ------ Proving...
% 117.13/16.31 ------ Problem Properties
% 117.13/16.31
% 117.13/16.31
% 117.13/16.31 clauses 363
% 117.13/16.31 conjectures 0
% 117.13/16.31 EPR 0
% 117.13/16.31 Horn 342
% 117.13/16.31 unary 165
% 117.13/16.31 binary 140
% 117.13/16.31 lits 630
% 117.13/16.31 lits eq 337
% 117.13/16.31 fd_pure 0
% 117.13/16.31 fd_pseudo 0
% 117.13/16.31 fd_cond 14
% 117.13/16.31 fd_pseudo_cond 54
% 117.13/16.31 AC symbols 4
% 117.13/16.31
% 117.13/16.31 ------ Input Options Time Limit: Unbounded
% 117.13/16.31
% 117.13/16.31
% 117.13/16.31 ------
% 117.13/16.31 Current options:
% 117.13/16.31 ------
% 117.13/16.31
% 117.13/16.31
% 117.13/16.31
% 117.13/16.31
% 117.13/16.31 ------ Proving...
% 117.13/16.31
% 117.13/16.31
% 117.13/16.31 % SZS status Theorem for theBenchmark.p
% 117.13/16.31
% 117.13/16.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 117.13/16.32
% 117.13/16.32
%------------------------------------------------------------------------------