%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : PHI044_1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 : Fri Sep 25 02:30:32 PM UTC 2026
% Result : Unsatisfiable 57.78s 9.84s
% Output : CNFRefutation 57.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 232 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 1515 ( 261 equ)
% Maximal formula atoms : 33 ( 6 avg)
% Number of connectives : 1416 ( 585 ~; 663 |; 135 &)
% ( 14 <=>; 15 =>; 0 <=; 4 <~>)
% Maximal formula depth : 28 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 452 ( 452 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 435 ( 0 sgn 393 !; 42 ?; 435 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
sK0: ( option_set * option_set ) > option ).
tff(pred_def_1,type,
subset: ( option_set * option_set ) > $o ).
tff(pred_def_2,type,
member: ( option_set * option ) > $o ).
tff(pred_def_3,type,
weakly_better: ( option_set * option_set ) > $o ).
tff(pred_def_4,type,
better: ( option_set * option_set ) > $o ).
tff(pred_def_5,type,
permitted_preference: ( option * option ) > $o ).
tff(pred_def_6,type,
required_preference: ( option * option ) > $o ).
tff(func_def_7,type,
sK7: option ).
tff(func_def_8,type,
sK8: option ).
tff(func_def_9,type,
sK9: option_set ).
tff(func_def_10,type,
sK10: option_set ).
tff(func_def_11,type,
sK11: option_set ).
tff(func_def_12,type,
sK12: option_set ).
tff(f1,axiom,
! [X0: option_set,X1: option_set] :
( subset(X0,X1)
<=> ! [X2: option] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
tff(f2,axiom,
! [X0: option_set,X1: option_set] :
( better(X0,X1)
<=> ( ~ weakly_better(X1,X0)
& weakly_better(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',better) ).
tff(f3,axiom,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ( ! [X4: option] :
( member(X4,X3)
=> ( X4 = X0 ) )
& ! [X4: option] :
( member(X4,X2)
=> ( ( X4 = X1 )
| ( X4 = X0 ) ) )
& member(X0,X3)
& member(X1,X2)
& member(X0,X2)
& permitted_preference(X1,X0)
& permitted_preference(X0,X1) )
=> better(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',value_of_rational_diversity) ).
tff(f4,axiom,
! [X0: option_set,X1: option_set] :
( ( ? [X2: option] :
( ! [X3: option] :
( ( ~ member(X3,X0)
& member(X3,X1) )
=> required_preference(X2,X3) )
& member(X2,X0) )
& subset(X0,X1) )
=> ~ better(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',insignificance_of_dominated_options) ).
tff(f5,axiom,
! [X0: option_set,X1: option_set] :
( subset(X0,X1)
=> weakly_better(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',harmlessness_of_expansions) ).
tff(f6,axiom,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ( ! [X4: option] :
( member(X4,X3)
<=> ( X4 = X1 ) )
& ! [X4: option] :
( member(X4,X2)
<=> ( X4 = X0 ) ) )
=> ~ better(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',parity_of_no_choice_situations) ).
tff(f7,axiom,
! [X0: option_set,X1: option_set,X2: option_set] :
( ( weakly_better(X1,X2)
& weakly_better(X0,X1) )
=> weakly_better(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_weakly_better_freedom_of_choice) ).
tff(f8,axiom,
? [X0: option,X1: option,X2: option,X3: option_set,X4: option_set,X5: option_set,X6: option_set] :
( ! [X7: option] :
( member(X7,X6)
<=> ( ( X7 = X2 )
| ( X7 = X1 )
| ( X7 = X0 ) ) )
& ! [X7: option] :
( member(X7,X5)
<=> ( ( X7 = X1 )
| ( X7 = X0 ) ) )
& ! [X7: option] :
( member(X7,X4)
<=> ( X7 = X2 ) )
& ! [X7: option] :
( member(X7,X3)
<=> ( X7 = X0 ) )
& member(X2,X6)
& member(X1,X6)
& member(X0,X6)
& member(X1,X5)
& member(X0,X5)
& member(X2,X4)
& member(X0,X3)
& required_preference(X2,X1)
& required_preference(X2,X0)
& permitted_preference(X1,X0)
& permitted_preference(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_dominated_diversity) ).
tff(f9,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ( ! [X5: option] :
( member(X5,X3)
=> ( X0 = X5 ) )
& ! [X4: option] :
( member(X4,X2)
=> ( ( X4 = X1 )
| ( X4 = X0 ) ) )
& member(X0,X3)
& member(X1,X2)
& member(X0,X2)
& permitted_preference(X1,X0)
& permitted_preference(X0,X1) )
=> better(X2,X3) ),
inference(rectify,[],[f3]) ).
tff(f10,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ( ! [X5: option] :
( member(X5,X3)
<=> ( X1 = X5 ) )
& ! [X4: option] :
( member(X4,X2)
<=> ( X4 = X0 ) ) )
=> ~ better(X2,X3) ),
inference(rectify,[],[f6]) ).
tff(f11,plain,
? [X0: option,X1: option,X2: option,X3: option_set,X4: option_set,X5: option_set,X6: option_set] :
( ! [X10: option] :
( member(X10,X6)
<=> ( ( X2 = X10 )
| ( X1 = X10 )
| ( X0 = X10 ) ) )
& ! [X9: option] :
( member(X9,X5)
<=> ( ( X1 = X9 )
| ( X0 = X9 ) ) )
& ! [X8: option] :
( member(X8,X4)
<=> ( X2 = X8 ) )
& ! [X7: option] :
( member(X7,X3)
<=> ( X7 = X0 ) )
& member(X2,X6)
& member(X1,X6)
& member(X0,X6)
& member(X1,X5)
& member(X0,X5)
& member(X2,X4)
& member(X0,X3)
& required_preference(X2,X1)
& required_preference(X2,X0)
& permitted_preference(X1,X0)
& permitted_preference(X0,X1) ),
inference(rectify,[],[f8]) ).
tff(f12,plain,
! [X0: option_set,X1: option_set] :
( ! [X2: option] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
tff(f13,plain,
! [X0: option_set,X1: option_set] :
( ? [X2: option] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
tff(f14,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ? [X5: option] :
( member(X5,X3)
& ( X0 != X5 ) )
| ? [X4: option] :
( member(X4,X2)
& ( X1 != X4 )
& ( X0 != X4 ) )
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(ennf_transformation,[],[f9]) ).
tff(f15,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ? [X5: option] :
( member(X5,X3)
& ( X0 != X5 ) )
| ? [X4: option] :
( member(X4,X2)
& ( X1 != X4 )
& ( X0 != X4 ) )
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(flattening,[],[f14]) ).
tff(f16,plain,
! [X0: option_set,X1: option_set] :
( ! [X2: option] :
( ? [X3: option] :
( ~ member(X3,X0)
& member(X3,X1)
& ~ required_preference(X2,X3) )
| ~ member(X2,X0) )
| ~ subset(X0,X1)
| ~ better(X1,X0) ),
inference(ennf_transformation,[],[f4]) ).
tff(f17,plain,
! [X0: option_set,X1: option_set] :
( ! [X2: option] :
( ? [X3: option] :
( ~ member(X3,X0)
& member(X3,X1)
& ~ required_preference(X2,X3) )
| ~ member(X2,X0) )
| ~ subset(X0,X1)
| ~ better(X1,X0) ),
inference(flattening,[],[f16]) ).
tff(f18,plain,
! [X0: option_set,X1: option_set] :
( ~ subset(X0,X1)
| weakly_better(X1,X0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f19,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ? [X5: option] :
( member(X5,X3)
<~> ( X1 = X5 ) )
| ? [X4: option] :
( member(X4,X2)
<~> ( X4 = X0 ) )
| ~ better(X2,X3) ),
inference(ennf_transformation,[],[f10]) ).
tff(f20,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ? [X5: option] :
( member(X5,X3)
<~> ( X1 = X5 ) )
| ? [X4: option] :
( member(X4,X2)
<~> ( X4 = X0 ) )
| ~ better(X2,X3) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
! [X0: option_set,X1: option_set,X2: option_set] :
( ~ weakly_better(X1,X2)
| ~ weakly_better(X0,X1)
| weakly_better(X0,X2) ),
inference(ennf_transformation,[],[f7]) ).
tff(f22,plain,
! [X0: option_set,X1: option_set,X2: option_set] :
( ~ weakly_better(X1,X2)
| ~ weakly_better(X0,X1)
| weakly_better(X0,X2) ),
inference(flattening,[],[f21]) ).
tff(f23,plain,
! [X0: option_set,X1: option_set] :
( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f13]) ).
tff(f24,plain,
! [X0: option_set,X1: option_set] :
( ( ~ better(X0,X1)
| ( ~ weakly_better(X1,X0)
& weakly_better(X0,X1) ) )
& ( weakly_better(X1,X0)
| ~ weakly_better(X0,X1)
| better(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
tff(f25,plain,
! [X0: option_set,X1: option_set] :
( ( ~ better(X0,X1)
| ( ~ weakly_better(X1,X0)
& weakly_better(X0,X1) ) )
& ( weakly_better(X1,X0)
| ~ weakly_better(X0,X1)
| better(X0,X1) ) ),
inference(flattening,[],[f24]) ).
tff(f26,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ( member(sK2(X0,X3),X3)
& ( sK2(X0,X3) != X0 ) )
| ( member(sK1(X0,X1,X2),X2)
& ( sK1(X0,X1,X2) != X1 )
& ( sK1(X0,X1,X2) != X0 ) )
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X4,sK1(X0,X1,X2)),skolemize(X5,sK2(X0,X3))],[f15]) ).
tff(f27,plain,
! [X0: option_set,X1: option_set] :
( ! [X2: option] :
( ( ~ member(sK3(X0,X1,X2),X0)
& member(sK3(X0,X1,X2),X1)
& ~ required_preference(X2,sK3(X0,X1,X2)) )
| ~ member(X2,X0) )
| ~ subset(X0,X1)
| ~ better(X1,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f17]) ).
tff(f28,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ? [X5: option] :
( ( member(X5,X3)
| ( X1 = X5 ) )
& ( ~ member(X5,X3)
| ( X1 != X5 ) ) )
| ? [X4: option] :
( ( member(X4,X2)
| ( X4 = X0 ) )
& ( ~ member(X4,X2)
| ( X0 != X4 ) ) )
| ~ better(X2,X3) ),
inference(nnf_transformation,[],[f20]) ).
tff(f29,plain,
! [X0: option,X1: option,X2: option_set,X3: option_set] :
( ( ( member(sK5(X1,X3),X3)
| ( sK5(X1,X3) = X1 ) )
& ( ~ member(sK5(X1,X3),X3)
| ( sK5(X1,X3) != X1 ) ) )
| ( ( member(sK4(X0,X2),X2)
| ( sK4(X0,X2) = X0 ) )
& ( ~ member(sK4(X0,X2),X2)
| ( sK4(X0,X2) != X0 ) ) )
| ~ better(X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X4,sK4(X0,X2)),skolemize(X5,sK5(X1,X3))],[f28]) ).
tff(f30,plain,
? [X0: option,X1: option,X2: option,X3: option_set,X4: option_set,X5: option_set,X6: option_set] :
( ! [X10: option] :
( ( ~ member(X10,X6)
| ( X2 = X10 )
| ( X1 = X10 )
| ( X0 = X10 ) )
& ( ( ( X2 != X10 )
& ( X1 != X10 )
& ( X0 != X10 ) )
| member(X10,X6) ) )
& ! [X9: option] :
( ( ~ member(X9,X5)
| ( X1 = X9 )
| ( X0 = X9 ) )
& ( ( ( X1 != X9 )
& ( X0 != X9 ) )
| member(X9,X5) ) )
& ! [X8: option] :
( ( ~ member(X8,X4)
| ( X2 = X8 ) )
& ( ( X2 != X8 )
| member(X8,X4) ) )
& ! [X7: option] :
( ( ~ member(X7,X3)
| ( X7 = X0 ) )
& ( ( X0 != X7 )
| member(X7,X3) ) )
& member(X2,X6)
& member(X1,X6)
& member(X0,X6)
& member(X1,X5)
& member(X0,X5)
& member(X2,X4)
& member(X0,X3)
& required_preference(X2,X1)
& required_preference(X2,X0)
& permitted_preference(X1,X0)
& permitted_preference(X0,X1) ),
inference(nnf_transformation,[],[f11]) ).
tff(f31,plain,
? [X0: option,X1: option,X2: option,X3: option_set,X4: option_set,X5: option_set,X6: option_set] :
( ! [X10: option] :
( ( ~ member(X10,X6)
| ( X2 = X10 )
| ( X1 = X10 )
| ( X0 = X10 ) )
& ( ( ( X2 != X10 )
& ( X1 != X10 )
& ( X0 != X10 ) )
| member(X10,X6) ) )
& ! [X9: option] :
( ( ~ member(X9,X5)
| ( X1 = X9 )
| ( X0 = X9 ) )
& ( ( ( X1 != X9 )
& ( X0 != X9 ) )
| member(X9,X5) ) )
& ! [X8: option] :
( ( ~ member(X8,X4)
| ( X2 = X8 ) )
& ( ( X2 != X8 )
| member(X8,X4) ) )
& ! [X7: option] :
( ( ~ member(X7,X3)
| ( X7 = X0 ) )
& ( ( X0 != X7 )
| member(X7,X3) ) )
& member(X2,X6)
& member(X1,X6)
& member(X0,X6)
& member(X1,X5)
& member(X0,X5)
& member(X2,X4)
& member(X0,X3)
& required_preference(X2,X1)
& required_preference(X2,X0)
& permitted_preference(X1,X0)
& permitted_preference(X0,X1) ),
inference(flattening,[],[f30]) ).
tff(f32,plain,
( ! [X10: option] :
( ( ~ member(X10,sK12)
| ( sK8 = X10 )
| ( sK7 = X10 )
| ( sK6 = X10 ) )
& ( ( ( sK8 != X10 )
& ( sK7 != X10 )
& ( sK6 != X10 ) )
| member(X10,sK12) ) )
& ! [X9: option] :
( ( ~ member(X9,sK11)
| ( sK7 = X9 )
| ( sK6 = X9 ) )
& ( ( ( sK7 != X9 )
& ( sK6 != X9 ) )
| member(X9,sK11) ) )
& ! [X8: option] :
( ( ~ member(X8,sK10)
| ( sK8 = X8 ) )
& ( ( sK8 != X8 )
| member(X8,sK10) ) )
& ! [X7: option] :
( ( ~ member(X7,sK9)
| ( sK6 = X7 ) )
& ( ( sK6 != X7 )
| member(X7,sK9) ) )
& member(sK8,sK12)
& member(sK7,sK12)
& member(sK6,sK12)
& member(sK7,sK11)
& member(sK6,sK11)
& member(sK8,sK10)
& member(sK6,sK9)
& required_preference(sK8,sK7)
& required_preference(sK8,sK6)
& permitted_preference(sK7,sK6)
& permitted_preference(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X4,sK10),skolemize(X5,sK11),skolemize(X6,sK12)],[f31]) ).
tff(f33,plain,
! [X0: option_set,X1: option_set] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tff(f34,plain,
! [X0: option_set,X1: option_set] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tff(f35,plain,
! [X0: option_set,X1: option_set] :
( ~ better(X0,X1)
| ~ weakly_better(X1,X0) ),
inference(cnf_transformation,[],[f25]) ).
tff(f36,plain,
! [X0: option_set,X1: option_set] :
( ~ better(X0,X1)
| weakly_better(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tff(f37,plain,
! [X0: option_set,X1: option_set] :
( weakly_better(X1,X0)
| ~ weakly_better(X0,X1)
| better(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tff(f38,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( member(sK2(X0,X3),X3)
| member(sK1(X0,X1,X2),X2)
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f39,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( ( sK2(X0,X3) != X0 )
| member(sK1(X0,X1,X2),X2)
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f40,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( member(sK2(X0,X3),X3)
| ( sK1(X0,X1,X2) != X1 )
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f41,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( ( sK2(X0,X3) != X0 )
| ( sK1(X0,X1,X2) != X1 )
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f42,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( member(sK2(X0,X3),X3)
| ( sK1(X0,X1,X2) != X0 )
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f43,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( ( sK2(X0,X3) != X0 )
| ( sK1(X0,X1,X2) != X0 )
| ~ member(X0,X3)
| ~ member(X1,X2)
| ~ member(X0,X2)
| ~ permitted_preference(X1,X0)
| ~ permitted_preference(X0,X1)
| better(X2,X3) ),
inference(cnf_transformation,[],[f26]) ).
tff(f44,plain,
! [X2: option,X0: option_set,X1: option_set] :
( ~ member(sK3(X0,X1,X2),X0)
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ better(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f45,plain,
! [X2: option,X0: option_set,X1: option_set] :
( member(sK3(X0,X1,X2),X1)
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ better(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f46,plain,
! [X2: option,X0: option_set,X1: option_set] :
( ~ required_preference(X2,sK3(X0,X1,X2))
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ better(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
tff(f47,plain,
! [X0: option_set,X1: option_set] :
( ~ subset(X0,X1)
| weakly_better(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f48,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( member(sK5(X1,X3),X3)
| ( sK5(X1,X3) = X1 )
| member(sK4(X0,X2),X2)
| ( sK4(X0,X2) = X0 )
| ~ better(X2,X3) ),
inference(cnf_transformation,[],[f29]) ).
tff(f49,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( ~ member(sK5(X1,X3),X3)
| ( sK5(X1,X3) != X1 )
| member(sK4(X0,X2),X2)
| ( sK4(X0,X2) = X0 )
| ~ better(X2,X3) ),
inference(cnf_transformation,[],[f29]) ).
tff(f50,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( member(sK5(X1,X3),X3)
| ( sK5(X1,X3) = X1 )
| ~ member(sK4(X0,X2),X2)
| ( sK4(X0,X2) != X0 )
| ~ better(X2,X3) ),
inference(cnf_transformation,[],[f29]) ).
tff(f51,plain,
! [X2: option_set,X3: option_set,X0: option,X1: option] :
( ~ member(sK5(X1,X3),X3)
| ( sK5(X1,X3) != X1 )
| ~ member(sK4(X0,X2),X2)
| ( sK4(X0,X2) != X0 )
| ~ better(X2,X3) ),
inference(cnf_transformation,[],[f29]) ).
tff(f52,plain,
! [X2: option_set,X0: option_set,X1: option_set] :
( ~ weakly_better(X1,X2)
| ~ weakly_better(X0,X1)
| weakly_better(X0,X2) ),
inference(cnf_transformation,[],[f22]) ).
tff(f53,plain,
! [X10: option] :
( ~ member(X10,sK12)
| ( sK8 = X10 )
| ( sK7 = X10 )
| ( sK6 = X10 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f54,plain,
! [X10: option] :
( ( sK8 != X10 )
| member(X10,sK12) ),
inference(cnf_transformation,[],[f32]) ).
tff(f55,plain,
! [X10: option] :
( ( sK7 != X10 )
| member(X10,sK12) ),
inference(cnf_transformation,[],[f32]) ).
tff(f56,plain,
! [X10: option] :
( ( sK6 != X10 )
| member(X10,sK12) ),
inference(cnf_transformation,[],[f32]) ).
tff(f57,plain,
! [X9: option] :
( ~ member(X9,sK11)
| ( sK7 = X9 )
| ( sK6 = X9 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f58,plain,
! [X9: option] :
( ( sK7 != X9 )
| member(X9,sK11) ),
inference(cnf_transformation,[],[f32]) ).
tff(f59,plain,
! [X9: option] :
( ( sK6 != X9 )
| member(X9,sK11) ),
inference(cnf_transformation,[],[f32]) ).
tff(f60,plain,
! [X8: option] :
( ~ member(X8,sK10)
| ( sK8 = X8 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f61,plain,
! [X8: option] :
( ( sK8 != X8 )
| member(X8,sK10) ),
inference(cnf_transformation,[],[f32]) ).
tff(f62,plain,
! [X7: option] :
( ~ member(X7,sK9)
| ( sK6 = X7 ) ),
inference(cnf_transformation,[],[f32]) ).
tff(f63,plain,
! [X7: option] :
( ( sK6 != X7 )
| member(X7,sK9) ),
inference(cnf_transformation,[],[f32]) ).
tff(f71,plain,
required_preference(sK8,sK7),
inference(cnf_transformation,[],[f32]) ).
tff(f72,plain,
required_preference(sK8,sK6),
inference(cnf_transformation,[],[f32]) ).
tff(f73,plain,
permitted_preference(sK7,sK6),
inference(cnf_transformation,[],[f32]) ).
tff(f74,plain,
permitted_preference(sK6,sK7),
inference(cnf_transformation,[],[f32]) ).
tff(f75,plain,
member(sK6,sK9),
inference(equality_resolution,[],[f63]) ).
tff(f76,plain,
member(sK8,sK10),
inference(equality_resolution,[],[f61]) ).
tff(f77,plain,
member(sK6,sK11),
inference(equality_resolution,[],[f59]) ).
tff(f78,plain,
member(sK7,sK11),
inference(equality_resolution,[],[f58]) ).
tff(f79,plain,
member(sK6,sK12),
inference(equality_resolution,[],[f56]) ).
tff(f80,plain,
member(sK7,sK12),
inference(equality_resolution,[],[f55]) ).
tff(f81,plain,
member(sK8,sK12),
inference(equality_resolution,[],[f54]) ).
tcf(c_49,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( subset(X0_option_set,X1_option_set)
| ~ member(sK0(X0_option_set,X1_option_set),X1_option_set) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( subset(X0_option_set,X1_option_set)
| member(sK0(X0_option_set,X1_option_set),X0_option_set) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_51,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| weakly_better(X1_option_set,X0_option_set)
| ~ weakly_better(X0_option_set,X1_option_set) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_52,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( weakly_better(X0_option_set,X1_option_set)
| ~ better(X0_option_set,X1_option_set) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_53,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( ~ better(X1_option_set,X0_option_set)
| ~ weakly_better(X0_option_set,X1_option_set) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_54,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X0_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set)
| ( sK2(X0_option,X1_option_set) != X0_option )
| ( sK1(X0_option,X1_option,X0_option_set) != X0_option ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_55,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| member(sK2(X0_option,X1_option_set),X1_option_set)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X0_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set)
| ( sK1(X0_option,X1_option,X0_option_set) != X0_option ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_56,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X0_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set)
| ( sK2(X0_option,X1_option_set) != X0_option )
| ( sK1(X0_option,X1_option,X0_option_set) != X1_option ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_57,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| member(sK2(X0_option,X1_option_set),X1_option_set)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X0_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set)
| ( sK1(X0_option,X1_option,X0_option_set) != X1_option ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_58,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( better(X1_option_set,X0_option_set)
| member(sK1(X0_option,X1_option,X1_option_set),X1_option_set)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X1_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set)
| ( sK2(X0_option,X0_option_set) != X0_option ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( better(X1_option_set,X0_option_set)
| member(sK2(X0_option,X0_option_set),X0_option_set)
| member(sK1(X0_option,X1_option,X1_option_set),X1_option_set)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X1_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_60,plain,
! [X0_option: option,X0_option_set: option_set,X1_option_set: option_set] :
( ~ better(X1_option_set,X0_option_set)
| ~ member(X0_option,X0_option_set)
| ~ subset(X0_option_set,X1_option_set)
| ~ required_preference(X0_option,sK3(X0_option_set,X1_option_set,X0_option)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_61,plain,
! [X0_option: option,X0_option_set: option_set,X1_option_set: option_set] :
( member(sK3(X0_option_set,X1_option_set,X0_option),X1_option_set)
| ~ better(X1_option_set,X0_option_set)
| ~ member(X0_option,X0_option_set)
| ~ subset(X0_option_set,X1_option_set) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,plain,
! [X0_option: option,X0_option_set: option_set,X1_option_set: option_set] :
( ~ better(X1_option_set,X0_option_set)
| ~ member(X0_option,X0_option_set)
| ~ subset(X0_option_set,X1_option_set)
| ~ member(sK3(X0_option_set,X1_option_set,X0_option),X0_option_set) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_63,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( weakly_better(X1_option_set,X0_option_set)
| ~ subset(X0_option_set,X1_option_set) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( ~ better(X0_option_set,X1_option_set)
| ~ member(sK5(X1_option,X1_option_set),X1_option_set)
| ~ member(sK4(X0_option,X0_option_set),X0_option_set)
| ( sK5(X1_option,X1_option_set) != X1_option )
| ( sK4(X0_option,X0_option_set) != X0_option ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_65,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( member(sK5(X1_option,X1_option_set),X1_option_set)
| ( sK5(X1_option,X1_option_set) = X1_option )
| ~ better(X0_option_set,X1_option_set)
| ~ member(sK4(X0_option,X0_option_set),X0_option_set)
| ( sK4(X0_option,X0_option_set) != X0_option ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_66,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( member(sK4(X1_option,X1_option_set),X1_option_set)
| ( sK4(X1_option,X1_option_set) = X1_option )
| ~ better(X1_option_set,X0_option_set)
| ~ member(sK5(X0_option,X0_option_set),X0_option_set)
| ( sK5(X0_option,X0_option_set) != X0_option ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_67,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( member(sK5(X1_option,X1_option_set),X1_option_set)
| member(sK4(X0_option,X0_option_set),X0_option_set)
| ( sK5(X1_option,X1_option_set) = X1_option )
| ( sK4(X0_option,X0_option_set) = X0_option )
| ~ better(X0_option_set,X1_option_set) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_68,plain,
! [X0_option_set: option_set,X1_option_set: option_set,X2_option_set: option_set] :
( weakly_better(X0_option_set,X2_option_set)
| ~ weakly_better(X1_option_set,X2_option_set)
| ~ weakly_better(X0_option_set,X1_option_set) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_69,plain,
permitted_preference(sK6,sK7),
inference(cnf_transformation,[],[f74]) ).
tcf(c_70,plain,
permitted_preference(sK7,sK6),
inference(cnf_transformation,[],[f73]) ).
tcf(c_71,plain,
required_preference(sK8,sK6),
inference(cnf_transformation,[],[f72]) ).
tcf(c_72,plain,
required_preference(sK8,sK7),
inference(cnf_transformation,[],[f71]) ).
tcf(c_80,plain,
member(sK6,sK9),
inference(cnf_transformation,[],[f75]) ).
tcf(c_81,plain,
! [X0_option: option] :
( ( X0_option = sK6 )
| ~ member(X0_option,sK9) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_82,plain,
member(sK8,sK10),
inference(cnf_transformation,[],[f76]) ).
tcf(c_83,plain,
! [X0_option: option] :
( ( X0_option = sK8 )
| ~ member(X0_option,sK10) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_84,plain,
member(sK6,sK11),
inference(cnf_transformation,[],[f77]) ).
tcf(c_85,plain,
member(sK7,sK11),
inference(cnf_transformation,[],[f78]) ).
tcf(c_86,plain,
! [X0_option: option] :
( ( X0_option = sK7 )
| ( X0_option = sK6 )
| ~ member(X0_option,sK11) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_87,plain,
member(sK6,sK12),
inference(cnf_transformation,[],[f79]) ).
tcf(c_88,plain,
member(sK7,sK12),
inference(cnf_transformation,[],[f80]) ).
tcf(c_89,plain,
member(sK8,sK12),
inference(cnf_transformation,[],[f81]) ).
tcf(c_90,plain,
! [X0_option: option] :
( ( X0_option = sK8 )
| ( X0_option = sK7 )
| ( X0_option = sK6 )
| ~ member(X0_option,sK12) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_126,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option] :
( member(X0_option,X0_option_set)
| ~ member(X1_option,X0_option_set)
| ( X0_option != X1_option ) ),
theory(equality) ).
tcf(c_128,plain,
! [X0_option: option,X1_option: option,X2_option: option,X3_option: option] :
( required_preference(X0_option,X2_option)
| ~ required_preference(X1_option,X3_option)
| ( X2_option != X3_option )
| ( X0_option != X1_option ) ),
theory(equality) ).
tcf(c_133,plain,
( ( sK8 = sK8 )
| ~ member(sK8,sK10) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_220,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( better(X1_option_set,X0_option_set)
| member(sK1(sK6,sK7,X1_option_set),X1_option_set)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,X1_option_set)
| ~ member(sK6,X1_option_set)
| ~ member(sK6,X0_option_set)
| ( sK2(sK6,X0_option_set) != sK6 ) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_303,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(X0_option,X0_option_set)
| ~ member(sK6,X0_option_set)
| ~ member(X0_option,sK9) ),
inference(resolution,[status(thm)],[c_126,c_81]) ).
tcf(c_304,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(X0_option,X0_option_set)
| ~ member(sK8,X0_option_set)
| ~ member(X0_option,sK10) ),
inference(resolution,[status(thm)],[c_126,c_83]) ).
tcf(c_305,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(X0_option,X0_option_set)
| ( X0_option = sK6 )
| ~ member(sK7,X0_option_set)
| ~ member(X0_option,sK11) ),
inference(resolution,[status(thm)],[c_126,c_86]) ).
tcf(c_334,plain,
! [X0_option: option] :
( member(X0_option,sK12)
| ~ member(X0_option,sK9) ),
inference(resolution,[status(thm)],[c_303,c_87]) ).
tcf(c_337,plain,
! [X0_option_set: option_set] :
( ( sK2(sK6,X0_option_set) = sK6 )
| ~ member(sK2(sK6,X0_option_set),sK9) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_385,plain,
! [X0_option_set: option_set] :
( subset(X0_option_set,sK12)
| ~ member(sK0(X0_option_set,sK12),sK9) ),
inference(resolution,[status(thm)],[c_334,c_49]) ).
tcf(c_505,plain,
! [X0_option_set: option_set] :
( ( sK1(sK6,sK7,X0_option_set) = sK7 )
| ( sK1(sK6,sK7,X0_option_set) = sK6 )
| ~ member(sK1(sK6,sK7,X0_option_set),sK11) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_603,plain,
! [X0_option: option,X0_option_set: option_set,X1_option_set: option_set] :
( better(X1_option_set,X0_option_set)
| member(sK2(X0_option,X0_option_set),X0_option_set)
| member(sK1(X0_option,sK7,X1_option_set),X1_option_set)
| ~ permitted_preference(sK7,X0_option)
| ~ permitted_preference(X0_option,sK7)
| ~ member(sK7,X1_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set) ),
inference(instantiation,[status(thm)],[c_59]) ).
tcf(c_637,plain,
( ( sK1(sK6,sK7,sK11) = sK7 )
| ( sK1(sK6,sK7,sK11) = sK6 )
| ~ member(sK1(sK6,sK7,sK11),sK11) ),
inference(instantiation,[status(thm)],[c_505]) ).
tcf(c_638,plain,
! [X0_option_set: option_set] :
( better(sK11,X0_option_set)
| member(sK1(sK6,sK7,sK11),sK11)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,sK11)
| ~ member(sK6,sK11)
| ~ member(sK6,X0_option_set)
| ( sK2(sK6,X0_option_set) != sK6 ) ),
inference(instantiation,[status(thm)],[c_220]) ).
tcf(c_668,plain,
subset(sK9,sK12),
inference(resolution,[status(thm)],[c_385,c_50]) ).
tcf(c_937,plain,
! [X0_option: option] :
( member(X0_option,sK12)
| ~ member(X0_option,sK10) ),
inference(resolution,[status(thm)],[c_304,c_89]) ).
tcf(c_944,plain,
! [X0_option_set: option_set] :
( subset(X0_option_set,sK12)
| ~ member(sK0(X0_option_set,sK12),sK10) ),
inference(resolution,[status(thm)],[c_937,c_49]) ).
tcf(c_951,plain,
subset(sK10,sK12),
inference(resolution,[status(thm)],[c_944,c_50]) ).
tcf(c_1420,plain,
! [X0_option_set: option_set] :
( ~ better(sK11,X0_option_set)
| ~ weakly_better(X0_option_set,sK11) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1503,plain,
! [X0_option_set: option_set] :
( weakly_better(X0_option_set,sK11)
| ~ subset(sK11,X0_option_set) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1504,plain,
( weakly_better(sK12,sK11)
| ~ subset(sK11,sK12) ),
inference(instantiation,[status(thm)],[c_1503]) ).
tcf(c_1506,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( weakly_better(X0_option_set,sK11)
| ~ weakly_better(X1_option_set,sK11)
| ~ weakly_better(X0_option_set,X1_option_set) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_1690,plain,
! [X0_option: option,X0_option_set: option_set] :
( better(sK11,X0_option_set)
| member(sK2(X0_option,X0_option_set),X0_option_set)
| member(sK1(X0_option,sK7,sK11),sK11)
| ~ member(sK7,sK11)
| ~ permitted_preference(sK7,X0_option)
| ~ permitted_preference(X0_option,sK7)
| ~ member(X0_option,sK11)
| ~ member(X0_option,X0_option_set) ),
inference(instantiation,[status(thm)],[c_603]) ).
tcf(c_4862,plain,
! [X0_option: option] :
( member(X0_option,sK12)
| ( X0_option = sK6 )
| ~ member(X0_option,sK11) ),
inference(resolution,[status(thm)],[c_305,c_88]) ).
tcf(c_5220,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(X0_option,sK12)
| member(X0_option,X0_option_set)
| ~ member(sK6,X0_option_set)
| ~ member(X0_option,sK11) ),
inference(resolution,[status(thm)],[c_4862,c_126]) ).
tcf(c_11592,plain,
! [X0_option: option] :
( member(X0_option,sK12)
| ~ member(X0_option,sK11) ),
inference(resolution,[status(thm)],[c_5220,c_87]) ).
tcf(c_11636,plain,
( ( sK2(sK6,sK9) = sK6 )
| ~ member(sK2(sK6,sK9),sK9) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_11637,plain,
( better(sK11,sK9)
| member(sK2(sK6,sK9),sK9)
| member(sK1(sK6,sK7,sK11),sK11)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,sK11)
| ~ member(sK6,sK11)
| ~ member(sK6,sK9) ),
inference(instantiation,[status(thm)],[c_1690]) ).
tcf(c_11660,plain,
! [X0_option_set: option_set] :
( subset(X0_option_set,sK12)
| ~ member(sK0(X0_option_set,sK12),sK11) ),
inference(resolution,[status(thm)],[c_11592,c_49]) ).
tcf(c_11774,plain,
subset(sK11,sK12),
inference(resolution,[status(thm)],[c_11660,c_50]) ).
tcf(c_15397,plain,
( better(sK11,sK9)
| member(sK1(sK6,sK7,sK11),sK11)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,sK11)
| ~ member(sK6,sK11)
| ~ member(sK6,sK9)
| ( sK2(sK6,sK9) != sK6 ) ),
inference(instantiation,[status(thm)],[c_638]) ).
tcf(c_15657,plain,
! [X0_option_set: option_set] :
( better(sK10,X0_option_set)
| weakly_better(X0_option_set,sK10)
| ~ weakly_better(sK10,X0_option_set) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_15658,plain,
! [X0_option_set: option_set] :
( weakly_better(X0_option_set,sK10)
| ~ subset(sK10,X0_option_set) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_15659,plain,
( weakly_better(sK12,sK10)
| ~ subset(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_15658]) ).
tcf(c_22329,plain,
( ~ better(sK11,sK9)
| ~ weakly_better(sK9,sK11) ),
inference(instantiation,[status(thm)],[c_1420]) ).
tcf(c_23468,plain,
! [X0_option_set: option_set] :
( better(X0_option_set,sK10)
| weakly_better(sK10,X0_option_set)
| ~ weakly_better(X0_option_set,sK10) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_23471,plain,
( better(sK12,sK10)
| weakly_better(sK10,sK12)
| ~ weakly_better(sK12,sK10) ),
inference(instantiation,[status(thm)],[c_23468]) ).
tcf(c_30986,plain,
! [X0_option_set: option_set] :
( weakly_better(sK9,sK11)
| ~ weakly_better(sK9,X0_option_set)
| ~ weakly_better(X0_option_set,sK11) ),
inference(instantiation,[status(thm)],[c_1506]) ).
tcf(c_30989,plain,
( weakly_better(sK9,sK11)
| ~ weakly_better(sK12,sK11)
| ~ weakly_better(sK9,sK12) ),
inference(instantiation,[status(thm)],[c_30986]) ).
tcf(c_34302,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option,X1_option_set: option_set] :
( weakly_better(X1_option_set,X0_option_set)
| member(sK2(X0_option,X0_option_set),X0_option_set)
| member(sK1(X0_option,X1_option,X1_option_set),X1_option_set)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X1_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set) ),
inference(superposition,[status(thm)],[c_59,c_52]) ).
tcf(c_35245,plain,
( better(sK10,sK9)
| weakly_better(sK9,sK10)
| ~ weakly_better(sK10,sK9) ),
inference(instantiation,[status(thm)],[c_15657]) ).
tcf(c_35459,plain,
! [X0_option: option,X0_option_set: option_set] :
( ( sK3(X0_option_set,sK12,X0_option) = sK8 )
| ( sK3(X0_option_set,sK12,X0_option) = sK7 )
| ( sK3(X0_option_set,sK12,X0_option) = sK6 )
| ~ better(sK12,X0_option_set)
| ~ subset(X0_option_set,sK12)
| ~ member(X0_option,X0_option_set) ),
inference(superposition,[status(thm)],[c_61,c_90]) ).
tcf(c_35922,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option] :
( weakly_better(X0_option_set,sK10)
| member(sK1(X0_option,X1_option,X0_option_set),X0_option_set)
| ( sK2(X0_option,sK10) = sK8 )
| ~ member(X0_option,sK10)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X0_option_set)
| ~ member(X0_option,X0_option_set) ),
inference(superposition,[status(thm)],[c_34302,c_83]) ).
tcf(c_35924,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option] :
( weakly_better(X0_option_set,sK12)
| member(sK1(X0_option,X1_option,X0_option_set),X0_option_set)
| ( sK2(X0_option,sK12) = sK8 )
| ( sK2(X0_option,sK12) = sK7 )
| ( sK2(X0_option,sK12) = sK6 )
| ~ member(X0_option,sK12)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option)
| ~ member(X1_option,X0_option_set)
| ~ member(X0_option,X0_option_set) ),
inference(superposition,[status(thm)],[c_34302,c_90]) ).
tcf(c_37869,plain,
! [X0_option: option,X1_option: option] :
( member(X0_option,sK10)
| ~ member(X1_option,sK10)
| ( X0_option != X1_option ) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_37872,plain,
! [X0_option: option,X1_option: option] :
( required_preference(X0_option,X1_option)
| ~ required_preference(sK8,sK6)
| ( X1_option != sK6 )
| ( X0_option != sK8 ) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_37875,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,X0_option_set)
| ~ member(sK6,X1_option_set)
| ~ member(sK6,X0_option_set)
| ( sK2(sK6,X1_option_set) != sK6 )
| ( sK1(sK6,sK7,X0_option_set) != sK6 ) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_37877,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| member(sK2(sK6,X1_option_set),X1_option_set)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,X0_option_set)
| ~ member(sK6,X1_option_set)
| ~ member(sK6,X0_option_set)
| ( sK1(sK6,sK7,X0_option_set) != sK6 ) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_37879,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,X0_option_set)
| ~ member(sK6,X1_option_set)
| ~ member(sK6,X0_option_set)
| ( sK2(sK6,X1_option_set) != sK6 )
| ( sK1(sK6,sK7,X0_option_set) != sK7 ) ),
inference(instantiation,[status(thm)],[c_56]) ).
tcf(c_37936,plain,
! [X0_option: option] :
( member(X0_option,sK10)
| ~ member(sK8,sK10)
| ( X0_option != sK8 ) ),
inference(instantiation,[status(thm)],[c_37869]) ).
tcf(c_37953,plain,
! [X0_option: option,X0_option_set: option_set,X1_option_set: option_set] :
( member(sK4(sK8,X0_option_set),X0_option_set)
| member(sK5(X0_option,X1_option_set),X1_option_set)
| ( sK4(sK8,X0_option_set) = sK8 )
| ( sK5(X0_option,X1_option_set) = X0_option )
| ~ better(X0_option_set,X1_option_set) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_37956,plain,
! [X0_option: option] :
( required_preference(sK8,X0_option)
| ~ required_preference(sK8,sK6)
| ( sK8 != sK8 )
| ( X0_option != sK6 ) ),
inference(instantiation,[status(thm)],[c_37872]) ).
tcf(c_38016,plain,
! [X0_option: option,X0_option_set: option_set,X1_option_set: option_set] :
( member(sK4(sK8,X1_option_set),X1_option_set)
| ( sK4(sK8,X1_option_set) = sK8 )
| ~ better(X1_option_set,X0_option_set)
| ~ member(sK5(X0_option,X0_option_set),X0_option_set)
| ( sK5(X0_option,X0_option_set) != X0_option ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_38028,plain,
! [X0_option: option,X1_option: option,X2_option: option] :
( required_preference(X0_option,X1_option)
| ~ required_preference(sK8,X2_option)
| ( X1_option != X2_option )
| ( X0_option != sK8 ) ),
inference(instantiation,[status(thm)],[c_128]) ).
tcf(c_38032,plain,
! [X0_option_set: option_set] :
( better(X0_option_set,sK9)
| member(sK2(sK6,sK9),sK9)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK6,sK9)
| ~ member(sK7,X0_option_set)
| ~ member(sK6,X0_option_set)
| ( sK1(sK6,sK7,X0_option_set) != sK6 ) ),
inference(instantiation,[status(thm)],[c_37877]) ).
tcf(c_38094,plain,
! [X0_option: option,X0_option_set: option_set,X1_option_set: option_set] :
( better(X0_option_set,X1_option_set)
| member(sK2(X0_option,X1_option_set),X1_option_set)
| ~ permitted_preference(sK7,X0_option)
| ~ permitted_preference(X0_option,sK7)
| ~ member(sK7,X0_option_set)
| ~ member(X0_option,X1_option_set)
| ~ member(X0_option,X0_option_set)
| ( sK1(X0_option,sK7,X0_option_set) != sK7 ) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_38138,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(sK5(X0_option,sK9),sK9)
| member(sK4(sK8,X0_option_set),X0_option_set)
| ( sK5(X0_option,sK9) = X0_option )
| ( sK4(sK8,X0_option_set) = sK8 )
| ~ better(X0_option_set,sK9) ),
inference(instantiation,[status(thm)],[c_37953]) ).
tcf(c_38140,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option] :
( member(sK5(X1_option,sK9),sK9)
| ( sK5(X1_option,sK9) = X1_option )
| ~ better(X0_option_set,sK9)
| ~ member(sK4(X0_option,X0_option_set),X0_option_set)
| ( sK4(X0_option,X0_option_set) != X0_option ) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_38141,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option] :
( ~ better(X0_option_set,sK9)
| ~ member(sK5(X1_option,sK9),sK9)
| ~ member(sK4(X0_option,X0_option_set),X0_option_set)
| ( sK5(X1_option,sK9) != X1_option )
| ( sK4(X0_option,X0_option_set) != X0_option ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_38227,plain,
! [X0_option: option,X1_option: option] :
( required_preference(sK8,X0_option)
| ~ required_preference(sK8,X1_option)
| ( sK8 != sK8 )
| ( X0_option != X1_option ) ),
inference(instantiation,[status(thm)],[c_38028]) ).
tcf(c_38237,plain,
! [X0_option: option,X0_option_set: option_set,X1_option: option] :
( member(sK5(X0_option,X0_option_set),X0_option_set)
| ~ member(X1_option,X0_option_set)
| ( sK5(X0_option,X0_option_set) != X1_option ) ),
inference(instantiation,[status(thm)],[c_126]) ).
tcf(c_38302,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( weakly_better(sK9,X1_option_set)
| ~ weakly_better(sK9,X0_option_set)
| ~ weakly_better(X0_option_set,X1_option_set) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_38435,plain,
! [X0_option: option,X0_option_set: option_set] :
( ( sK5(X0_option,X0_option_set) = sK6 )
| ~ member(sK5(X0_option,X0_option_set),sK9) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_38479,plain,
! [X0_option: option] :
( member(sK5(X0_option,sK9),sK9)
| ~ member(X0_option,sK9)
| ( sK5(X0_option,sK9) != X0_option ) ),
inference(instantiation,[status(thm)],[c_38237]) ).
tcf(c_38480,plain,
( member(sK5(sK6,sK9),sK9)
| ~ member(sK6,sK9)
| ( sK5(sK6,sK9) != sK6 ) ),
inference(instantiation,[status(thm)],[c_38479]) ).
tcf(c_38910,plain,
! [X0_option_set: option_set] :
( weakly_better(X0_option_set,sK9)
| ~ subset(sK9,X0_option_set) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_38911,plain,
( weakly_better(sK12,sK9)
| ~ subset(sK9,sK12) ),
inference(instantiation,[status(thm)],[c_38910]) ).
tcf(c_38913,plain,
! [X0_option_set: option_set,X1_option_set: option_set] :
( weakly_better(X0_option_set,sK9)
| ~ weakly_better(X1_option_set,sK9)
| ~ weakly_better(X0_option_set,X1_option_set) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_39058,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(sK4(sK8,X0_option_set),X0_option_set)
| ( sK4(sK8,X0_option_set) = sK8 )
| ~ better(X0_option_set,sK9)
| ~ member(sK5(X0_option,sK9),sK9)
| ( sK5(X0_option,sK9) != X0_option ) ),
inference(instantiation,[status(thm)],[c_38016]) ).
tcf(c_39062,plain,
! [X0_option: option] :
( ( sK5(X0_option,sK9) = sK6 )
| ~ member(sK5(X0_option,sK9),sK9) ),
inference(instantiation,[status(thm)],[c_38435]) ).
tcf(c_39063,plain,
( ( sK5(sK6,sK9) = sK6 )
| ~ member(sK5(sK6,sK9),sK9) ),
inference(instantiation,[status(thm)],[c_39062]) ).
tcf(c_39152,plain,
! [X0_option_set: option_set] :
( member(sK5(sK6,sK9),sK9)
| member(sK4(sK8,X0_option_set),X0_option_set)
| ( sK5(sK6,sK9) = sK6 )
| ( sK4(sK8,X0_option_set) = sK8 )
| ~ better(X0_option_set,sK9) ),
inference(instantiation,[status(thm)],[c_38138]) ).
tcf(c_39372,plain,
! [X0_option: option,X0_option_set: option_set] :
( ~ better(X0_option_set,sK10)
| ~ member(X0_option,sK10)
| ~ subset(sK10,X0_option_set)
| ~ member(sK3(sK10,X0_option_set,X0_option),sK10) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_39373,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(sK3(sK10,X0_option_set,X0_option),X0_option_set)
| ~ better(X0_option_set,sK10)
| ~ member(X0_option,sK10)
| ~ subset(sK10,X0_option_set) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_39374,plain,
! [X0_option: option,X0_option_set: option_set] :
( ~ better(X0_option_set,sK10)
| ~ member(X0_option,sK10)
| ~ subset(sK10,X0_option_set)
| ~ required_preference(X0_option,sK3(sK10,X0_option_set,X0_option)) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_39459,plain,
! [X0_option: option] :
( ( sK4(X0_option,sK10) = sK8 )
| ~ member(sK4(X0_option,sK10),sK10) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_40291,plain,
! [X0_option: option,X0_option_set: option_set] :
( better(X0_option_set,sK9)
| member(sK2(X0_option,sK9),sK9)
| ~ permitted_preference(sK7,X0_option)
| ~ permitted_preference(X0_option,sK7)
| ~ member(sK7,X0_option_set)
| ~ member(X0_option,sK9)
| ~ member(X0_option,X0_option_set)
| ( sK1(X0_option,sK7,X0_option_set) != sK7 ) ),
inference(instantiation,[status(thm)],[c_38094]) ).
tcf(c_40724,plain,
! [X0_option_set: option_set] :
( member(sK3(sK10,X0_option_set,sK8),X0_option_set)
| ~ member(sK8,sK10)
| ~ better(X0_option_set,sK10)
| ~ subset(sK10,X0_option_set) ),
inference(instantiation,[status(thm)],[c_39373]) ).
tcf(c_40725,plain,
( member(sK3(sK10,sK12,sK8),sK12)
| ~ better(sK12,sK10)
| ~ member(sK8,sK10)
| ~ subset(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_40724]) ).
tcf(c_40746,plain,
( member(sK5(sK6,sK9),sK9)
| member(sK4(sK8,sK10),sK10)
| ( sK5(sK6,sK9) = sK6 )
| ( sK4(sK8,sK10) = sK8 )
| ~ better(sK10,sK9) ),
inference(instantiation,[status(thm)],[c_39152]) ).
tcf(c_40781,plain,
! [X0_option_set: option_set] :
( ~ member(sK8,sK10)
| ~ better(X0_option_set,sK10)
| ~ subset(sK10,X0_option_set)
| ~ required_preference(sK8,sK3(sK10,X0_option_set,sK8)) ),
inference(instantiation,[status(thm)],[c_39374]) ).
tcf(c_40782,plain,
! [X0_option: option,X0_option_set: option_set] :
( required_preference(sK8,sK3(sK10,X0_option_set,sK8))
| ~ required_preference(sK8,X0_option)
| ( sK8 != sK8 )
| ( sK3(sK10,X0_option_set,sK8) != X0_option ) ),
inference(instantiation,[status(thm)],[c_38227]) ).
tcf(c_40783,plain,
! [X0_option_set: option_set] :
( required_preference(sK8,sK3(sK10,X0_option_set,sK8))
| ~ required_preference(sK8,sK6)
| ( sK8 != sK8 )
| ( sK3(sK10,X0_option_set,sK8) != sK6 ) ),
inference(instantiation,[status(thm)],[c_37956]) ).
tcf(c_40784,plain,
( ~ better(sK12,sK10)
| ~ member(sK8,sK10)
| ~ subset(sK10,sK12)
| ~ required_preference(sK8,sK3(sK10,sK12,sK8)) ),
inference(instantiation,[status(thm)],[c_40781]) ).
tcf(c_40785,plain,
( required_preference(sK8,sK3(sK10,sK12,sK8))
| ~ required_preference(sK8,sK6)
| ( sK8 != sK8 )
| ( sK3(sK10,sK12,sK8) != sK6 ) ),
inference(instantiation,[status(thm)],[c_40783]) ).
tcf(c_41052,plain,
! [X0_option: option,X0_option_set: option_set] :
( ~ better(X0_option_set,sK9)
| ~ member(sK5(X0_option,sK9),sK9)
| ~ member(sK4(sK8,X0_option_set),X0_option_set)
| ( sK5(X0_option,sK9) != X0_option )
| ( sK4(sK8,X0_option_set) != sK8 ) ),
inference(instantiation,[status(thm)],[c_38141]) ).
tcf(c_41053,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(sK5(X0_option,sK9),sK9)
| ( sK5(X0_option,sK9) = X0_option )
| ~ better(X0_option_set,sK9)
| ~ member(sK4(sK8,X0_option_set),X0_option_set)
| ( sK4(sK8,X0_option_set) != sK8 ) ),
inference(instantiation,[status(thm)],[c_38140]) ).
tcf(c_41062,plain,
! [X0_option: option,X0_option_set: option_set] :
( member(sK4(X0_option,X0_option_set),sK10)
| ~ member(sK8,sK10)
| ( sK4(X0_option,X0_option_set) != sK8 ) ),
inference(instantiation,[status(thm)],[c_37936]) ).
tcf(c_41521,plain,
( ( sK4(sK8,sK10) = sK8 )
| ~ member(sK4(sK8,sK10),sK10) ),
inference(instantiation,[status(thm)],[c_39459]) ).
tcf(c_41524,plain,
! [X0_option: option] :
( member(sK4(sK8,sK10),sK10)
| ( sK4(sK8,sK10) = sK8 )
| ~ better(sK10,sK9)
| ~ member(sK5(X0_option,sK9),sK9)
| ( sK5(X0_option,sK9) != X0_option ) ),
inference(instantiation,[status(thm)],[c_39058]) ).
tcf(c_41530,plain,
( member(sK4(sK8,sK10),sK10)
| ( sK4(sK8,sK10) = sK8 )
| ~ better(sK10,sK9)
| ~ member(sK5(sK6,sK9),sK9)
| ( sK5(sK6,sK9) != sK6 ) ),
inference(instantiation,[status(thm)],[c_41524]) ).
tcf(c_41562,plain,
! [X0_option_set: option_set] :
( weakly_better(sK10,sK9)
| ~ weakly_better(sK10,X0_option_set)
| ~ weakly_better(X0_option_set,sK9) ),
inference(instantiation,[status(thm)],[c_38913]) ).
tcf(c_41566,plain,
( weakly_better(sK10,sK9)
| ~ weakly_better(sK12,sK9)
| ~ weakly_better(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_41562]) ).
tcf(c_42135,plain,
! [X0_option_set: option_set] :
( ( sK3(sK10,X0_option_set,sK8) = sK8 )
| ( sK3(sK10,X0_option_set,sK8) = sK7 )
| ( sK3(sK10,X0_option_set,sK8) = sK6 )
| ~ member(sK3(sK10,X0_option_set,sK8),sK12) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_42140,plain,
( ( sK3(sK10,sK12,sK8) = sK8 )
| ( sK3(sK10,sK12,sK8) = sK7 )
| ( sK3(sK10,sK12,sK8) = sK6 )
| ~ member(sK3(sK10,sK12,sK8),sK12) ),
inference(instantiation,[status(thm)],[c_42135]) ).
tcf(c_45329,plain,
( member(sK4(sK8,sK10),sK10)
| ~ member(sK8,sK10)
| ( sK4(sK8,sK10) != sK8 ) ),
inference(instantiation,[status(thm)],[c_41062]) ).
tcf(c_47603,plain,
( better(sK11,sK9)
| member(sK2(sK6,sK9),sK9)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,sK11)
| ~ member(sK6,sK11)
| ~ member(sK6,sK9)
| ( sK1(sK6,sK7,sK11) != sK6 ) ),
inference(instantiation,[status(thm)],[c_38032]) ).
tcf(c_49442,plain,
! [X0_option_set: option_set] :
( required_preference(sK8,sK3(sK10,X0_option_set,sK8))
| ~ required_preference(sK8,sK7)
| ( sK8 != sK8 )
| ( sK3(sK10,X0_option_set,sK8) != sK7 ) ),
inference(instantiation,[status(thm)],[c_40782]) ).
tcf(c_49443,plain,
( required_preference(sK8,sK3(sK10,sK12,sK8))
| ~ required_preference(sK8,sK7)
| ( sK8 != sK8 )
| ( sK3(sK10,sK12,sK8) != sK7 ) ),
inference(instantiation,[status(thm)],[c_49442]) ).
tcf(c_51583,plain,
( ( sK3(sK10,sK12,sK8) = sK8 )
| ( sK3(sK10,sK12,sK8) = sK7 )
| ( sK3(sK10,sK12,sK8) = sK6 )
| ~ better(sK12,sK10)
| ~ subset(sK10,sK12) ),
inference(superposition,[status(thm)],[c_82,c_35459]) ).
tcf(c_51613,plain,
( ( sK3(sK10,sK12,sK8) = sK8 )
| ~ better(sK12,sK10) ),
inference(global_subsumption_just,[status(thm)],[c_51583,c_82,c_72,c_71,c_133,c_951,c_40725,c_40784,c_40785,c_42140,c_49443]) ).
tcf(c_53640,plain,
( better(sK11,sK9)
| member(sK2(sK6,sK9),sK9)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,sK11)
| ~ member(sK6,sK11)
| ~ member(sK6,sK9)
| ( sK1(sK6,sK7,sK11) != sK7 ) ),
inference(instantiation,[status(thm)],[c_40291]) ).
tcf(c_57881,plain,
! [X0_option: option,X1_option: option] :
( weakly_better(sK12,sK10)
| ( sK2(X0_option,sK10) = sK8 )
| ( sK1(X0_option,X1_option,sK12) = sK8 )
| ( sK1(X0_option,X1_option,sK12) = sK7 )
| ( sK1(X0_option,X1_option,sK12) = sK6 )
| ~ member(X1_option,sK12)
| ~ member(X0_option,sK12)
| ~ member(X0_option,sK10)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option) ),
inference(superposition,[status(thm)],[c_35922,c_90]) ).
tcf(c_57917,plain,
weakly_better(sK12,sK10),
inference(global_subsumption_just,[status(thm)],[c_57881,c_951,c_15659]) ).
tcf(c_58320,plain,
! [X0_option_set: option_set] :
( better(X0_option_set,sK9)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK6,sK9)
| ~ member(sK7,X0_option_set)
| ~ member(sK6,X0_option_set)
| ( sK2(sK6,sK9) != sK6 )
| ( sK1(sK6,sK7,X0_option_set) != sK7 ) ),
inference(instantiation,[status(thm)],[c_37879]) ).
tcf(c_58321,plain,
! [X0_option_set: option_set] :
( better(X0_option_set,sK9)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK6,sK9)
| ~ member(sK7,X0_option_set)
| ~ member(sK6,X0_option_set)
| ( sK2(sK6,sK9) != sK6 )
| ( sK1(sK6,sK7,X0_option_set) != sK6 ) ),
inference(instantiation,[status(thm)],[c_37875]) ).
tcf(c_59291,plain,
! [X0_option_set: option_set] :
( member(sK3(sK10,X0_option_set,sK8),sK10)
| ~ member(sK8,sK10)
| ( sK3(sK10,X0_option_set,sK8) != sK8 ) ),
inference(instantiation,[status(thm)],[c_37936]) ).
tcf(c_59294,plain,
( member(sK3(sK10,sK12,sK8),sK10)
| ~ member(sK8,sK10)
| ( sK3(sK10,sK12,sK8) != sK8 ) ),
inference(instantiation,[status(thm)],[c_59291]) ).
tcf(c_61368,plain,
( better(sK11,sK9)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,sK11)
| ~ member(sK6,sK11)
| ~ member(sK6,sK9)
| ( sK2(sK6,sK9) != sK6 )
| ( sK1(sK6,sK7,sK11) != sK6 ) ),
inference(instantiation,[status(thm)],[c_58321]) ).
tcf(c_62627,plain,
( better(sK12,sK10)
| weakly_better(sK10,sK12) ),
inference(superposition,[status(thm)],[c_57917,c_51]) ).
tcf(c_62849,plain,
( weakly_better(sK10,sK12)
| ( sK3(sK10,sK12,sK8) = sK8 ) ),
inference(superposition,[status(thm)],[c_62627,c_51613]) ).
tcf(c_62910,plain,
( better(sK11,sK9)
| ~ permitted_preference(sK7,sK6)
| ~ permitted_preference(sK6,sK7)
| ~ member(sK7,sK11)
| ~ member(sK6,sK11)
| ~ member(sK6,sK9)
| ( sK2(sK6,sK9) != sK6 )
| ( sK1(sK6,sK7,sK11) != sK7 ) ),
inference(instantiation,[status(thm)],[c_58320]) ).
tcf(c_65793,plain,
! [X0_option_set: option_set] :
( ~ member(sK8,sK10)
| ~ better(X0_option_set,sK10)
| ~ subset(sK10,X0_option_set)
| ~ member(sK3(sK10,X0_option_set,sK8),sK10) ),
inference(instantiation,[status(thm)],[c_39372]) ).
tcf(c_65794,plain,
( ~ better(sK12,sK10)
| ~ member(sK8,sK10)
| ~ subset(sK10,sK12)
| ~ member(sK3(sK10,sK12,sK8),sK10) ),
inference(instantiation,[status(thm)],[c_65793]) ).
tcf(c_65802,plain,
! [X0_option: option,X1_option: option] :
( weakly_better(sK10,sK12)
| ( sK2(X0_option,sK12) = sK8 )
| ( sK2(X0_option,sK12) = sK7 )
| ( sK2(X0_option,sK12) = sK6 )
| ( sK1(X0_option,X1_option,sK10) = sK8 )
| ~ member(X1_option,sK10)
| ~ member(X0_option,sK12)
| ~ member(X0_option,sK10)
| ~ permitted_preference(X1_option,X0_option)
| ~ permitted_preference(X0_option,X1_option) ),
inference(superposition,[status(thm)],[c_35924,c_83]) ).
tcf(c_65805,plain,
weakly_better(sK10,sK12),
inference(global_subsumption_just,[status(thm)],[c_65802,c_82,c_951,c_15659,c_23471,c_59294,c_62849,c_65794]) ).
tcf(c_72402,plain,
! [X0_option: option] :
( member(sK5(X0_option,sK9),sK9)
| ( sK5(X0_option,sK9) = X0_option )
| ~ better(sK10,sK9)
| ~ member(sK4(sK8,sK10),sK10)
| ( sK4(sK8,sK10) != sK8 ) ),
inference(instantiation,[status(thm)],[c_41053]) ).
tcf(c_72403,plain,
! [X0_option: option] :
( ~ better(sK10,sK9)
| ~ member(sK4(sK8,sK10),sK10)
| ~ member(sK5(X0_option,sK9),sK9)
| ( sK4(sK8,sK10) != sK8 )
| ( sK5(X0_option,sK9) != X0_option ) ),
inference(instantiation,[status(thm)],[c_41052]) ).
tcf(c_72407,plain,
( ~ better(sK10,sK9)
| ~ member(sK5(sK6,sK9),sK9)
| ~ member(sK4(sK8,sK10),sK10)
| ( sK5(sK6,sK9) != sK6 )
| ( sK4(sK8,sK10) != sK8 ) ),
inference(instantiation,[status(thm)],[c_72403]) ).
tcf(c_72408,plain,
( member(sK5(sK6,sK9),sK9)
| ( sK5(sK6,sK9) = sK6 )
| ~ better(sK10,sK9)
| ~ member(sK4(sK8,sK10),sK10)
| ( sK4(sK8,sK10) != sK8 ) ),
inference(instantiation,[status(thm)],[c_72402]) ).
tcf(c_76774,plain,
! [X0_option_set: option_set] :
( weakly_better(sK9,X0_option_set)
| ~ weakly_better(sK9,sK10)
| ~ weakly_better(sK10,X0_option_set) ),
inference(instantiation,[status(thm)],[c_38302]) ).
tcf(c_76776,plain,
( weakly_better(sK9,sK12)
| ~ weakly_better(sK10,sK12)
| ~ weakly_better(sK9,sK10) ),
inference(instantiation,[status(thm)],[c_76774]) ).
tcf(c_80664,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_76776,c_72408,c_72407,c_65805,c_62910,c_61368,c_53640,c_47603,c_45329,c_41566,c_41530,c_41521,c_40746,c_39063,c_38911,c_38480,c_35245,c_30989,c_22329,c_15397,c_11774,c_11637,c_11636,c_1504,c_668,c_637,c_69,c_70,c_80,c_82,c_84,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI044_1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 06:08:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 57.78/9.84 % SZS status Started for theBenchmark.p
% 57.78/9.84 % SZS status Unsatisfiable for theBenchmark.p
% 57.78/9.84
% 57.78/9.84 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 57.78/9.84
% 57.78/9.84 % ------ iProver source info
% 57.78/9.84
% 57.78/9.84 % git: date: 2026-07-19 20:42:38 +0200
% 57.78/9.84 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 57.78/9.84 % git: non_committed_changes: false
% 57.78/9.84
% 57.78/9.84 % ------ Parsing...
% 57.78/9.84 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 57.78/9.84
% 57.78/9.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 57.78/9.84
% 57.78/9.84 % ------ Preprocessing...%
% 57.78/9.84
% 57.78/9.84 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 57.78/9.84 % ------ Proving...
% 57.78/9.84 % ------ Problem Properties
% 57.78/9.84
% 57.78/9.84 %
% 57.78/9.84 % clauses 35
% 57.78/9.84 % conjectures 0
% 57.78/9.84 % EPR 20
% 57.78/9.84 % Horn 24
% 57.78/9.84 % unary 11
% 57.78/9.84 % binary 7
% 57.78/9.84 % lits 118
% 57.78/9.84 % lits eq 22
% 57.78/9.84 % fd_pure 0
% 57.78/9.84 % fd_pseudo 0
% 57.78/9.84 % fd_cond 4
% 57.78/9.84 % fd_pseudo_cond 0
% 57.78/9.84 % AC symbols 0
% 57.78/9.84
% 57.78/9.84 % ------ Input Options Time Limit: Unbounded
% 57.78/9.84
% 57.78/9.84
% 57.78/9.84 % ------
% 57.78/9.84 % Current options:
% 57.78/9.84 % ------
% 57.78/9.84
% 57.78/9.84
% 57.78/9.84 %
% 57.78/9.84
% 57.78/9.84 % ------ Proving...
% 57.78/9.84 %
% 57.78/9.84
% 57.78/9.84 % SZS status Unsatisfiable for theBenchmark.p
% 57.78/9.84
% 57.78/9.84 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 57.78/9.85
% 57.78/9.85
%------------------------------------------------------------------------------