%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET563-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : Sat Jun 21 05:25:52 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 16
% Syntax : Number of formulae : 36 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 109 ( 51 ~; 44 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 78 ( 72 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
tff(subclass_type,type,
subclass: ( $i * $i ) > $o ).
tff(domain_of_type,type,
domain_of: $i > $i ).
tff(xf2_type,type,
xf2: $i ).
tff(range_of_type,type,
range_of: $i > $i ).
tff(xh1_type,type,
xh1: $i ).
tff(xh2_type,type,
xh2: $i ).
tff(compatible_type,type,
compatible: ( $i * $i * $i ) > $o ).
tff(xf3_type,type,
xf3: $i ).
tff(xf1_type,type,
xf1: $i ).
tff(1,plain,
( compatible(xh2,xf2,xf3)
<=> compatible(xh2,xf2,xf3) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
compatible(xh2,xf2,xf3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_function_property3_2) ).
tff(3,plain,
compatible(xh2,xf2,xf3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Xf2: $i,Xf1: $i,Xh: $i] :
refl(( ( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
<=> ( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
<=> ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
<=> ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible2) ).
tff(8,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
| ~ compatible(xh2,xf2,xf3)
| ( domain_of(domain_of(xf2)) = domain_of(xh2) ) )
<=> ( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
| ~ compatible(xh2,xf2,xf3)
| ( domain_of(domain_of(xf2)) = domain_of(xh2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
| ~ compatible(xh2,xf2,xf3)
| ( domain_of(domain_of(xf2)) = domain_of(xh2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
| ~ compatible(xh2,xf2,xf3)
| ( domain_of(domain_of(xf2)) = domain_of(xh2) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
domain_of(domain_of(xf2)) = domain_of(xh2),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( subclass(range_of(xh1),domain_of(domain_of(xf2)))
<=> subclass(range_of(xh1),domain_of(xh2)) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( subclass(range_of(xh1),domain_of(xh2))
<=> subclass(range_of(xh1),domain_of(domain_of(xf2))) ),
inference(symmetry,[status(thm)],[15]) ).
tff(17,plain,
( ~ subclass(range_of(xh1),domain_of(xh2))
<=> ~ subclass(range_of(xh1),domain_of(domain_of(xf2))) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ~ subclass(range_of(xh1),domain_of(xh2))
<=> ~ subclass(range_of(xh1),domain_of(xh2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
~ subclass(range_of(xh1),domain_of(xh2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_function_property3_3) ).
tff(20,plain,
~ subclass(range_of(xh1),domain_of(xh2)),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
~ subclass(range_of(xh1),domain_of(domain_of(xf2))),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( compatible(xh1,xf1,xf2)
<=> compatible(xh1,xf1,xf2) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
compatible(xh1,xf1,xf2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_function_property3_1) ).
tff(24,plain,
compatible(xh1,xf1,xf2),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [Xf2: $i,Xf1: $i,Xh: $i] :
refl(( ( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) )
<=> ( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) )
<=> ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) )
<=> ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',compatible3) ).
tff(29,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) )
| ~ compatible(xh1,xf1,xf2)
| subclass(range_of(xh1),domain_of(domain_of(xf2))) )
<=> ( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) )
| ~ compatible(xh1,xf1,xf2)
| subclass(range_of(xh1),domain_of(domain_of(xf2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) )
| ~ compatible(xh1,xf1,xf2)
| subclass(range_of(xh1),domain_of(domain_of(xf2))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| subclass(range_of(Xh),domain_of(domain_of(Xf2))) )
| ~ compatible(xh1,xf1,xf2)
| subclass(range_of(xh1),domain_of(domain_of(xf2))) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
subclass(range_of(xh1),domain_of(domain_of(xf2))),
inference(unit_resolution,[status(thm)],[34,31,24]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET563-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 05:28:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------