%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET558-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 35 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 92 ( 45 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 103 ( 48 ~; 44 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 ( 48 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(domain_of_type,type,
domain_of: $i > $i ).
tff(xf1_type,type,
xf1: $i ).
tff(cross_product_type,type,
cross_product: ( $i * $i ) > $i ).
tff(xh_type,type,
xh: $i ).
tff(operation_type,type,
operation: $i > $o ).
tff(compatible_type,type,
compatible: ( $i * $i * $i ) > $o ).
tff(xf2_type,type,
xf2: $i ).
tff(1,plain,
( operation(xf1)
<=> operation(xf1) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
operation(xf1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_1) ).
tff(3,plain,
operation(xf1),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Xf: $i] :
refl(( ( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) )
<=> ( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) )
<=> ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) )
<=> ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',operation2) ).
tff(8,plain,
! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) )
| ~ operation(xf1)
| ( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1) ) )
<=> ( ~ ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) )
| ~ operation(xf1)
| ( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) )
| ~ operation(xf1)
| ( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [Xf: $i] :
( ~ operation(Xf)
| ( cross_product(domain_of(domain_of(Xf)),domain_of(domain_of(Xf))) = domain_of(Xf) ) )
| ~ operation(xf1)
| ( cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))) = domain_of(xf1),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( compatible(xh,xf1,xf2)
<=> compatible(xh,xf1,xf2) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
compatible(xh,xf1,xf2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_2) ).
tff(17,plain,
compatible(xh,xf1,xf2),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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(22,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ compatible(Xh,Xf1,Xf2)
| ( domain_of(domain_of(Xf1)) = domain_of(Xh) ) )
| ~ 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) ) )
| ~ compatible(xh,xf1,xf2)
| ( domain_of(domain_of(xf1)) = domain_of(xh) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ 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(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [Xf2: $i,Xf1: $i,Xh: $i] :
( ~ 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(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
domain_of(domain_of(xf1)) = domain_of(xh),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
domain_of(xh) = domain_of(domain_of(xf1)),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
cross_product(domain_of(xh),domain_of(xh)) = cross_product(domain_of(domain_of(xf1)),domain_of(domain_of(xf1))),
inference(monotonicity,[status(thm)],[29,29]) ).
tff(31,plain,
cross_product(domain_of(xh),domain_of(xh)) = domain_of(xf1),
inference(transitivity,[status(thm)],[30,14]) ).
tff(32,plain,
( ( cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1) )
<=> ( cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_compatible_functions_alternate_defn1_3) ).
tff(34,plain,
cross_product(domain_of(xh),domain_of(xh)) != domain_of(xf1),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
$false,
inference(unit_resolution,[status(thm)],[34,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET558-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 05:26:52 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------