%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 : Sun Sep 27 07:23:24 AM UTC 2026
% Result : Theorem 16.84s 3.21s
% Output : CNFRefutation 16.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 18 unt; 0 def)
% Number of atoms : 104 ( 36 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 92 ( 40 ~; 42 |; 4 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 10 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(homomorphism1,axiom,
! [X0] :
( 'group$umember'(X0,f)
=> 'group$umember'(phi(X0),h) ) ).
fof(homomorphism2,axiom,
! [X0,X1] :
( ( 'group$umember'(X1,f)
& 'group$umember'(X0,f) )
=> multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1)) ) ).
fof(surjective,axiom,
! [X0] :
( 'group$umember'(X0,h)
=> ? [X1] :
( phi(X1) = X0
& 'group$umember'(X1,f) ) ) ).
fof(left_zero,axiom,
! [X0,X1] :
( 'left$uzero'(X0,X1)
<=> ( ! [X2] :
( 'group$umember'(X2,X0)
=> multiply(X0,X1,X2) = X1 )
& 'group$umember'(X1,X0) ) ) ).
fof(left_zero_for_f,hypothesis,
'left$uzero'(f,'f$uleft$uzero') ).
fof(total_function,axiom,
! [X0,X1,X2] :
( ( 'group$umember'(X2,X0)
& 'group$umember'(X1,X0) )
=> 'group$umember'(multiply(X0,X1,X2),X0) ) ).
fof(prove_left_zero_h,conjecture,
'left$uzero'(h,phi('f$uleft$uzero')) ).
fof(negated_conjecture,negated_conjecture,
~ 'left$uzero'(h,phi('f$uleft$uzero')),
inference(negate_conjecture,[status(cth)],[prove_left_zero_h]) ).
cnf(c0,plain,
( 'group$umember'(phi(X0),h)
| ~ 'group$umember'(X0,f) ),
inference(clausification,[status(esa)],[homomorphism1]) ).
cnf(c1,plain,
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ 'group$umember'(X1,f)
| ~ 'group$umember'(X0,f) ),
inference(clausification,[status(esa)],[homomorphism2]) ).
cnf(c2,plain,
( 'group$umember'(sK4(X0),f)
| ~ 'group$umember'(X0,h) ),
inference(clausification,[status(esa)],[surjective]) ).
cnf(c3,plain,
( phi(sK4(X0)) = X0
| ~ 'group$umember'(X0,h) ),
inference(clausification,[status(esa)],[surjective]) ).
cnf(c4,plain,
( 'group$umember'(X1,X0)
| ~ 'left$uzero'(X0,X1) ),
inference(clausification,[status(esa)],[left_zero]) ).
cnf(c5,plain,
( multiply(X0,X1,X2) = X1
| ~ 'group$umember'(X2,X0)
| ~ 'left$uzero'(X0,X1) ),
inference(clausification,[status(esa)],[left_zero]) ).
cnf(c6,plain,
( 'group$umember'(sK8(X0,X1),X0)
| ~ 'group$umember'(X1,X0)
| 'left$uzero'(X0,X1) ),
inference(clausification,[status(esa)],[left_zero]) ).
cnf(c7,plain,
( multiply(X0,X1,sK8(X0,X1)) != X1
| ~ 'group$umember'(X1,X0)
| 'left$uzero'(X0,X1) ),
inference(clausification,[status(esa)],[left_zero]) ).
cnf(c8,plain,
'left$uzero'(f,'f$uleft$uzero'),
inference(clausification,[status(esa)],[left_zero_for_f]) ).
cnf(c9,plain,
( 'group$umember'(multiply(X1,X0,X2),X1)
| ~ 'group$umember'(X2,X1)
| ~ 'group$umember'(X0,X1) ),
inference(clausification,[status(esa)],[total_function]) ).
cnf(c11,plain,
~ 'left$uzero'(h,phi('f$uleft$uzero')),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'group$umember'(X0,f)
| multiply(f,'f$uleft$uzero',X0) = 'f$uleft$uzero' ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(d1,plain,
( ~ 'group$umember'(X0,h)
| multiply(f,'f$uleft$uzero',sK4(X0)) = 'f$uleft$uzero' ),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
( 'left$uzero'(h,X0)
| ~ 'group$umember'(X0,h)
| multiply(f,'f$uleft$uzero',sK4(sK8(h,X0))) = 'f$uleft$uzero' ),
inference(resolution,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
( ~ 'group$umember'(X0,f)
| 'left$uzero'(h,phi(X0))
| multiply(f,'f$uleft$uzero',sK4(sK8(h,phi(X0)))) = 'f$uleft$uzero' ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( ~ 'group$umember'('f$uleft$uzero',f)
| multiply(f,'f$uleft$uzero',sK4(sK8(h,phi('f$uleft$uzero')))) = 'f$uleft$uzero' ),
inference(resolution,[status(thm)],[d3,c11]) ).
cnf(d5,plain,
'group$umember'('f$uleft$uzero',f),
inference(resolution,[status(thm)],[c4,c8]) ).
cnf(d6,plain,
multiply(f,'f$uleft$uzero',sK4(sK8(h,phi('f$uleft$uzero')))) = 'f$uleft$uzero',
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( phi(sK4(sK8(h,X0))) = sK8(h,X0)
| 'left$uzero'(h,X0)
| ~ 'group$umember'(X0,h) ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d8,plain,
( ~ 'group$umember'(X0,f)
| 'left$uzero'(h,phi(X0))
| phi(sK4(sK8(h,phi(X0)))) = sK8(h,phi(X0)) ),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
( ~ 'group$umember'('f$uleft$uzero',f)
| phi(sK4(sK8(h,phi('f$uleft$uzero')))) = sK8(h,phi('f$uleft$uzero')) ),
inference(resolution,[status(thm)],[d8,c11]) ).
cnf(d10,plain,
phi(sK4(sK8(h,phi('f$uleft$uzero')))) = sK8(h,phi('f$uleft$uzero')),
inference(resolution,[status(thm)],[d5,d9]) ).
cnf(d11,plain,
( ~ 'group$umember'(X0,f)
| multiply(h,phi('f$uleft$uzero'),phi(X0)) = phi(multiply(f,'f$uleft$uzero',X0)) ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d12,plain,
( ~ 'group$umember'(X0,h)
| multiply(h,phi('f$uleft$uzero'),phi(sK4(X0))) = phi(multiply(f,'f$uleft$uzero',sK4(X0))) ),
inference(resolution,[status(thm)],[d11,c2]) ).
cnf(d13,plain,
( 'left$uzero'(h,X0)
| ~ 'group$umember'(X0,h)
| multiply(h,phi('f$uleft$uzero'),phi(sK4(sK8(h,X0)))) = phi(multiply(f,'f$uleft$uzero',sK4(sK8(h,X0)))) ),
inference(resolution,[status(thm)],[d12,c6]) ).
cnf(d14,plain,
( ~ 'group$umember'(X0,f)
| 'left$uzero'(h,phi(X0))
| multiply(h,phi('f$uleft$uzero'),phi(sK4(sK8(h,phi(X0))))) = phi(multiply(f,'f$uleft$uzero',sK4(sK8(h,phi(X0))))) ),
inference(resolution,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
( ~ 'group$umember'('f$uleft$uzero',f)
| multiply(h,phi('f$uleft$uzero'),phi(sK4(sK8(h,phi('f$uleft$uzero'))))) = phi(multiply(f,'f$uleft$uzero',sK4(sK8(h,phi('f$uleft$uzero'))))) ),
inference(resolution,[status(thm)],[d14,c11]) ).
cnf(d16,plain,
( ~ 'group$umember'('f$uleft$uzero',f)
| multiply(h,phi('f$uleft$uzero'),sK8(h,phi('f$uleft$uzero'))) = phi(multiply(f,'f$uleft$uzero',sK4(sK8(h,phi('f$uleft$uzero'))))) ),
inference(demodulation,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
( ~ 'group$umember'('f$uleft$uzero',f)
| multiply(h,phi('f$uleft$uzero'),sK8(h,phi('f$uleft$uzero'))) = phi('f$uleft$uzero') ),
inference(demodulation,[status(thm)],[d16,d6]) ).
cnf(d18,plain,
multiply(h,phi('f$uleft$uzero'),sK8(h,phi('f$uleft$uzero'))) = phi('f$uleft$uzero'),
inference(resolution,[status(thm)],[d5,d17]) ).
cnf(d19,plain,
( 'left$uzero'(h,phi('f$uleft$uzero'))
| ~ 'group$umember'(phi('f$uleft$uzero'),h)
| phi('f$uleft$uzero') != phi('f$uleft$uzero') ),
inference(superposition,[status(thm)],[d18,c7]) ).
cnf(d20,plain,
( ~ 'group$umember'(phi('f$uleft$uzero'),h)
| phi('f$uleft$uzero') != phi('f$uleft$uzero') ),
inference(resolution,[status(thm)],[c11,d19]) ).
cnf(d21,plain,
multiply(f,'f$uleft$uzero','f$uleft$uzero') = 'f$uleft$uzero',
inference(resolution,[status(thm)],[d0,d5]) ).
cnf(d22,plain,
( ~ 'group$umember'(X0,f)
| phi(sK4(phi(X0))) = phi(X0) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d23,plain,
phi(sK4(phi('f$uleft$uzero'))) = phi('f$uleft$uzero'),
inference(resolution,[status(thm)],[d22,d5]) ).
cnf(d24,plain,
( phi(sK4(phi(multiply(f,X1,X0)))) = phi(multiply(f,X1,X0))
| ~ 'group$umember'(X1,f)
| ~ 'group$umember'(X0,f) ),
inference(resolution,[status(thm)],[c9,d22]) ).
cnf(d25,plain,
( ~ 'group$umember'(X0,f)
| phi(sK4(phi(multiply(f,X0,'f$uleft$uzero')))) = phi(multiply(f,X0,'f$uleft$uzero')) ),
inference(resolution,[status(thm)],[d24,d5]) ).
cnf(d26,plain,
phi(sK4(phi(multiply(f,'f$uleft$uzero','f$uleft$uzero')))) = phi(multiply(f,'f$uleft$uzero','f$uleft$uzero')),
inference(resolution,[status(thm)],[d25,d5]) ).
cnf(d27,plain,
phi(sK4(phi('f$uleft$uzero'))) = phi(multiply(f,'f$uleft$uzero','f$uleft$uzero')),
inference(demodulation,[status(thm)],[d26,d21]) ).
cnf(d28,plain,
phi('f$uleft$uzero') = phi(multiply(f,'f$uleft$uzero','f$uleft$uzero')),
inference(demodulation,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
phi('f$uleft$uzero') = phi('f$uleft$uzero'),
inference(demodulation,[status(thm)],[d28,d21]) ).
cnf(d30,plain,
~ 'group$umember'(phi('f$uleft$uzero'),h),
inference(resolution,[status(thm)],[d29,d20]) ).
cnf(d31,plain,
~ 'group$umember'('f$uleft$uzero',f),
inference(resolution,[status(thm)],[d30,c0]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d5,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n002.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 14:40:04 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.84/3.21 % SZS status Theorem for theBenchmark.p
% 16.84/3.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------