%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ALG235-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 04:58:49 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 46 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 8 ~; 4 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 62 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(c_type,type,
c: $i ).
tff(d_type,type,
d: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [B: $i,D: $i,A: $i,C: $i] :
refl(( ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) )
<=> ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) )
<=> ! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
tff(5,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) )
| ( mult(a,mult(b,mult(d,c))) = mult(d,mult(b,mult(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
mult(a,mult(b,mult(d,c))) = mult(d,mult(b,mult(a,c))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(d,mult(b,mult(a,c))) = mult(a,mult(b,mult(d,c))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,mult(B,mult(A,B))) = mult(A,B) )
<=> ( mult(A,mult(B,mult(A,B))) = mult(A,B) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
tff(15,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,mult(A,B))) = mult(A,B) )
| ( mult(a,mult(c,mult(a,c))) = mult(a,c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
mult(a,mult(c,mult(a,c))) = mult(a,c),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
mult(b,mult(a,mult(c,mult(a,c)))) = mult(b,mult(a,c)),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
mult(b,mult(a,c)) = mult(b,mult(a,mult(c,mult(a,c)))),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
mult(d,mult(b,mult(a,c))) = mult(d,mult(b,mult(a,mult(c,mult(a,c))))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
mult(d,mult(b,mult(a,mult(c,mult(a,c))))) = mult(d,mult(b,mult(a,c))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) )
| ( mult(a,mult(b,mult(d,mult(c,mult(a,c))))) = mult(d,mult(b,mult(a,mult(c,mult(a,c))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
mult(a,mult(b,mult(d,mult(c,mult(a,c))))) = mult(d,mult(b,mult(a,mult(c,mult(a,c))))),
inference(unit_resolution,[status(thm)],[24,7]) ).
tff(26,plain,
( ~ ! [B: $i,D: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(C,D))) = mult(C,mult(B,mult(A,D))) )
| ( mult(a,mult(c,mult(d,c))) = mult(d,mult(c,mult(a,c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
mult(a,mult(c,mult(d,c))) = mult(d,mult(c,mult(a,c))),
inference(unit_resolution,[status(thm)],[26,7]) ).
tff(28,plain,
mult(d,mult(c,mult(a,c))) = mult(a,mult(c,mult(d,c))),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
mult(b,mult(d,mult(c,mult(a,c)))) = mult(b,mult(a,mult(c,mult(d,c)))),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
mult(b,mult(a,mult(c,mult(d,c)))) = mult(b,mult(d,mult(c,mult(a,c)))),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) = mult(a,mult(b,mult(d,mult(c,mult(a,c))))),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) = mult(a,mult(b,mult(d,c))),
inference(transitivity,[status(thm)],[31,25,23,10]) ).
tff(33,plain,
( ( mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))) )
<=> ( mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(35,plain,
mult(a,mult(b,mult(a,mult(c,mult(d,c))))) != mult(a,mult(b,mult(d,c))),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
$false,
inference(unit_resolution,[status(thm)],[35,32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG235-1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Thu Jun 19 11:03:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------