%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP704-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:08:30 AM UTC 2025
% Result : Unsatisfiable 0.48s 0.65s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 51 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 67 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 8 ~; 4 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 4 ( 4 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 80 ( 72 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x5_type,type,
x5: $i ).
tff(x4_type,type,
x4: $i ).
tff(op_f_type,type,
op_f: $i ).
tff(op_c_type,type,
op_c: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(( ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
<=> ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
<=> ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
<=> ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f13) ).
tff(5,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( op_f = mult(A,mult(B,ld(mult(A,B),op_c))) )
| ( op_f = mult(mult(x4,x5),mult(op_c,ld(mult(mult(x4,x5),op_c),op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
op_f = mult(mult(x4,x5),mult(op_c,ld(mult(mult(x4,x5),op_c),op_c))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(mult(x4,x5),mult(op_c,ld(mult(mult(x4,x5),op_c),op_c))) = op_f,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
tff(15,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
| ( mult(mult(x4,x5),mult(op_c,ld(mult(mult(x4,x5),op_c),op_c))) = mult(mult(mult(x4,x5),op_c),ld(mult(mult(x4,x5),op_c),op_c)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
mult(mult(x4,x5),mult(op_c,ld(mult(mult(x4,x5),op_c),op_c))) = mult(mult(mult(x4,x5),op_c),ld(mult(mult(x4,x5),op_c),op_c)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
mult(mult(mult(x4,x5),op_c),ld(mult(mult(x4,x5),op_c),op_c)) = mult(mult(x4,x5),mult(op_c,ld(mult(mult(x4,x5),op_c),op_c))),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,ld(A,B)) = B )
<=> ( mult(A,ld(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
<=> ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
tff(25,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,ld(A,B)) = B )
| ( mult(mult(mult(x4,x5),op_c),ld(mult(mult(x4,x5),op_c),op_c)) = op_c ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
mult(mult(mult(x4,x5),op_c),ld(mult(mult(x4,x5),op_c),op_c)) = op_c,
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
op_c = mult(mult(mult(x4,x5),op_c),ld(mult(mult(x4,x5),op_c),op_c)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
op_c = op_f,
inference(transitivity,[status(thm)],[30,20,10]) ).
tff(32,plain,
mult(op_c,x4) = mult(op_f,x4),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
mult(op_f,x4) = mult(op_c,x4),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
mult(mult(op_f,x4),x5) = mult(mult(op_c,x4),x5),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
mult(mult(op_c,x4),x5) = mult(mult(op_f,x4),x5),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
^ [B: $i,A: $i] :
refl(( ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
<=> ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
<=> ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
<=> ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
tff(40,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
( ~ ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
| ( mult(op_c,mult(x4,x5)) = mult(mult(op_c,x4),x5) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
mult(op_c,mult(x4,x5)) = mult(mult(op_c,x4),x5),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
mult(op_c,mult(x4,x5)) = mult(op_f,mult(x4,x5)),
inference(monotonicity,[status(thm)],[31]) ).
tff(46,plain,
mult(op_f,mult(x4,x5)) = mult(op_c,mult(x4,x5)),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
mult(op_f,mult(x4,x5)) = mult(mult(op_f,x4),x5),
inference(transitivity,[status(thm)],[46,44,35]) ).
tff(48,plain,
( ( mult(op_f,mult(x4,x5)) != mult(mult(op_f,x4),x5) )
<=> ( mult(op_f,mult(x4,x5)) != mult(mult(op_f,x4),x5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
mult(op_f,mult(x4,x5)) != mult(mult(op_f,x4),x5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(50,plain,
mult(op_f,mult(x4,x5)) != mult(mult(op_f,x4),x5),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
$false,
inference(unit_resolution,[status(thm)],[50,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP704-10 : TPTP v9.0.0. Released v8.1.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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 16:58:16 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.48/0.65 % SZS status Unsatisfiable
% 0.48/0.65 % SZS output start Proof
% See solution above
% 0.48/0.65 % E exiting
%------------------------------------------------------------------------------