TSTP Solution File: GRP704-12 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP704-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.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 : Fri Sep 16 22:29:33 EDT 2022
% Result : Unsatisfiable 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 35
% Syntax : Number of formulae : 94 ( 66 unt; 7 typ; 0 def)
% Number of atoms : 120 ( 113 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 39 ( 12 ~; 8 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 102 ( 92 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x5_type,type,
x5: $i ).
tff(op_f_type,type,
op_f: $i ).
tff(x4_type,type,
x4: $i ).
tff(op_c_type,type,
op_c: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(unit_type,type,
unit: $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(op_c,mult(mult(mult(unit,unit),unit),ld(mult(op_c,mult(mult(unit,unit),unit)),op_c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
op_f = mult(op_c,mult(mult(mult(unit,unit),unit),ld(mult(op_c,mult(mult(unit,unit),unit)),op_c))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(op_c,mult(mult(mult(unit,unit),unit),ld(mult(op_c,mult(mult(unit,unit),unit)),op_c))) = op_f,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [A: $i] :
refl(
( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
tff(15,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(unit,unit),unit) = mult(unit,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
mult(mult(unit,unit),unit) = mult(unit,unit),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
mult(unit,unit) = mult(mult(unit,unit),unit),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
^ [A: $i] :
refl(
( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
tff(25,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,unit) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
mult(unit,unit) = unit,
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
mult(mult(unit,unit),unit) = unit,
inference(transitivity,[status(thm)],[19,29]) ).
tff(31,plain,
mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit)) = mult(unit,unit),
inference(monotonicity,[status(thm)],[30,30]) ).
tff(32,plain,
unit = mult(unit,unit),
inference(symmetry,[status(thm)],[29]) ).
tff(33,plain,
^ [B: $i,A: $i] :
refl(
( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
tff(37,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(op_c,unit),mult(mult(op_c,unit),unit)) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
ld(mult(op_c,unit),mult(mult(op_c,unit),unit)) = unit,
inference(unit_resolution,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(op_c,unit),unit) = mult(op_c,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
mult(mult(op_c,unit),unit) = mult(op_c,unit),
inference(unit_resolution,[status(thm)],[42,17]) ).
tff(44,plain,
mult(op_c,unit) = mult(mult(op_c,unit),unit),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_c,unit) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
mult(op_c,unit) = op_c,
inference(unit_resolution,[status(thm)],[45,17]) ).
tff(47,plain,
op_c = mult(op_c,unit),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
op_c = mult(mult(op_c,unit),unit),
inference(transitivity,[status(thm)],[47,44]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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(53,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
| ( mult(op_c,mult(unit,unit)) = mult(mult(op_c,unit),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
mult(op_c,mult(unit,unit)) = mult(mult(op_c,unit),unit),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
mult(op_c,mult(mult(unit,unit),unit)) = mult(op_c,mult(unit,unit)),
inference(monotonicity,[status(thm)],[19]) ).
tff(59,plain,
mult(op_c,mult(mult(unit,unit),unit)) = mult(op_c,unit),
inference(transitivity,[status(thm)],[58,57,43]) ).
tff(60,plain,
ld(mult(op_c,mult(mult(unit,unit),unit)),op_c) = ld(mult(op_c,unit),mult(mult(op_c,unit),unit)),
inference(monotonicity,[status(thm)],[59,48]) ).
tff(61,plain,
ld(mult(op_c,mult(mult(unit,unit),unit)),op_c) = mult(mult(unit,unit),unit),
inference(transitivity,[status(thm)],[60,41,32,20]) ).
tff(62,plain,
mult(mult(mult(unit,unit),unit),ld(mult(op_c,mult(mult(unit,unit),unit)),op_c)) = mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
mult(mult(mult(unit,unit),unit),ld(mult(op_c,mult(mult(unit,unit),unit)),op_c)) = mult(mult(unit,unit),unit),
inference(transitivity,[status(thm)],[62,31,20]) ).
tff(64,plain,
mult(op_c,mult(mult(mult(unit,unit),unit),ld(mult(op_c,mult(mult(unit,unit),unit)),op_c))) = mult(op_c,mult(mult(unit,unit),unit)),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
mult(op_c,mult(mult(unit,unit),unit)) = mult(op_c,mult(mult(mult(unit,unit),unit),ld(mult(op_c,mult(mult(unit,unit),unit)),op_c))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
mult(op_c,mult(unit,unit)) = mult(op_c,mult(mult(unit,unit),unit)),
inference(symmetry,[status(thm)],[58]) ).
tff(67,plain,
mult(mult(op_c,unit),unit) = mult(op_c,mult(unit,unit)),
inference(symmetry,[status(thm)],[57]) ).
tff(68,plain,
op_c = op_f,
inference(transitivity,[status(thm)],[47,44,67,66,65,10]) ).
tff(69,plain,
mult(x4,op_c) = mult(x4,op_f),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
mult(mult(x4,op_c),x5) = mult(mult(x4,op_f),x5),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,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(72,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)],[71]) ).
tff(73,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(74,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(75,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
| ( mult(x4,mult(op_c,x5)) = mult(mult(x4,op_c),x5) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
mult(x4,mult(op_c,x5)) = mult(mult(x4,op_c),x5),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
mult(op_c,x5) = mult(op_f,x5),
inference(monotonicity,[status(thm)],[68]) ).
tff(81,plain,
mult(op_f,x5) = mult(op_c,x5),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
mult(x4,mult(op_f,x5)) = mult(x4,mult(op_c,x5)),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
mult(x4,mult(op_f,x5)) = mult(mult(x4,op_f),x5),
inference(transitivity,[status(thm)],[82,79,70]) ).
tff(84,plain,
( ( mult(x4,mult(op_f,x5)) != mult(mult(x4,op_f),x5) )
<=> ( mult(x4,mult(op_f,x5)) != mult(mult(x4,op_f),x5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
mult(x4,mult(op_f,x5)) != mult(mult(x4,op_f),x5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(86,plain,
mult(x4,mult(op_f,x5)) != mult(mult(x4,op_f),x5),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP704-12 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 20:09:58 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------