TSTP Solution File: GRP703-10 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP703-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 22:29:32 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 32
% Syntax : Number of formulae : 86 ( 60 unt; 7 typ; 0 def)
% Number of atoms : 108 ( 102 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 36 ( 12 ~; 8 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 5 ( 5 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 : 84 ( 76 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x3_type,type,
x3: $i ).
tff(x2_type,type,
x2: $i ).
tff(op_e_type,type,
op_e: $i ).
tff(op_c_type,type,
op_c: $i ).
tff(unit_type,type,
unit: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
<=> ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
<=> ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
<=> ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f12) ).
tff(5,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) )
| ( op_e = mult(mult(rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))),mult(mult(unit,unit),unit)),mult(mult(unit,unit),unit)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
op_e = mult(mult(rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))),mult(mult(unit,unit),unit)),mult(mult(unit,unit),unit)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(mult(rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))),mult(mult(unit,unit),unit)),mult(mult(unit,unit),unit)) = op_e,
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/sandbox2/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(op_c,unit) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
mult(op_c,unit) = op_c,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(op_c,unit),unit) = mult(op_c,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(21,plain,
mult(mult(op_c,unit),unit) = mult(op_c,unit),
inference(unit_resolution,[status(thm)],[20,17]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,axiom,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
tff(26,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,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(30,plain,
mult(op_c,mult(unit,unit)) = mult(mult(op_c,unit),unit),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(unit,unit),unit) = mult(unit,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
mult(mult(unit,unit),unit) = mult(unit,unit),
inference(unit_resolution,[status(thm)],[31,17]) ).
tff(33,plain,
mult(op_c,mult(mult(unit,unit),unit)) = mult(op_c,mult(unit,unit)),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
tff(38,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(op_c,unit),unit),unit) = mult(op_c,unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
rd(mult(mult(op_c,unit),unit),unit) = mult(op_c,unit),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
^ [A: $i] :
refl(
( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
tff(47,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,unit) = unit ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
mult(unit,unit) = unit,
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
mult(mult(unit,unit),unit) = unit,
inference(transitivity,[status(thm)],[32,51]) ).
tff(53,plain,
mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit)) = mult(unit,unit),
inference(monotonicity,[status(thm)],[52,52]) ).
tff(54,plain,
mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit)) = unit,
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
mult(op_c,unit) = mult(mult(op_c,unit),unit),
inference(symmetry,[status(thm)],[21]) ).
tff(56,plain,
op_c = mult(op_c,unit),
inference(symmetry,[status(thm)],[19]) ).
tff(57,plain,
op_c = mult(mult(op_c,unit),unit),
inference(transitivity,[status(thm)],[56,55]) ).
tff(58,plain,
rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))) = rd(mult(mult(op_c,unit),unit),unit),
inference(monotonicity,[status(thm)],[57,54]) ).
tff(59,plain,
rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))) = op_c,
inference(transitivity,[status(thm)],[58,42,19]) ).
tff(60,plain,
mult(rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))),mult(mult(unit,unit),unit)) = mult(op_c,mult(mult(unit,unit),unit)),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
mult(rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))),mult(mult(unit,unit),unit)) = op_c,
inference(transitivity,[status(thm)],[60,33,30,21,19]) ).
tff(62,plain,
mult(mult(rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))),mult(mult(unit,unit),unit)),mult(mult(unit,unit),unit)) = mult(op_c,mult(mult(unit,unit),unit)),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
mult(op_c,mult(mult(unit,unit),unit)) = mult(mult(rd(op_c,mult(mult(mult(unit,unit),unit),mult(mult(unit,unit),unit))),mult(mult(unit,unit),unit)),mult(mult(unit,unit),unit)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
mult(op_c,mult(unit,unit)) = mult(op_c,mult(mult(unit,unit),unit)),
inference(symmetry,[status(thm)],[33]) ).
tff(65,plain,
mult(mult(op_c,unit),unit) = mult(op_c,mult(unit,unit)),
inference(symmetry,[status(thm)],[30]) ).
tff(66,plain,
op_c = op_e,
inference(transitivity,[status(thm)],[56,55,65,64,63,10]) ).
tff(67,plain,
mult(op_c,x2) = mult(op_e,x2),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
mult(op_e,x2) = mult(op_c,x2),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
mult(mult(op_e,x2),x3) = mult(mult(op_c,x2),x3),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
mult(mult(op_c,x2),x3) = mult(mult(op_e,x2),x3),
inference(symmetry,[status(thm)],[69]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i] : ( mult(op_c,mult(A,B)) = mult(mult(op_c,A),B) )
| ( mult(op_c,mult(x2,x3)) = mult(mult(op_c,x2),x3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
mult(op_c,mult(x2,x3)) = mult(mult(op_c,x2),x3),
inference(unit_resolution,[status(thm)],[71,28]) ).
tff(73,plain,
op_e = op_c,
inference(transitivity,[status(thm)],[9,62,33,30,21,19]) ).
tff(74,plain,
mult(op_e,mult(x2,x3)) = mult(op_c,mult(x2,x3)),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
mult(op_e,mult(x2,x3)) = mult(mult(op_e,x2),x3),
inference(transitivity,[status(thm)],[74,72,70]) ).
tff(76,plain,
( ( mult(op_e,mult(x2,x3)) != mult(mult(op_e,x2),x3) )
<=> ( mult(op_e,mult(x2,x3)) != mult(mult(op_e,x2),x3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,axiom,
mult(op_e,mult(x2,x3)) != mult(mult(op_e,x2),x3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(78,plain,
mult(op_e,mult(x2,x3)) != mult(mult(op_e,x2),x3),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : GRP703-10 : TPTP v8.1.0. Released v8.1.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 20:30:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Unsatisfiable
% 0.21/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------