TSTP Solution File: GRP703-12 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP703-12 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 31
% Syntax : Number of formulae : 80 ( 55 unt; 7 typ; 0 def)
% Number of atoms : 101 ( 95 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 34 ( 11 ~; 7 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 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 : 102 ( 92 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x3_type,type,
x3: $i ).
tff(op_e_type,type,
op_e: $i ).
tff(x2_type,type,
x2: $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,
^ [A: $i] :
refl(
( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
tff(5,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_e,unit) = op_e ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
mult(op_e,unit) = op_e,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,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(11,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)],[10]) ).
tff(12,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(13,axiom,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f12) ).
tff(14,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i] : ( op_e = mult(mult(rd(op_c,mult(A,B)),B),A) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,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(op_e,op_e)),op_e),op_e) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
op_e = mult(mult(rd(op_c,mult(op_e,op_e)),op_e),op_e),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
mult(mult(rd(op_c,mult(op_e,op_e)),op_e),op_e) = op_e,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
mult(mult(mult(rd(op_c,mult(op_e,op_e)),op_e),op_e),unit) = mult(op_e,unit),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
tff(25,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(rd(op_c,mult(op_e,op_e)),mult(op_e,mult(op_e,unit))) = mult(mult(mult(rd(op_c,mult(op_e,op_e)),op_e),op_e),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
mult(rd(op_c,mult(op_e,op_e)),mult(op_e,mult(op_e,unit))) = mult(mult(mult(rd(op_c,mult(op_e,op_e)),op_e),op_e),unit),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(rd(op_c,mult(op_e,op_e)),unit) = rd(op_c,mult(op_e,op_e)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
mult(rd(op_c,mult(op_e,op_e)),unit) = rd(op_c,mult(op_e,op_e)),
inference(unit_resolution,[status(thm)],[30,7]) ).
tff(32,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(rd(op_c,mult(op_e,op_e)),unit),unit) = mult(rd(op_c,mult(op_e,op_e)),unit) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
mult(mult(rd(op_c,mult(op_e,op_e)),unit),unit) = mult(rd(op_c,mult(op_e,op_e)),unit),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
mult(mult(rd(op_c,mult(op_e,op_e)),unit),unit) = rd(op_c,mult(op_e,op_e)),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
mult(mult(mult(rd(op_c,mult(op_e,op_e)),unit),unit),mult(op_e,mult(op_e,unit))) = mult(rd(op_c,mult(op_e,op_e)),mult(op_e,mult(op_e,unit))),
inference(monotonicity,[status(thm)],[34]) ).
tff(36,plain,
mult(op_e,mult(op_e,unit)) = mult(op_e,op_e),
inference(monotonicity,[status(thm)],[9]) ).
tff(37,plain,
mult(op_e,op_e) = mult(op_e,mult(op_e,unit)),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
mult(rd(op_c,mult(op_e,op_e)),unit) = mult(mult(rd(op_c,mult(op_e,op_e)),unit),unit),
inference(symmetry,[status(thm)],[33]) ).
tff(39,plain,
rd(op_c,mult(op_e,op_e)) = mult(rd(op_c,mult(op_e,op_e)),unit),
inference(symmetry,[status(thm)],[31]) ).
tff(40,plain,
rd(op_c,mult(op_e,op_e)) = mult(mult(rd(op_c,mult(op_e,op_e)),unit),unit),
inference(transitivity,[status(thm)],[39,38]) ).
tff(41,plain,
mult(rd(op_c,mult(op_e,op_e)),mult(op_e,op_e)) = mult(mult(mult(rd(op_c,mult(op_e,op_e)),unit),unit),mult(op_e,mult(op_e,unit))),
inference(monotonicity,[status(thm)],[40,37]) ).
tff(42,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(rd(A,B),B) = A )
<=> ( mult(rd(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
tff(46,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(op_c,mult(op_e,op_e)),mult(op_e,op_e)) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(50,plain,
mult(rd(op_c,mult(op_e,op_e)),mult(op_e,op_e)) = op_c,
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
op_c = mult(rd(op_c,mult(op_e,op_e)),mult(op_e,op_e)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
op_c = op_e,
inference(transitivity,[status(thm)],[51,41,35,29,20,9]) ).
tff(53,plain,
mult(x2,op_c) = mult(x2,op_e),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
mult(x2,op_e) = mult(x2,op_c),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
mult(mult(x2,op_e),x3) = mult(mult(x2,op_c),x3),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
mult(mult(x2,op_c),x3) = mult(mult(x2,op_e),x3),
inference(symmetry,[status(thm)],[55]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(op_c,B)) = mult(mult(A,op_c),B) )
| ( mult(x2,mult(op_c,x3)) = mult(mult(x2,op_c),x3) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
mult(x2,mult(op_c,x3)) = mult(mult(x2,op_c),x3),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
mult(op_c,x3) = mult(op_e,x3),
inference(monotonicity,[status(thm)],[52]) ).
tff(67,plain,
mult(x2,mult(op_c,x3)) = mult(x2,mult(op_e,x3)),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
mult(x2,mult(op_e,x3)) = mult(x2,mult(op_c,x3)),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
mult(x2,mult(op_e,x3)) = mult(mult(x2,op_e),x3),
inference(transitivity,[status(thm)],[68,65,56]) ).
tff(70,plain,
( ( mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3) )
<=> ( mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(72,plain,
mult(x2,mult(op_e,x3)) != mult(mult(x2,op_e),x3),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP703-12 : TPTP v8.1.0. Released v8.1.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 20:16:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------