TSTP Solution File: GRP709-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP709-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 22:29:35 EDT 2022
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 102 ( 72 unt; 5 typ; 0 def)
% Number of atoms : 132 ( 126 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 48 ( 18 ~; 14 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 5 ( 5 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 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 : 96 ( 88 !; 0 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(op_c_type,type,
op_c: $i ).
tff(unit_type,type,
unit: $i ).
tff(1,plain,
^ [A: $i] :
refl(
( ( mult(op_c,A) = mult(A,op_c) )
<=> ( mult(op_c,A) = mult(A,op_c) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
tff(5,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,a) = mult(a,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
mult(op_c,a) = mult(a,op_c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(a,op_c) = mult(op_c,a),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [A: $i] :
refl(
( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
tff(15,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_c) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
mult(unit,op_c) = op_c,
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
mult(a,mult(unit,op_c)) = mult(a,op_c),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
<=> ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
tff(25,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
| ( mult(a,mult(unit,op_c)) = mult(mult(a,unit),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
mult(a,mult(unit,op_c)) = mult(mult(a,unit),op_c),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
mult(mult(a,unit),op_c) = mult(a,mult(unit,op_c)),
inference(symmetry,[status(thm)],[29]) ).
tff(31,plain,
mult(mult(a,unit),op_c) = mult(op_c,a),
inference(transitivity,[status(thm)],[30,20,10]) ).
tff(32,plain,
mult(op_c,mult(mult(a,unit),op_c)) = mult(op_c,mult(op_c,a)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
mult(op_c,mult(op_c,a)) = mult(op_c,mult(mult(a,unit),op_c)),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
^ [A: $i] :
refl(
( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
tff(38,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_c,unit) = op_c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
mult(op_c,unit) = op_c,
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
mult(unit,mult(op_c,unit)) = mult(unit,op_c),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
mult(unit,mult(op_c,unit)) = op_c,
inference(transitivity,[status(thm)],[43,19]) ).
tff(45,plain,
mult(mult(unit,mult(op_c,unit)),mult(op_c,a)) = mult(op_c,mult(op_c,a)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
tff(50,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(unit,mult(op_c,mult(unit,mult(op_c,a)))) = mult(mult(unit,mult(op_c,unit)),mult(op_c,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
mult(unit,mult(op_c,mult(unit,mult(op_c,a)))) = mult(mult(unit,mult(op_c,unit)),mult(op_c,a)),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
mult(op_c,mult(unit,mult(op_c,a))) = mult(mult(op_c,mult(unit,op_c)),a),
inference(unit_resolution,[status(thm)],[55,52]) ).
tff(57,plain,
mult(mult(op_c,mult(unit,op_c)),a) = mult(op_c,mult(unit,mult(op_c,a))),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
mult(op_c,mult(unit,op_c)) = mult(op_c,op_c),
inference(monotonicity,[status(thm)],[19]) ).
tff(59,plain,
mult(mult(op_c,mult(unit,op_c)),a) = mult(mult(op_c,op_c),a),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
mult(mult(op_c,op_c),a) = mult(mult(op_c,mult(unit,op_c)),a),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
mult(mult(op_c,op_c),a) = mult(op_c,mult(unit,mult(op_c,a))),
inference(transitivity,[status(thm)],[60,57]) ).
tff(62,plain,
mult(unit,mult(mult(op_c,op_c),a)) = mult(unit,mult(op_c,mult(unit,mult(op_c,a)))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(mult(op_c,op_c),a)) = mult(mult(op_c,op_c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(64,plain,
mult(unit,mult(mult(op_c,op_c),a)) = mult(mult(op_c,op_c),a),
inference(unit_resolution,[status(thm)],[63,17]) ).
tff(65,plain,
mult(mult(op_c,op_c),a) = mult(unit,mult(mult(op_c,op_c),a)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
mult(mult(op_c,op_c),a) = mult(op_c,mult(mult(a,unit),op_c)),
inference(transitivity,[status(thm)],[65,62,54,45,33]) ).
tff(67,plain,
mult(mult(mult(op_c,op_c),a),b) = mult(mult(op_c,mult(mult(a,unit),op_c)),b),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
mult(mult(op_c,mult(mult(a,unit),op_c)),b) = mult(mult(mult(op_c,op_c),a),b),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(mult(a,unit),mult(op_c,b))) = mult(mult(op_c,mult(mult(a,unit),op_c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
mult(op_c,mult(mult(a,unit),mult(op_c,b))) = mult(mult(op_c,mult(mult(a,unit),op_c)),b),
inference(unit_resolution,[status(thm)],[69,52]) ).
tff(71,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(op_c,mult(a,b))) = mult(op_c,mult(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
mult(unit,mult(op_c,mult(a,b))) = mult(op_c,mult(a,b)),
inference(unit_resolution,[status(thm)],[71,17]) ).
tff(73,plain,
mult(op_c,mult(a,b)) = mult(unit,mult(op_c,mult(a,b))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(a,b)) = mult(mult(a,b),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
mult(op_c,mult(a,b)) = mult(mult(a,b),op_c),
inference(unit_resolution,[status(thm)],[74,7]) ).
tff(76,plain,
mult(mult(a,b),op_c) = mult(op_c,mult(a,b)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,op_c)) = mult(mult(A,B),op_c) )
| ( mult(a,mult(b,op_c)) = mult(mult(a,b),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
mult(a,mult(b,op_c)) = mult(mult(a,b),op_c),
inference(unit_resolution,[status(thm)],[77,27]) ).
tff(79,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,b) = mult(b,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
mult(op_c,b) = mult(b,op_c),
inference(unit_resolution,[status(thm)],[79,7]) ).
tff(81,plain,
mult(a,mult(op_c,b)) = mult(a,mult(b,op_c)),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(a,unit) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
mult(a,unit) = a,
inference(unit_resolution,[status(thm)],[82,40]) ).
tff(84,plain,
mult(mult(a,unit),mult(op_c,b)) = mult(a,mult(op_c,b)),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
mult(mult(a,unit),mult(op_c,b)) = mult(unit,mult(op_c,mult(a,b))),
inference(transitivity,[status(thm)],[84,81,78,76,73]) ).
tff(86,plain,
mult(op_c,mult(mult(a,unit),mult(op_c,b))) = mult(op_c,mult(unit,mult(op_c,mult(a,b)))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
mult(op_c,mult(unit,mult(op_c,mult(a,b)))) = mult(op_c,mult(mult(a,unit),mult(op_c,b))),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(unit,mult(op_c,mult(a,b)))) = mult(mult(op_c,mult(unit,op_c)),mult(a,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
mult(op_c,mult(unit,mult(op_c,mult(a,b)))) = mult(mult(op_c,mult(unit,op_c)),mult(a,b)),
inference(unit_resolution,[status(thm)],[88,52]) ).
tff(90,plain,
mult(mult(op_c,mult(unit,op_c)),mult(a,b)) = mult(op_c,mult(unit,mult(op_c,mult(a,b)))),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
mult(mult(op_c,mult(unit,op_c)),mult(a,b)) = mult(mult(op_c,op_c),mult(a,b)),
inference(monotonicity,[status(thm)],[58]) ).
tff(92,plain,
mult(mult(op_c,op_c),mult(a,b)) = mult(mult(op_c,mult(unit,op_c)),mult(a,b)),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
mult(mult(op_c,op_c),mult(a,b)) = mult(mult(mult(op_c,op_c),a),b),
inference(transitivity,[status(thm)],[92,90,87,70,68]) ).
tff(94,plain,
( ( mult(mult(op_c,op_c),mult(a,b)) != mult(mult(mult(op_c,op_c),a),b) )
<=> ( mult(mult(op_c,op_c),mult(a,b)) != mult(mult(mult(op_c,op_c),a),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,axiom,
mult(mult(op_c,op_c),mult(a,b)) != mult(mult(mult(op_c,op_c),a),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(96,plain,
mult(mult(op_c,op_c),mult(a,b)) != mult(mult(mult(op_c,op_c),a),b),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
$false,
inference(unit_resolution,[status(thm)],[96,93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP709-1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.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 20:42:18 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.
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------