%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP665-11 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:08:25 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 24
% Syntax : Number of formulae : 68 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 96 ( 90 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 : 4 ( 2 avg)
% Number of FOOLs : 5 ( 5 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; 3 con; 0-2 aty)
% Number of variables : 112 ( 101 !; 0 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(op_c_type,type,
op_c: $i ).
tff(x0_type,type,
x0: $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $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/sandbox/benchmark/theBenchmark.p',f09) ).
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,x0) = mult(x0,op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
mult(op_c,x0) = mult(x0,op_c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
rd(mult(op_c,x0),op_c) = rd(mult(x0,op_c),op_c),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
rd(mult(x0,op_c),op_c) = rd(mult(op_c,x0),op_c),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
^ [B: $i,A: $i] :
refl(( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],[]) ).
tff(13,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)],[12]) ).
tff(14,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(15,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
tff(16,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(x0,op_c),op_c) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
rd(mult(x0,op_c),op_c) = x0,
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
x0 = rd(mult(x0,op_c),op_c),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
x0 = rd(mult(op_c,x0),op_c),
inference(transitivity,[status(thm)],[21,11]) ).
tff(23,plain,
mult(x0,mult(op_c,x1)) = mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)) = mult(x0,mult(op_c,x1)),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
<=> ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
tff(29,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) )
| ( mult(op_c,mult(x0,x1)) = mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
mult(op_c,mult(x0,x1)) = mult(rd(mult(op_c,x0),op_c),mult(op_c,x1)),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(x0,x1)) = mult(mult(x0,x1),op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
mult(op_c,mult(x0,x1)) = mult(mult(x0,x1),op_c),
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
mult(mult(x0,x1),op_c) = mult(op_c,mult(x0,x1)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) )
<=> ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
tff(41,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) )
| ( mult(mult(x0,x1),op_c) = mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
mult(mult(x0,x1),op_c) = mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))) = mult(mult(x0,x1),op_c),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,x1) = mult(x1,op_c) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
mult(op_c,x1) = mult(x1,op_c),
inference(unit_resolution,[status(thm)],[47,7]) ).
tff(49,plain,
mult(x1,op_c) = mult(op_c,x1),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
ld(op_c,mult(x1,op_c)) = ld(op_c,mult(op_c,x1)),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
ld(op_c,mult(op_c,x1)) = ld(op_c,mult(x1,op_c)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [B: $i,A: $i] :
refl(( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],[]) ).
tff(53,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)],[52]) ).
tff(54,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(55,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
tff(56,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,x1)) = x1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
ld(op_c,mult(op_c,x1)) = x1,
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
x1 = ld(op_c,mult(op_c,x1)),
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
x1 = ld(op_c,mult(x1,op_c)),
inference(transitivity,[status(thm)],[61,51]) ).
tff(63,plain,
mult(mult(x0,op_c),x1) = mult(mult(x0,op_c),ld(op_c,mult(x1,op_c))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
mult(mult(x0,op_c),x1) = mult(x0,mult(op_c,x1)),
inference(transitivity,[status(thm)],[63,46,36,33,24]) ).
tff(65,plain,
( ( mult(mult(x0,op_c),x1) != mult(x0,mult(op_c,x1)) )
<=> ( mult(mult(x0,op_c),x1) != mult(x0,mult(op_c,x1)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,axiom,
mult(mult(x0,op_c),x1) != mult(x0,mult(op_c,x1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(67,plain,
mult(mult(x0,op_c),x1) != mult(x0,mult(op_c,x1)),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
$false,
inference(unit_resolution,[status(thm)],[67,64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP665-11 : TPTP v9.0.0. Released v8.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n009.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 : Thu Jun 19 16:47:33 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------