%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP035-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:06:54 AM UTC 2025
% Result : Unsatisfiable 0.54s 0.72s
% Output : Proof 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 45
% Syntax : Number of formulae : 98 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 597 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 919 ( 439 ~; 431 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 317 ( 296 !; 0 ?; 317 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(identity_type,type,
identity: $i ).
tff(subgroup_member_type,type,
subgroup_member: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(( product(X,identity,X)
<=> product(X,identity,X) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : product(X,identity,X)
<=> ! [X: $i] : product(X,identity,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_identity) ).
tff(5,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : product(X,identity,X),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : product(X,identity,X),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(a,identity,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
product(a,identity,a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( product(X,inverse(X),identity)
<=> product(X,inverse(X),identity) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : product(X,inverse(X),identity)
<=> ! [X: $i] : product(X,inverse(X),identity) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
tff(14,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : product(X,inverse(X),identity),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(b,inverse(b),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
product(b,inverse(b),identity),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( product(a,b,c)
<=> product(a,b,c) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
tff(21,plain,
product(a,b,c),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(( ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W)
| product(U,Z,W) ) )),
rewrite(( ( ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
( ( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ product(X,Y,U)
| ~ product(Y,Z,V)
| ~ product(X,V,W)
| product(U,Z,W) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',associativity2) ).
tff(28,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a)
| product(c,inverse(b),a) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a)
| product(c,inverse(b),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( product(c,inverse(b),a)
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a) )
<=> ( ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a)
| product(c,inverse(b),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,inverse(b),a)
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a)
| product(c,inverse(b),a) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,inverse(b),a)
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a)
| product(c,inverse(b),a) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(c,inverse(b),a)
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(b,inverse(b),identity)
| ~ product(a,b,c)
| ~ product(a,identity,a)
| product(c,inverse(b),a) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
product(c,inverse(b),a),
inference(unit_resolution,[status(thm)],[37,31,21,18,9]) ).
tff(39,plain,
( ~ ! [X: $i] : product(X,inverse(X),identity)
| product(inverse(b),inverse(inverse(b)),identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
product(inverse(b),inverse(inverse(b)),identity),
inference(unit_resolution,[status(thm)],[39,16]) ).
tff(41,plain,
( ~ ! [X: $i] : product(X,identity,X)
| product(c,identity,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
product(c,identity,c),
inference(unit_resolution,[status(thm)],[41,7]) ).
tff(43,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(c,identity,c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| product(a,inverse(inverse(b)),c)
| ~ product(c,inverse(b),a) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(c,identity,c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| product(a,inverse(inverse(b)),c)
| ~ product(c,inverse(b),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( product(a,inverse(inverse(b)),c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| ~ product(c,inverse(b),a)
| ~ product(c,identity,c) )
<=> ( ~ product(c,identity,c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| product(a,inverse(inverse(b)),c)
| ~ product(c,inverse(b),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(a,inverse(inverse(b)),c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| ~ product(c,inverse(b),a)
| ~ product(c,identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(c,identity,c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| product(a,inverse(inverse(b)),c)
| ~ product(c,inverse(b),a) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(a,inverse(inverse(b)),c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| ~ product(c,inverse(b),a)
| ~ product(c,identity,c) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(c,identity,c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| product(a,inverse(inverse(b)),c)
| ~ product(c,inverse(b),a) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| product(a,inverse(inverse(b)),c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| ~ product(c,inverse(b),a)
| ~ product(c,identity,c) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| ~ product(X,V,W) )
| ~ product(c,identity,c)
| ~ product(inverse(b),inverse(inverse(b)),identity)
| product(a,inverse(inverse(b)),c)
| ~ product(c,inverse(b),a) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
product(a,inverse(inverse(b)),c),
inference(unit_resolution,[status(thm)],[48,31,42,40,38]) ).
tff(50,plain,
^ [X: $i] :
refl(( product(identity,X,X)
<=> product(identity,X,X) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X: $i] : product(identity,X,X)
<=> ! [X: $i] : product(identity,X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
! [X: $i] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-0.ax',left_identity) ).
tff(54,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [X: $i] : product(identity,X,X),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X: $i] : product(identity,X,X),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
( ~ ! [X: $i] : product(identity,X,X)
| product(identity,inverse(b),inverse(b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
product(identity,inverse(b),inverse(b)),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( subgroup_member(b)
<=> subgroup_member(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,axiom,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_in_subgroup) ).
tff(61,plain,
subgroup_member(b),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
<=> ( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
<=> ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
<=> ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [B: $i,A: $i,C: $i] :
trans(monotonicity(rewrite(( ( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C) )
<=> ( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) )),
( ( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) )
<=> ( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A)
| subgroup_member(C) ) )),
rewrite(( ( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A)
| subgroup_member(C) )
<=> ( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) )),
( ( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) )
<=> ( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) )
<=> ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [B: $i,A: $i,C: $i] :
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP003-2.ax',closure_of_product_and_inverse) ).
tff(68,plain,
! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| subgroup_member(identity) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| subgroup_member(identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( subgroup_member(identity)
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| ~ subgroup_member(b) )
<=> ( ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| subgroup_member(identity) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(identity)
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| ~ subgroup_member(b) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| subgroup_member(identity) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(identity)
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| ~ subgroup_member(b) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| subgroup_member(identity) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(identity)
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| ~ subgroup_member(b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ product(b,inverse(b),identity)
| ~ subgroup_member(b)
| subgroup_member(identity) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
subgroup_member(identity),
inference(unit_resolution,[status(thm)],[77,71,61,18]) ).
tff(79,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ subgroup_member(identity)
| ~ subgroup_member(b)
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ subgroup_member(identity)
| ~ subgroup_member(b)
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b))
| ~ subgroup_member(b)
| ~ subgroup_member(identity) )
<=> ( ~ subgroup_member(identity)
| ~ subgroup_member(b)
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b))
| ~ subgroup_member(b)
| ~ subgroup_member(identity) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ subgroup_member(identity)
| ~ subgroup_member(b)
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b)) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b))
| ~ subgroup_member(b)
| ~ subgroup_member(identity) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ subgroup_member(identity)
| ~ subgroup_member(b)
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b)) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b))
| ~ subgroup_member(b)
| ~ subgroup_member(identity) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| ~ subgroup_member(identity)
| ~ subgroup_member(b)
| subgroup_member(inverse(b))
| ~ product(identity,inverse(b),inverse(b)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
subgroup_member(inverse(b)),
inference(unit_resolution,[status(thm)],[84,71,61,78,58]) ).
tff(86,plain,
( ~ subgroup_member(c)
<=> ~ subgroup_member(c) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,axiom,
~ subgroup_member(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_in_subgroup) ).
tff(88,plain,
~ subgroup_member(c),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( subgroup_member(a)
<=> subgroup_member(a) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
subgroup_member(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_in_subgroup) ).
tff(91,plain,
subgroup_member(a),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ subgroup_member(a)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ subgroup_member(a)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ( subgroup_member(c)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(a) )
<=> ( subgroup_member(c)
| ~ subgroup_member(a)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ subgroup_member(a)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b)) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(a) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ subgroup_member(a)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b)) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b))
| ~ subgroup_member(a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) )
| subgroup_member(c)
| ~ subgroup_member(a)
| ~ product(a,inverse(inverse(b)),c)
| ~ subgroup_member(inverse(b)) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
$false,
inference(unit_resolution,[status(thm)],[97,71,91,88,85,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP035-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.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 15:27:53 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.54/0.72 % SZS status Unsatisfiable
% 0.54/0.72 % SZS output start Proof
% See solution above
% 0.54/0.73 % E exiting
%------------------------------------------------------------------------------