%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:41:05 AM UTC 2026
% Result : Theorem 2.24s 2.55s
% Output : Proof 2.34s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity,conjecture,
! [E] :
( ( ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( ( product(X,V,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(U,Z,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(U,Z,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(X,V,W) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) )
=> ( ! [X] : product(X,X,E)
=> ! [U,V,W] :
( product(U,V,W)
=> product(V,U,W) ) ) ),
file('theBenchmark.p',commutativity) ).
fof(f_1_1,negated_conjecture,
~ ! [E] :
( ( ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( ( product(X,V,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(U,Z,W) )
& ! [X,Y,Z,U,V,W] :
( ( product(U,Z,W)
& product(Y,Z,V)
& product(X,Y,U) )
=> product(X,V,W) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) )
=> ( ! [X] : product(X,X,E)
=> ! [U,V,W] :
( product(U,V,W)
=> product(V,U,W) ) ) ),
inference(negate,[status(cth)],[commutativity]) ).
fof(f_1_2,negated_conjecture,
? [E] :
( ? [U,V,W] :
( ~ product(V,U,W)
& product(U,V,W) )
& ! [X] : product(X,X,E)
& ! [X] : product(inverse(X),X,E)
& ! [X] : product(X,inverse(X),E)
& ! [X] : product(E,X,X)
& ! [X] : product(X,E,X)
& ! [X,Y,Z,U,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
& ! [X,Y,Z,U,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) )
& ! [X,Y] :
? [Z] : product(X,Y,Z) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_23] :
( ? [U_22,U_21,U_20] :
( ~ product(U_21,U_22,U_20)
& product(U_22,U_21,U_20) )
& ! [U_19] : product(U_19,U_19,U_23)
& ! [U_18] : product(inverse(U_18),U_18,U_23)
& ! [U_17] : product(U_17,inverse(U_17),U_23)
& ! [U_16] : product(U_23,U_16,U_16)
& ! [U_15] : product(U_15,U_23,U_15)
& ! [U_14,U_13,U_12,U_11,U_10,U_9] :
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) )
& ! [U_8,U_7,U_6,U_5,U_4,U_3] :
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) )
& ! [U_2,U_1] :
? [U_0] : product(U_2,U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ? [U_22,U_21,U_20] :
( ~ product(U_21,U_22,U_20)
& product(U_22,U_21,U_20) )
& ! [U_19] : product(U_19,U_19,sK1)
& ! [U_18] : product(inverse(U_18),U_18,sK1)
& ! [U_17] : product(U_17,inverse(U_17),sK1)
& ! [U_16] : product(sK1,U_16,U_16)
& ! [U_15] : product(U_15,sK1,U_15)
& ! [U_14,U_13,U_12,U_11,U_10,U_9] :
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) )
& ! [U_8,U_7,U_6,U_5,U_4,U_3] :
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) )
& ! [U_2,U_1] :
? [U_0] : product(U_2,U_1,U_0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_23,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ? [U_22,U_21,U_20] :
( ~ product(U_21,U_22,U_20)
& product(U_22,U_21,U_20) )
& ! [U_19] : product(U_19,U_19,sK1)
& ! [U_18] : product(inverse(U_18),U_18,sK1)
& ! [U_17] : product(U_17,inverse(U_17),sK1)
& ! [U_16] : product(sK1,U_16,U_16)
& ! [U_15] : product(U_15,sK1,U_15)
& ! [U_14,U_13,U_12,U_11,U_10,U_9] :
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) )
& ! [U_8,U_7,U_6,U_5,U_4,U_3] :
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) )
& ! [U_2,U_1] : product(U_2,U_1,sK2(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_0,sK2(U_2,U_1))],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ? [U_21,U_20] :
( ~ product(U_21,sK3,U_20)
& product(sK3,U_21,U_20) )
& ! [U_19] : product(U_19,U_19,sK1)
& ! [U_18] : product(inverse(U_18),U_18,sK1)
& ! [U_17] : product(U_17,inverse(U_17),sK1)
& ! [U_16] : product(sK1,U_16,U_16)
& ! [U_15] : product(U_15,sK1,U_15)
& ! [U_14,U_13,U_12,U_11,U_10,U_9] :
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) )
& ! [U_8,U_7,U_6,U_5,U_4,U_3] :
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) )
& ! [U_2,U_1] : product(U_2,U_1,sK2(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_22,sK3)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ? [U_20] :
( ~ product(sK4,sK3,U_20)
& product(sK3,sK4,U_20) )
& ! [U_19] : product(U_19,U_19,sK1)
& ! [U_18] : product(inverse(U_18),U_18,sK1)
& ! [U_17] : product(U_17,inverse(U_17),sK1)
& ! [U_16] : product(sK1,U_16,U_16)
& ! [U_15] : product(U_15,sK1,U_15)
& ! [U_14,U_13,U_12,U_11,U_10,U_9] :
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) )
& ! [U_8,U_7,U_6,U_5,U_4,U_3] :
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) )
& ! [U_2,U_1] : product(U_2,U_1,sK2(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ~ product(sK4,sK3,sK5)
& product(sK3,sK4,sK5)
& ! [U_19] : product(U_19,U_19,sK1)
& ! [U_18] : product(inverse(U_18),U_18,sK1)
& ! [U_17] : product(U_17,inverse(U_17),sK1)
& ! [U_16] : product(sK1,U_16,U_16)
& ! [U_15] : product(U_15,sK1,U_15)
& ! [U_14,U_13,U_12,U_11,U_10,U_9] :
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) )
& ! [U_8,U_7,U_6,U_5,U_4,U_3] :
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) )
& ! [U_2,U_1] : product(U_2,U_1,sK2(U_2,U_1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_20,sK5)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( ~ product(sK4,sK3,sK5)
& product(sK3,sK4,sK5)
& ! [U_19] : product(U_19,U_19,sK1)
& ! [U_18] : product(inverse(U_18),U_18,sK1)
& ! [U_17] : product(U_17,inverse(U_17),sK1)
& ! [U_16] : product(sK1,U_16,U_16)
& ! [U_15] : product(U_15,sK1,U_15)
& ! [U_12,U_9,U_10,U_14,U_11,U_13] :
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) )
& ! [U_7,U_4,U_5,U_3,U_8,U_6] :
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) )
& ! [U_1,U_2] : product(U_2,U_1,sK2(U_2,U_1)) ),
inference(definitional_conversion,[status(esa)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
product(U_2,U_1,sK2(U_2,U_1)),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_11,negated_conjecture,
( product(U_8,U_4,U_3)
| ~ product(U_5,U_6,U_3)
| ~ product(U_7,U_6,U_4)
| ~ product(U_8,U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_12,negated_conjecture,
( product(U_11,U_12,U_9)
| ~ product(U_14,U_10,U_9)
| ~ product(U_13,U_12,U_10)
| ~ product(U_14,U_13,U_11) ),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_13,negated_conjecture,
product(U_15,sK1,U_15),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_14,negated_conjecture,
product(sK1,U_16,U_16),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_15,negated_conjecture,
product(U_17,inverse(U_17),sK1),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_16,negated_conjecture,
product(inverse(U_18),U_18,sK1),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_17,negated_conjecture,
product(U_19,U_19,sK1),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_18,negated_conjecture,
product(sK3,sK4,sK5),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(f_1_19,negated_conjecture,
~ product(sK4,sK3,sK5),
inference(clausify,[status(thm)],[f_1_9]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP001+6 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.02/0.35 % DateTime : Sat Sep 19 08:30:40 UTC 2026
% 0.02/0.36 % CPUTime :
% 2.24/2.55 % SZS status Theorem for theBenchmark
% 2.24/2.55 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------