%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:41:35 AM UTC 2026
% Result : Theorem 221.76s 222.10s
% Output : Proof 225.38s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(total_function,axiom,
! [G,X,Y] :
( ( group_member(Y,G)
& group_member(X,G) )
=> group_member(multiply(G,X,Y),G) ),
file('GRP007+0.ax',total_function) ).
fof(associativity,axiom,
! [G,X,Y,Z] :
( ( group_member(Z,G)
& group_member(Y,G)
& group_member(X,G) )
=> multiply(G,multiply(G,X,Y),Z) = multiply(G,X,multiply(G,Y,Z)) ),
file('GRP007+0.ax',associativity) ).
fof(homomorphism1,axiom,
! [X] :
( group_member(X,f)
=> group_member(phi(X),h) ),
file('theBenchmark.p',homomorphism1) ).
fof(homomorphism2,axiom,
! [X,Y] :
( ( group_member(Y,f)
& group_member(X,f) )
=> multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)) ),
file('theBenchmark.p',homomorphism2) ).
fof(surjective,axiom,
! [X] :
( group_member(X,h)
=> ? [Y] :
( phi(Y) = X
& group_member(Y,f) ) ),
file('theBenchmark.p',surjective) ).
fof(left_zero,axiom,
! [G,X] :
( left_zero(G,X)
<=> ( ! [Y] :
( group_member(Y,G)
=> multiply(G,X,Y) = X )
& group_member(X,G) ) ),
file('theBenchmark.p',left_zero) ).
fof(left_zero_for_f,hypothesis,
left_zero(f,f_left_zero),
file('theBenchmark.p',left_zero_for_f) ).
fof(prove_left_zero_h,conjecture,
left_zero(h,phi(f_left_zero)),
file('theBenchmark.p',prove_left_zero_h) ).
fof(f_1_1,plain,
! [G,X,Y] :
( group_member(multiply(G,X,Y),G)
| ~ group_member(Y,G)
| ~ group_member(X,G) ),
inference(fof_nnf,[status(thm)],[total_function]) ).
fof(f_1_2,plain,
! [U_2,U_1,U_0] :
( group_member(multiply(U_2,U_1,U_0),U_2)
| ~ group_member(U_0,U_2)
| ~ group_member(U_1,U_2) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_2,U_0] :
( group_member(multiply(U_2,U_1,U_0),U_2)
| ~ group_member(U_0,U_2)
| ~ group_member(U_1,U_2) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( group_member(multiply(U_2,U_1,U_0),U_2)
| ~ group_member(U_0,U_2)
| ~ group_member(U_1,U_2) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [G,X,Y,Z] :
( multiply(G,multiply(G,X,Y),Z) = multiply(G,X,multiply(G,Y,Z))
| ~ group_member(Z,G)
| ~ group_member(Y,G)
| ~ group_member(X,G) ),
inference(fof_nnf,[status(thm)],[associativity]) ).
fof(f_2_2,plain,
! [U_6,U_5,U_4,U_3] :
( multiply(U_6,multiply(U_6,U_5,U_4),U_3) = multiply(U_6,U_5,multiply(U_6,U_4,U_3))
| ~ group_member(U_3,U_6)
| ~ group_member(U_4,U_6)
| ~ group_member(U_5,U_6) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_5,U_4,U_6] :
( multiply(U_6,multiply(U_6,U_5,U_4),U_3) = multiply(U_6,U_5,multiply(U_6,U_4,U_3))
| ~ group_member(U_3,U_6)
| ~ group_member(U_4,U_6)
| ~ group_member(U_5,U_6) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( multiply(U_6,multiply(U_6,U_5,U_4),U_3) = multiply(U_6,U_5,multiply(U_6,U_4,U_3))
| ~ group_member(U_3,U_6)
| ~ group_member(U_4,U_6)
| ~ group_member(U_5,U_6) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [X] :
( group_member(phi(X),h)
| ~ group_member(X,f) ),
inference(fof_nnf,[status(thm)],[homomorphism1]) ).
fof(f_3_2,plain,
! [U_7] :
( group_member(phi(U_7),h)
| ~ group_member(U_7,f) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_7] :
( group_member(phi(U_7),h)
| ~ group_member(U_7,f) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( group_member(phi(U_7),h)
| ~ group_member(U_7,f) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X,Y] :
( multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y))
| ~ group_member(Y,f)
| ~ group_member(X,f) ),
inference(fof_nnf,[status(thm)],[homomorphism2]) ).
fof(f_4_2,plain,
! [U_9,U_8] :
( multiply(h,phi(U_9),phi(U_8)) = phi(multiply(f,U_9,U_8))
| ~ group_member(U_8,f)
| ~ group_member(U_9,f) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_9,U_8] :
( multiply(h,phi(U_9),phi(U_8)) = phi(multiply(f,U_9,U_8))
| ~ group_member(U_8,f)
| ~ group_member(U_9,f) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( multiply(h,phi(U_9),phi(U_8)) = phi(multiply(f,U_9,U_8))
| ~ group_member(U_8,f)
| ~ group_member(U_9,f) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X] :
( ? [Y] :
( phi(Y) = X
& group_member(Y,f) )
| ~ group_member(X,h) ),
inference(fof_nnf,[status(thm)],[surjective]) ).
fof(f_5_2,plain,
! [U_11] :
( ? [U_10] :
( phi(U_10) = U_11
& group_member(U_10,f) )
| ~ group_member(U_11,h) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_11] :
( ( phi(sK1(U_11)) = U_11
& group_member(sK1(U_11),f) )
| ~ group_member(U_11,h) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_11))],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_11] :
( phi(sK1(U_11)) = U_11
| ~ sP0(U_11) )
& ! [U_11] :
( group_member(sK1(U_11),f)
| ~ sP0(U_11) )
& ! [U_11] :
( sP0(U_11)
| ~ group_member(U_11,h) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_5_3]) ).
cnf(f_5_5,plain,
( sP0(U_11)
| ~ group_member(U_11,h) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( group_member(sK1(U_11),f)
| ~ sP0(U_11) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( phi(sK1(U_11)) = U_11
| ~ sP0(U_11) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
! [G,X] :
( ( left_zero(G,X)
| ? [Y] :
( multiply(G,X,Y) != X
& group_member(Y,G) )
| ~ group_member(X,G) )
& ( ( ! [Y] :
( multiply(G,X,Y) = X
| ~ group_member(Y,G) )
& group_member(X,G) )
| ~ left_zero(G,X) ) ),
inference(fof_nnf,[status(thm)],[left_zero]) ).
fof(f_6_2,plain,
! [U_15,U_14] :
( ( left_zero(U_15,U_14)
| ? [U_13] :
( multiply(U_15,U_14,U_13) != U_14
& group_member(U_13,U_15) )
| ~ group_member(U_14,U_15) )
& ( ( ! [U_12] :
( multiply(U_15,U_14,U_12) = U_14
| ~ group_member(U_12,U_15) )
& group_member(U_14,U_15) )
| ~ left_zero(U_15,U_14) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_19,U_17] :
( left_zero(U_19,U_17)
| ? [U_13] :
( multiply(U_19,U_17,U_13) != U_17
& group_member(U_13,U_19) )
| ~ group_member(U_17,U_19) )
& ! [U_18,U_16] :
( ( ! [U_12] :
( multiply(U_18,U_16,U_12) = U_16
| ~ group_member(U_12,U_18) )
& group_member(U_16,U_18) )
| ~ left_zero(U_18,U_16) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_19,U_17] :
( left_zero(U_19,U_17)
| ( multiply(U_19,U_17,sK2(U_19,U_17)) != U_17
& group_member(sK2(U_19,U_17),U_19) )
| ~ group_member(U_17,U_19) )
& ! [U_18,U_16] :
( ( ! [U_12] :
( multiply(U_18,U_16,U_12) = U_16
| ~ group_member(U_12,U_18) )
& group_member(U_16,U_18) )
| ~ left_zero(U_18,U_16) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_13,sK2(U_19,U_17))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_19,U_17] :
( multiply(U_19,U_17,sK2(U_19,U_17)) != U_17
| ~ sP2(U_19,U_17) )
& ! [U_19,U_17] :
( group_member(sK2(U_19,U_17),U_19)
| ~ sP2(U_19,U_17) )
& ! [U_18,U_12,U_16] :
( multiply(U_18,U_16,U_12) = U_16
| ~ group_member(U_12,U_18)
| ~ sP1(U_18,U_12,U_16) )
& ! [U_18,U_12,U_16] :
( group_member(U_16,U_18)
| ~ sP1(U_18,U_12,U_16) )
& ! [U_19,U_17] :
( left_zero(U_19,U_17)
| sP2(U_19,U_17)
| ~ group_member(U_17,U_19) )
& ! [U_18,U_12,U_16] :
( sP1(U_18,U_12,U_16)
| ~ left_zero(U_18,U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2])],[f_6_4]) ).
cnf(f_6_6,plain,
( sP1(U_18,U_12,U_16)
| ~ left_zero(U_18,U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( left_zero(U_19,U_17)
| sP2(U_19,U_17)
| ~ group_member(U_17,U_19) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( group_member(U_16,U_18)
| ~ sP1(U_18,U_12,U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( multiply(U_18,U_16,U_12) = U_16
| ~ group_member(U_12,U_18)
| ~ sP1(U_18,U_12,U_16) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_10,plain,
( group_member(sK2(U_19,U_17),U_19)
| ~ sP2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_11,plain,
( multiply(U_19,U_17,sK2(U_19,U_17)) != U_17
| ~ sP2(U_19,U_17) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_1,plain,
left_zero(f,f_left_zero),
inference(fof_nnf,[status(thm)],[left_zero_for_f]) ).
fof(f_7_2,plain,
left_zero(f,f_left_zero),
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
left_zero(f,f_left_zero),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negate,[status(cth)],[prove_left_zero_h]) ).
fof(f_8_2,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( multiply(Eq_x_0,Eq_x_1,Eq_x_2) = multiply(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( phi(Eq_x_0) = phi(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( group_member(Eq_y_0,Eq_y_1)
| ~ group_member(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_9,axiom,
( left_zero(Eq_y_0,Eq_y_1)
| ~ left_zero(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP194+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 09:00:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 221.76/222.10 % SZS status Theorem for theBenchmark
% 221.76/222.10 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------