%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : n005.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 09:09:23 AM UTC 2026
% Result : Theorem 150.04s 150.59s
% Output : Proof 150.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(pel38,conjecture,
( ! [X] :
( ( ( big_p(X)
=> ? [Y] :
( big_r(X,Y)
& big_p(Y) ) )
& big_p(a) )
=> ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) ) )
<=> ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ~ ? [Y1] :
( big_r(X1,Y1)
& big_p(Y1) )
| ~ big_p(a) )
& ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a) ) ) ),
file('theBenchmark.p',pel38) ).
fof(f_1_1,negated_conjecture,
~ ( ! [X] :
( ( ( big_p(X)
=> ? [Y] :
( big_r(X,Y)
& big_p(Y) ) )
& big_p(a) )
=> ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) ) )
<=> ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ~ ? [Y1] :
( big_r(X1,Y1)
& big_p(Y1) )
| ~ big_p(a) )
& ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(negate,[status(cth)],[pel38]) ).
fof(f_1_2,negated_conjecture,
( ( ? [X] :
( ! [Z,W] :
( ~ big_r(W,Z)
| ~ big_r(X,W)
| ~ big_p(Z) )
& ( ? [Y] :
( big_r(X,Y)
& big_p(Y) )
| ~ big_p(X) )
& big_p(a) )
& ! [X1] :
( ( ? [Z2,W2] :
( big_r(W2,Z2)
& big_r(X1,W2)
& big_p(Z2) )
| ! [Y1] :
( ~ big_r(X1,Y1)
| ~ big_p(Y1) )
| ~ big_p(a) )
& ( ? [Z1,W1] :
( big_r(W1,Z1)
& big_r(X1,W1)
& big_p(Z1) )
| big_p(X1)
| ~ big_p(a) ) ) )
| ( ? [X1] :
( ( ! [Z2,W2] :
( ~ big_r(W2,Z2)
| ~ big_r(X1,W2)
| ~ big_p(Z2) )
& ? [Y1] :
( big_r(X1,Y1)
& big_p(Y1) )
& big_p(a) )
| ( ! [Z1,W1] :
( ~ big_r(W1,Z1)
| ~ big_r(X1,W1)
| ~ big_p(Z1) )
& ~ big_p(X1)
& big_p(a) ) )
& ! [X] :
( ? [Z,W] :
( big_r(W,Z)
& big_r(X,W)
& big_p(Z) )
| ( ! [Y] :
( ~ big_r(X,Y)
| ~ big_p(Y) )
& big_p(X) )
| ~ big_p(a) ) ) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
( ( ? [U_19] :
( ! [U_18,U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17)
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ! [U_15] :
( ( ? [U_14,U_13] :
( big_r(U_13,U_14)
& big_r(U_15,U_13)
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_15,U_12)
| ~ big_p(U_12) )
| ~ big_p(a) )
& ( ? [U_11,U_10] :
( big_r(U_10,U_11)
& big_r(U_15,U_10)
& big_p(U_11) )
| big_p(U_15)
| ~ big_p(a) ) ) )
| ( ? [U_9] :
( ( ! [U_8,U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(U_9,U_7)
| ~ big_p(U_8) )
& ? [U_6] :
( big_r(U_9,U_6)
& big_p(U_6) )
& big_p(a) )
| ( ! [U_5,U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(U_9,U_4)
| ~ big_p(U_5) )
& ~ big_p(U_9)
& big_p(a) ) )
& ! [U_3] :
( ? [U_2,U_1] :
( big_r(U_1,U_2)
& big_r(U_3,U_1)
& big_p(U_2) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ? [U_11] :
( ? [U_10] :
( big_r(U_10,U_11)
& big_r(U_22,U_10) )
& big_p(U_11) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ? [U_21] :
( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(U_21,U_7) )
| ~ big_p(U_8) )
& ? [U_6] :
( big_r(U_21,U_6)
& big_p(U_6) ) )
& big_p(a) )
| ( ? [U_20] :
( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(U_20,U_4) )
| ~ big_p(U_5) )
& ~ big_p(U_20) )
& big_p(a) ) )
& ! [U_3] :
( ? [U_2] :
( ? [U_1] :
( big_r(U_1,U_2)
& big_r(U_3,U_1) )
& big_p(U_2) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(miniscope,[status(thm)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ? [U_11] :
( ? [U_10] :
( big_r(U_10,U_11)
& big_r(U_22,U_10) )
& big_p(U_11) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ? [U_21] :
( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(U_21,U_7) )
| ~ big_p(U_8) )
& ? [U_6] :
( big_r(U_21,U_6)
& big_p(U_6) ) )
& big_p(a) )
| ( ? [U_20] :
( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(U_20,U_4) )
| ~ big_p(U_5) )
& ~ big_p(U_20) )
& big_p(a) ) )
& ! [U_3] :
( ( ? [U_1] :
( big_r(U_1,sK1(U_3))
& big_r(U_3,U_1) )
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_2,sK1(U_3))],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ? [U_11] :
( ? [U_10] :
( big_r(U_10,U_11)
& big_r(U_22,U_10) )
& big_p(U_11) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ? [U_21] :
( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(U_21,U_7) )
| ~ big_p(U_8) )
& ? [U_6] :
( big_r(U_21,U_6)
& big_p(U_6) ) )
& big_p(a) )
| ( ? [U_20] :
( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(U_20,U_4) )
| ~ big_p(U_5) )
& ~ big_p(U_20) )
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2(U_3))],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ? [U_11] :
( ? [U_10] :
( big_r(U_10,U_11)
& big_r(U_22,U_10) )
& big_p(U_11) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ? [U_21] :
( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(U_21,U_7) )
| ~ big_p(U_8) )
& ? [U_6] :
( big_r(U_21,U_6)
& big_p(U_6) ) )
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_20,sK3)],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ? [U_11] :
( ? [U_10] :
( big_r(U_10,U_11)
& big_r(U_22,U_10) )
& big_p(U_11) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& ? [U_6] :
( big_r(sK4,U_6)
& big_p(U_6) )
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4)],[f_1_7]) ).
fof(f_1_9,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ? [U_11] :
( ? [U_10] :
( big_r(U_10,U_11)
& big_r(U_22,U_10) )
& big_p(U_11) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& big_r(sK4,sK5)
& big_p(sK5)
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_6,sK5)],[f_1_8]) ).
fof(f_1_10,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ( ? [U_10] :
( big_r(U_10,sK6(U_22))
& big_r(U_22,U_10) )
& big_p(sK6(U_22)) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& big_r(sK4,sK5)
& big_p(sK5)
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_11,sK6(U_22))],[f_1_9]) ).
fof(f_1_11,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ? [U_14] :
( ? [U_13] :
( big_r(U_13,U_14)
& big_r(U_23,U_13) )
& big_p(U_14) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ( big_r(sK7(U_22),sK6(U_22))
& big_r(U_22,sK7(U_22))
& big_p(sK6(U_22)) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& big_r(sK4,sK5)
& big_p(sK5)
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_10,sK7(U_22))],[f_1_10]) ).
fof(f_1_12,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ( ? [U_13] :
( big_r(U_13,sK8(U_23))
& big_r(U_23,U_13) )
& big_p(sK8(U_23)) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ( big_r(sK7(U_22),sK6(U_22))
& big_r(U_22,sK7(U_22))
& big_p(sK6(U_22)) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& big_r(sK4,sK5)
& big_p(sK5)
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_14,sK8(U_23))],[f_1_11]) ).
fof(f_1_13,negated_conjecture,
( ( ? [U_19] :
( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(U_19,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(U_19,U_16)
& big_p(U_16) )
| ~ big_p(U_19) )
& big_p(a) )
& ( ! [U_23] :
( ( big_r(sK9(U_23),sK8(U_23))
& big_r(U_23,sK9(U_23))
& big_p(sK8(U_23)) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ( big_r(sK7(U_22),sK6(U_22))
& big_r(U_22,sK7(U_22))
& big_p(sK6(U_22)) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& big_r(sK4,sK5)
& big_p(sK5)
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_13,sK9(U_23))],[f_1_12]) ).
fof(f_1_14,negated_conjecture,
( ( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(sK10,U_17) )
| ~ big_p(U_18) )
& ( ? [U_16] :
( big_r(sK10,U_16)
& big_p(U_16) )
| ~ big_p(sK10) )
& big_p(a)
& ( ! [U_23] :
( ( big_r(sK9(U_23),sK8(U_23))
& big_r(U_23,sK9(U_23))
& big_p(sK8(U_23)) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ( big_r(sK7(U_22),sK6(U_22))
& big_r(U_22,sK7(U_22))
& big_p(sK6(U_22)) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& big_r(sK4,sK5)
& big_p(sK5)
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_19,sK10)],[f_1_13]) ).
fof(f_1_15,negated_conjecture,
( ( ! [U_18] :
( ! [U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(sK10,U_17) )
| ~ big_p(U_18) )
& ( ( big_r(sK10,sK11)
& big_p(sK11) )
| ~ big_p(sK10) )
& big_p(a)
& ( ! [U_23] :
( ( big_r(sK9(U_23),sK8(U_23))
& big_r(U_23,sK9(U_23))
& big_p(sK8(U_23)) )
| ! [U_12] :
( ~ big_r(U_23,U_12)
| ~ big_p(U_12) ) )
| ~ big_p(a) )
& ( ! [U_22] :
( ( big_r(sK7(U_22),sK6(U_22))
& big_r(U_22,sK7(U_22))
& big_p(sK6(U_22)) )
| big_p(U_22) )
| ~ big_p(a) ) )
| ( ( ( ! [U_8] :
( ! [U_7] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7) )
| ~ big_p(U_8) )
& big_r(sK4,sK5)
& big_p(sK5)
& big_p(a) )
| ( ! [U_5] :
( ! [U_4] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4) )
| ~ big_p(U_5) )
& ~ big_p(sK3)
& big_p(a) ) )
& ! [U_3] :
( ( big_r(sK2(U_3),sK1(U_3))
& big_r(U_3,sK2(U_3))
& big_p(sK1(U_3)) )
| ( ! [U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0) )
& big_p(U_3) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_16,sK11)],[f_1_14]) ).
fof(f_1_16,negated_conjecture,
( ( big_r(sK10,sK11)
| ~ sP7 )
& ( big_p(sK11)
| ~ sP7 )
& ! [U_23] :
( big_r(sK9(U_23),sK8(U_23))
| ~ sP6(U_23) )
& ! [U_23] :
( big_r(U_23,sK9(U_23))
| ~ sP6(U_23) )
& ! [U_23] :
( big_p(sK8(U_23))
| ~ sP6(U_23) )
& ! [U_22] :
( big_r(sK7(U_22),sK6(U_22))
| ~ sP5(U_22) )
& ! [U_22] :
( big_r(U_22,sK7(U_22))
| ~ sP5(U_22) )
& ! [U_22] :
( big_p(sK6(U_22))
| ~ sP5(U_22) )
& ! [U_22,U_12,U_18,U_23,U_17] :
( ~ big_r(U_17,U_18)
| ~ big_r(sK10,U_17)
| ~ big_p(U_18)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) )
& ! [U_22,U_12,U_18,U_23,U_17] :
( sP7
| ~ big_p(sK10)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) )
& ! [U_22,U_12,U_18,U_23,U_17] :
( big_p(a)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) )
& ! [U_22,U_12,U_18,U_23,U_17] :
( sP6(U_23)
| ~ big_r(U_23,U_12)
| ~ big_p(U_12)
| ~ big_p(a)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) )
& ! [U_22,U_12,U_18,U_23,U_17] :
( sP5(U_22)
| big_p(U_22)
| ~ big_p(a)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) )
& ! [U_7,U_8] :
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7)
| ~ big_p(U_8)
| ~ sP3(U_7,U_8) )
& ! [U_7,U_8] :
( big_r(sK4,sK5)
| ~ sP3(U_7,U_8) )
& ! [U_7,U_8] :
( big_p(sK5)
| ~ sP3(U_7,U_8) )
& ! [U_7,U_8] :
( big_p(a)
| ~ sP3(U_7,U_8) )
& ! [U_4,U_5] :
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4)
| ~ big_p(U_5)
| ~ sP2(U_4,U_5) )
& ! [U_4,U_5] :
( ~ big_p(sK3)
| ~ sP2(U_4,U_5) )
& ! [U_4,U_5] :
( big_p(a)
| ~ sP2(U_4,U_5) )
& ! [U_3] :
( big_r(sK2(U_3),sK1(U_3))
| ~ sP1(U_3) )
& ! [U_3] :
( big_r(U_3,sK2(U_3))
| ~ sP1(U_3) )
& ! [U_3] :
( big_p(sK1(U_3))
| ~ sP1(U_3) )
& ! [U_3,U_0] :
( ~ big_r(U_3,U_0)
| ~ big_p(U_0)
| ~ sP0(U_3,U_0) )
& ! [U_3,U_0] :
( big_p(U_3)
| ~ sP0(U_3,U_0) )
& ! [U_4,U_5,U_3,U_7,U_8,U_0] :
( sP3(U_7,U_8)
| sP2(U_4,U_5)
| ~ sP4(U_4,U_5,U_3,U_7,U_8,U_0) )
& ! [U_4,U_5,U_3,U_7,U_8,U_0] :
( sP1(U_3)
| sP0(U_3,U_0)
| ~ big_p(a)
| ~ sP4(U_4,U_5,U_3,U_7,U_8,U_0) )
& ! [U_4,U_5,U_3,U_7,U_8,U_22,U_12,U_18,U_23,U_0,U_17] :
( sP8(U_22,U_12,U_18,U_23,U_17)
| sP4(U_4,U_5,U_3,U_7,U_8,U_0) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3,sP4,sP5,sP6,sP7,sP8])],[f_1_15]) ).
cnf(f_1_17,negated_conjecture,
( sP8(U_22,U_12,U_18,U_23,U_17)
| sP4(U_4,U_5,U_3,U_7,U_8,U_0) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_18,negated_conjecture,
( sP1(U_3)
| sP0(U_3,U_0)
| ~ big_p(a)
| ~ sP4(U_4,U_5,U_3,U_7,U_8,U_0) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_19,negated_conjecture,
( sP3(U_7,U_8)
| sP2(U_4,U_5)
| ~ sP4(U_4,U_5,U_3,U_7,U_8,U_0) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_20,negated_conjecture,
( big_p(U_3)
| ~ sP0(U_3,U_0) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_21,negated_conjecture,
( ~ big_r(U_3,U_0)
| ~ big_p(U_0)
| ~ sP0(U_3,U_0) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_22,negated_conjecture,
( big_p(sK1(U_3))
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_23,negated_conjecture,
( big_r(U_3,sK2(U_3))
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_24,negated_conjecture,
( big_r(sK2(U_3),sK1(U_3))
| ~ sP1(U_3) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_25,negated_conjecture,
( big_p(a)
| ~ sP2(U_4,U_5) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_26,negated_conjecture,
( ~ big_p(sK3)
| ~ sP2(U_4,U_5) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_27,negated_conjecture,
( ~ big_r(U_4,U_5)
| ~ big_r(sK3,U_4)
| ~ big_p(U_5)
| ~ sP2(U_4,U_5) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_28,negated_conjecture,
( big_p(a)
| ~ sP3(U_7,U_8) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_29,negated_conjecture,
( big_p(sK5)
| ~ sP3(U_7,U_8) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_30,negated_conjecture,
( big_r(sK4,sK5)
| ~ sP3(U_7,U_8) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_31,negated_conjecture,
( ~ big_r(U_7,U_8)
| ~ big_r(sK4,U_7)
| ~ big_p(U_8)
| ~ sP3(U_7,U_8) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_32,negated_conjecture,
( sP5(U_22)
| big_p(U_22)
| ~ big_p(a)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_33,negated_conjecture,
( sP6(U_23)
| ~ big_r(U_23,U_12)
| ~ big_p(U_12)
| ~ big_p(a)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_34,negated_conjecture,
( big_p(a)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_35,negated_conjecture,
( sP7
| ~ big_p(sK10)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_36,negated_conjecture,
( ~ big_r(U_17,U_18)
| ~ big_r(sK10,U_17)
| ~ big_p(U_18)
| ~ sP8(U_22,U_12,U_18,U_23,U_17) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_37,negated_conjecture,
( big_p(sK6(U_22))
| ~ sP5(U_22) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_38,negated_conjecture,
( big_r(U_22,sK7(U_22))
| ~ sP5(U_22) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_39,negated_conjecture,
( big_r(sK7(U_22),sK6(U_22))
| ~ sP5(U_22) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_40,negated_conjecture,
( big_p(sK8(U_23))
| ~ sP6(U_23) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_41,negated_conjecture,
( big_r(U_23,sK9(U_23))
| ~ sP6(U_23) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_42,negated_conjecture,
( big_r(sK9(U_23),sK8(U_23))
| ~ sP6(U_23) ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_43,negated_conjecture,
( big_p(sK11)
| ~ sP7 ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(f_1_44,negated_conjecture,
( big_r(sK10,sK11)
| ~ sP7 ),
inference(clausify,[status(thm)],[f_1_16]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN067+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n005.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sun Sep 20 06:23:19 UTC 2026
% 0.10/0.58 % CPUTime :
% 150.04/150.59 % SZS status Theorem for theBenchmark
% 150.04/150.59 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------