%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : n026.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 08:14:44 AM UTC 2026
% Result : Theorem 1.88s 2.18s
% Output : Proof 1.93s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(mElmSort,axiom,
! [W0] :
( aElement0(W0)
=> $true ),
file('theBenchmark.p',mElmSort) ).
fof(mRelSort,axiom,
! [W0] :
( aRewritingSystem0(W0)
=> $true ),
file('theBenchmark.p',mRelSort) ).
fof(mReduct,axiom,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ),
file('theBenchmark.p',mReduct) ).
fof(mWFOrd,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( iLess0(W0,W1)
=> $true ) ),
file('theBenchmark.p',mWFOrd) ).
fof(mTCbr,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
=> $true ) ),
file('theBenchmark.p',mTCbr) ).
fof(mTCDef,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1) ) ) ),
file('theBenchmark.p',mTCDef) ).
fof(mTCTrans,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W2,W1,W3)
& sdtmndtplgtdt0(W0,W1,W2) )
=> sdtmndtplgtdt0(W0,W1,W3) ) ),
file('theBenchmark.p',mTCTrans) ).
fof(mTCRDef,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2 ) ) ),
file('theBenchmark.p',mTCRDef) ).
fof(m__349,hypothesis,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
file('theBenchmark.p',m__349) ).
fof(m__,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
file('theBenchmark.p',m__) ).
fof(f_1_1,plain,
! [W0] :
( $true
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mElmSort]) ).
fof(f_1_2,plain,
! [U_0] :
( $true
| ~ aElement0(U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_0] : ~ aElement0(U_0)
| $true ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ aElement0(U_0)
| $true ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [W0] :
( $true
| ~ aRewritingSystem0(W0) ),
inference(fof_nnf,[status(thm)],[mRelSort]) ).
fof(f_2_2,plain,
! [U_1] :
( $true
| ~ aRewritingSystem0(U_1) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_1] : ~ aRewritingSystem0(U_1)
| $true ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( ~ aRewritingSystem0(U_1)
| $true ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [W0,W1] :
( ! [W2] :
( aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mReduct]) ).
fof(f_3_2,plain,
! [U_4,U_3] :
( ! [U_2] :
( aElement0(U_2)
| ~ aReductOfIn0(U_2,U_4,U_3) )
| ~ aRewritingSystem0(U_3)
| ~ aElement0(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( aElement0(U_2)
| ~ aReductOfIn0(U_2,U_4,U_3)
| ~ aRewritingSystem0(U_3)
| ~ aElement0(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [W0,W1] :
( $true
| ~ iLess0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mWFOrd]) ).
fof(f_4_2,plain,
! [U_6,U_5] :
( $true
| ~ iLess0(U_6,U_5)
| ~ aElement0(U_5)
| ~ aElement0(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( $true
| ~ iLess0(U_6,U_5)
| ~ aElement0(U_5)
| ~ aElement0(U_6) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [W0,W1,W2] :
( $true
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCbr]) ).
fof(f_5_2,plain,
! [U_9,U_8,U_7] :
( $true
| ~ sdtmndtplgtdt0(U_9,U_8,U_7)
| ~ aElement0(U_7)
| ~ aRewritingSystem0(U_8)
| ~ aElement0(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( $true
| ~ sdtmndtplgtdt0(U_9,U_8,U_7)
| ~ aElement0(U_7)
| ~ aRewritingSystem0(U_8)
| ~ aElement0(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [W0,W1,W2] :
( ( ( sdtmndtplgtdt0(W0,W1,W2)
| ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) ) )
& ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCDef]) ).
fof(f_6_2,plain,
! [U_14,U_13,U_12] :
( ( ( sdtmndtplgtdt0(U_14,U_13,U_12)
| ( ! [U_11] :
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11) )
& ~ aReductOfIn0(U_12,U_14,U_13) ) )
& ( ? [U_10] :
( sdtmndtplgtdt0(U_10,U_13,U_12)
& aReductOfIn0(U_10,U_14,U_13)
& aElement0(U_10) )
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12) ) )
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_14,U_13,U_12] :
( ( ( sdtmndtplgtdt0(U_14,U_13,U_12)
| ( ! [U_11] :
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11) )
& ~ aReductOfIn0(U_12,U_14,U_13) ) )
& ( ( sdtmndtplgtdt0(sK1(U_14,U_13,U_12),U_13,U_12)
& aReductOfIn0(sK1(U_14,U_13,U_12),U_14,U_13)
& aElement0(sK1(U_14,U_13,U_12)) )
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12) ) )
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_14,U_13,U_12))],[f_6_2]) ).
cnf(f_6_4,plain,
( aElement0(sK1(U_14,U_13,U_12))
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( aReductOfIn0(sK1(U_14,U_13,U_12),U_14,U_13)
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( sdtmndtplgtdt0(sK1(U_14,U_13,U_12),U_13,U_12)
| aReductOfIn0(U_12,U_14,U_13)
| ~ sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( ~ aReductOfIn0(U_12,U_14,U_13)
| sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( ~ sdtmndtplgtdt0(U_11,U_13,U_12)
| ~ aReductOfIn0(U_11,U_14,U_13)
| ~ aElement0(U_11)
| sdtmndtplgtdt0(U_14,U_13,U_12)
| ~ aElement0(U_12)
| ~ aRewritingSystem0(U_13)
| ~ aElement0(U_14) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [W0,W1,W2,W3] :
( sdtmndtplgtdt0(W0,W1,W3)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCTrans]) ).
fof(f_7_2,plain,
! [U_18,U_17,U_16,U_15] :
( sdtmndtplgtdt0(U_18,U_17,U_15)
| ~ sdtmndtplgtdt0(U_16,U_17,U_15)
| ~ sdtmndtplgtdt0(U_18,U_17,U_16)
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aRewritingSystem0(U_17)
| ~ aElement0(U_18) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( sdtmndtplgtdt0(U_18,U_17,U_15)
| ~ sdtmndtplgtdt0(U_16,U_17,U_15)
| ~ sdtmndtplgtdt0(U_18,U_17,U_16)
| ~ aElement0(U_15)
| ~ aElement0(U_16)
| ~ aRewritingSystem0(U_17)
| ~ aElement0(U_18) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [W0,W1,W2] :
( ( ( sdtmndtasgtdt0(W0,W1,W2)
| ( ~ sdtmndtplgtdt0(W0,W1,W2)
& W0 != W2 ) )
& ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2
| ~ sdtmndtasgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(fof_nnf,[status(thm)],[mTCRDef]) ).
fof(f_8_2,plain,
! [U_21,U_20,U_19] :
( ( ( sdtmndtasgtdt0(U_21,U_20,U_19)
| ( ~ sdtmndtplgtdt0(U_21,U_20,U_19)
& U_21 != U_19 ) )
& ( sdtmndtplgtdt0(U_21,U_20,U_19)
| U_21 = U_19
| ~ sdtmndtasgtdt0(U_21,U_20,U_19) ) )
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( sdtmndtplgtdt0(U_21,U_20,U_19)
| U_21 = U_19
| ~ sdtmndtasgtdt0(U_21,U_20,U_19)
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( U_21 != U_19
| sdtmndtasgtdt0(U_21,U_20,U_19)
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( ~ sdtmndtplgtdt0(U_21,U_20,U_19)
| sdtmndtasgtdt0(U_21,U_20,U_19)
| ~ aElement0(U_19)
| ~ aRewritingSystem0(U_20)
| ~ aElement0(U_21) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
inference(fof_nnf,[status(thm)],[m__349]) ).
cnf(f_9_2,plain,
aElement0(xx),
inference(clausify,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
aRewritingSystem0(xR),
inference(clausify,[status(thm)],[f_9_1]) ).
cnf(f_9_4,plain,
aElement0(xy),
inference(clausify,[status(thm)],[f_9_1]) ).
cnf(f_9_5,plain,
aElement0(xz),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,negated_conjecture,
( ~ ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz )
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(negate,[status(cth)],[m__]) ).
fof(f_10_2,negated_conjecture,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [W0] :
( ~ sdtmndtplgtdt0(W0,xR,xz)
| ~ aReductOfIn0(W0,xx,xR)
| ~ aElement0(W0) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(fof_nnf,[status(thm)],[f_10_1]) ).
fof(f_10_3,negated_conjecture,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [U_24] :
( ~ sdtmndtplgtdt0(U_24,xR,xz)
| ~ aReductOfIn0(U_24,xx,xR)
| ~ aElement0(U_24) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [U_23] :
( sdtmndtplgtdt0(U_23,xR,xz)
& aReductOfIn0(U_23,xy,xR)
& aElement0(U_23) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [U_22] :
( sdtmndtplgtdt0(U_22,xR,xy)
& aReductOfIn0(U_22,xx,xR)
& aElement0(U_22) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(variable_rename,[status(thm)],[f_10_2]) ).
fof(f_10_4,negated_conjecture,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [U_24] :
( ~ sdtmndtplgtdt0(U_24,xR,xz)
| ~ aReductOfIn0(U_24,xx,xR)
| ~ aElement0(U_24) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [U_23] :
( sdtmndtplgtdt0(U_23,xR,xz)
& aReductOfIn0(U_23,xy,xR)
& aElement0(U_23) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(sK2,xR,xy)
& aReductOfIn0(sK2,xx,xR)
& aElement0(sK2) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_22,sK2)],[f_10_3]) ).
fof(f_10_5,negated_conjecture,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [U_24] :
( ~ sdtmndtplgtdt0(U_24,xR,xz)
| ~ aReductOfIn0(U_24,xx,xR)
| ~ aElement0(U_24) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(sK3,xR,xz)
& aReductOfIn0(sK3,xy,xR)
& aElement0(sK3) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(sK2,xR,xy)
& aReductOfIn0(sK2,xx,xR)
& aElement0(sK2) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_23,sK3)],[f_10_4]) ).
fof(f_10_6,negated_conjecture,
( ( sdtmndtplgtdt0(sK3,xR,xz)
| ~ sP2 )
& ( aReductOfIn0(sK3,xy,xR)
| ~ sP2 )
& ( aElement0(sK3)
| ~ sP2 )
& ( sdtmndtplgtdt0(xy,xR,xz)
| ~ sP3 )
& ( sP2
| aReductOfIn0(xz,xy,xR)
| ~ sP3 )
& ( sdtmndtplgtdt0(sK2,xR,xy)
| ~ sP0 )
& ( aReductOfIn0(sK2,xx,xR)
| ~ sP0 )
& ( aElement0(sK2)
| ~ sP0 )
& ( sdtmndtplgtdt0(xx,xR,xy)
| ~ sP1 )
& ( sP0
| aReductOfIn0(xy,xx,xR)
| ~ sP1 )
& ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [U_24] :
( ~ sdtmndtplgtdt0(U_24,xR,xz)
| ~ aReductOfIn0(U_24,xx,xR)
| ~ aElement0(U_24) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( sP3
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( sP1
| xx = xy ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2,sP3])],[f_10_5]) ).
cnf(f_10_7,negated_conjecture,
( sP1
| xx = xy ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_8,negated_conjecture,
sdtmndtasgtdt0(xx,xR,xy),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_9,negated_conjecture,
( sP3
| xy = xz ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_10,negated_conjecture,
sdtmndtasgtdt0(xy,xR,xz),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_11,negated_conjecture,
xx != xz,
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_12,negated_conjecture,
~ aReductOfIn0(xz,xx,xR),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_13,negated_conjecture,
( ~ sdtmndtplgtdt0(U_24,xR,xz)
| ~ aReductOfIn0(U_24,xx,xR)
| ~ aElement0(U_24) ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_14,negated_conjecture,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_15,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_16,negated_conjecture,
( sP0
| aReductOfIn0(xy,xx,xR)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_17,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_18,negated_conjecture,
( aElement0(sK2)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_19,negated_conjecture,
( aReductOfIn0(sK2,xx,xR)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_20,negated_conjecture,
( sdtmndtplgtdt0(sK2,xR,xy)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_21,negated_conjecture,
( sP2
| aReductOfIn0(xz,xy,xR)
| ~ sP3 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_22,negated_conjecture,
( sdtmndtplgtdt0(xy,xR,xz)
| ~ sP3 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_23,negated_conjecture,
( aElement0(sK3)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_24,negated_conjecture,
( aReductOfIn0(sK3,xy,xR)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_10_25,negated_conjecture,
( sdtmndtplgtdt0(sK3,xR,xz)
| ~ sP2 ),
inference(clausify,[status(thm)],[f_10_6]) ).
cnf(f_1_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_1_4]) ).
cnf(f_2_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_4]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
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,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(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,
( aElement0(Eq_y_0)
| ~ aElement0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_6,axiom,
( aRewritingSystem0(Eq_y_0)
| ~ aRewritingSystem0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_7,axiom,
( aReductOfIn0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ aReductOfIn0(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_8,axiom,
( iLess0(Eq_y_0,Eq_y_1)
| ~ iLess0(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,
( sdtmndtplgtdt0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sdtmndtplgtdt0(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_10,axiom,
( sdtmndtasgtdt0(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sdtmndtasgtdt0(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 15:14:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 1.88/2.18 % SZS status Theorem for theBenchmark
% 1.88/2.18 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------