%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 01:03:30 PM UTC 2026
% Result : Theorem 23.08s 8.65s
% Output : Proof 23.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 28 unt; 2 def)
% Number of atoms : 178 ( 18 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 193 ( 70 ~; 62 |; 56 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 66 ( 1 sgn 27 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isLocallyConfluent0(W0)
<=> ! [W1,W2,W3] :
( ( aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
=> ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mWCRDef) ).
fof(f10_nnf,plain,
! [W0] :
( ( ( ? [W1,W2,W3] :
( ! [W4] :
( ~ sdtmndtasgtdt0(W3,W0,W4)
| ~ sdtmndtasgtdt0(W2,W0,W4)
| ~ aElement0(W4) )
& aReductOfIn0(W3,W1,W0)
& aReductOfIn0(W2,W1,W0)
& aElement0(W3)
& aElement0(W2)
& aElement0(W1) )
| isLocallyConfluent0(W0) )
& ( ! [W1,W2,W3] :
( ? [W4] :
( sdtmndtasgtdt0(W3,W0,W4)
& sdtmndtasgtdt0(W2,W0,W4)
& aElement0(W4) )
| ~ aReductOfIn0(W3,W1,W0)
| ~ aReductOfIn0(W2,W1,W0)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1) )
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [W0,W1,W2,W3,W4] :
( ( ( ( ( ~ sdtmndtasgtdt0(sk8(W0),W0,W4)
| ~ sdtmndtasgtdt0(sk7(W0),W0,W4)
| ~ aElement0(W4) )
& aReductOfIn0(sk8(W0),sk6(W0),W0)
& aReductOfIn0(sk7(W0),sk6(W0),W0)
& aElement0(sk8(W0))
& aElement0(sk7(W0))
& aElement0(sk6(W0)) )
| isLocallyConfluent0(W0) )
& ( ( sdtmndtasgtdt0(W3,W0,sk5(W0,W1,W2,W3))
& sdtmndtasgtdt0(W2,W0,sk5(W0,W1,W2,W3))
& aElement0(sk5(W0,W1,W2,W3)) )
| ~ aReductOfIn0(W3,W1,W0)
| ~ aReductOfIn0(W2,W1,W0)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ isLocallyConfluent0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6,sk7,sk8])],[f10_nnf]) ).
cnf(c26,plain,
( sdtmndtasgtdt0(X3,X0,sk5(X0,X1,X2,X3))
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi22,axiom,
ifeq(aRewritingSystem0(X0),true,ifeq(isLocallyConfluent0(X0),true,ifeq(aElement0(X1),true,ifeq(aElement0(X2),true,ifeq(aElement0(X3),true,ifeq(aReductOfIn0(X2,X1,X0),true,ifeq(aReductOfIn0(X3,X1,X0),true,sdtmndtasgtdt0(X3,X0,sk5(X0,X1,X2,X3)),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
fof(f14,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f14_nnf,plain,
aRewritingSystem0(xR),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c43,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi38,axiom,
aRewritingSystem0(xR) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
fof(f15,hypothesis,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
fof(f15_nnf,plain,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c44,plain,
isLocallyConfluent0(xR),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi39,axiom,
isLocallyConfluent0(xR) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
fof(f16,hypothesis,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f16_nnf,plain,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c46,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi41,axiom,
aElement0(xa) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
fof(f19,hypothesis,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
fof(f19_nnf,plain,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c54,plain,
aElement0(xu),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi49,axiom,
aElement0(xu) = true,
inference(equality_encoding,[status(esa)],[c54]) ).
fof(f20,hypothesis,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__779) ).
fof(f20_nnf,plain,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c57,plain,
aElement0(xv),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi52,axiom,
aElement0(xv) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(c55,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi50,axiom,
aReductOfIn0(xu,xa,xR) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(c58,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi53,axiom,
aReductOfIn0(xv,xa,xR) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(h34,plain,
sdtmndtasgtdt0(xv,xR,sk5(xR,xa,xu,xv)) = true,
inference(hyper_resolution,[status(thm)],[hi22,hi38,hi39,hi41,hi49,hi52,hi50,hi53]) ).
cnf(c25,plain,
( sdtmndtasgtdt0(X2,X0,sk5(X0,X1,X2,X3))
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi21,axiom,
ifeq(aRewritingSystem0(X0),true,ifeq(isLocallyConfluent0(X0),true,ifeq(aElement0(X1),true,ifeq(aElement0(X2),true,ifeq(aElement0(X3),true,ifeq(aReductOfIn0(X2,X1,X0),true,ifeq(aReductOfIn0(X3,X1,X0),true,sdtmndtasgtdt0(X2,X0,sk5(X0,X1,X2,X3)),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(h36,plain,
sdtmndtasgtdt0(xu,xR,sk5(xR,xa,xu,xv)) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi38,hi39,hi41,hi49,hi52,hi50,hi53]) ).
cnf(c24,plain,
( aElement0(sk5(X0,X1,X2,X3))
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isLocallyConfluent0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi20,axiom,
ifeq(aRewritingSystem0(X0),true,ifeq(isLocallyConfluent0(X0),true,ifeq(aElement0(X1),true,ifeq(aElement0(X2),true,ifeq(aElement0(X3),true,ifeq(aReductOfIn0(X2,X1,X0),true,ifeq(aReductOfIn0(X3,X1,X0),true,aElement0(sk5(X0,X1,X2,X3)),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h39,plain,
aElement0(sk5(xR,xa,xu,xv)) = true,
inference(hyper_resolution,[status(thm)],[hi20,hi38,hi39,hi41,hi49,hi52,hi50,hi53]) ).
fof(f21,conjecture,
? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f21_neg,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(xv,xR,W0)
& sdtmndtasgtdt0(xu,xR,W0)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f21_nnf,plain,
! [W0] :
( ~ sdtmndtasgtdt0(xv,xR,W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f21_neg]) ).
fof(f21_sk,plain,
! [W0] :
( ~ sdtmndtasgtdt0(xv,xR,W0)
| ~ sdtmndtasgtdt0(xu,xR,W0)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c60,plain,
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi56,negated_conjecture,
ifeq(aElement0(X0),true,ifeq(sdtmndtasgtdt0(xu,xR,X0),true,ifeq(sdtmndtasgtdt0(xv,xR,X0),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi56,h39,h36,h34]) ).
cnf(t2615,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f12,definition,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aNormalFormOfIn0(W2,W0,W1)
<=> ( ~ ? [W3] : aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNFRDef) ).
fof(f12_nnf,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] : aReductOfIn0(W3,W2,W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W2)
| aNormalFormOfIn0(W2,W0,W1) )
& ( ( ! [W3] : ~ aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) )
| ~ aNormalFormOfIn0(W2,W0,W1) ) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [W0,W1,W2,W3] :
( ( ( aReductOfIn0(sk11(W0,W1,W2),W2,W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W2)
| aNormalFormOfIn0(W2,W0,W1) )
& ( ( ~ aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) )
| ~ aNormalFormOfIn0(W2,W0,W1) ) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f12_nnf]) ).
cnf(c40,plain,
( ~ aReductOfIn0(X3,X2,X1)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c40,c60]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2615]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COM017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/5.68 % Computer : n010.cluster.edu
% 0.18/5.68 % Model : x86_64 x86_64
% 0.18/5.68 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.68 % Memory : 8046.5625MB
% 0.18/5.68 % OS : Linux 6.8.0-71-generic
% 0.18/5.68 % CPULimit : 300
% 0.18/5.68 % WCLimit : 300
% 0.18/5.68 % DateTime : Fri Sep 25 07:48:10 UTC 2026
% 0.18/5.68 % CPUTime :
% 0.18/5.68 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.08/8.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.08/8.65 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------