%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM018+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 : n001.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 5.99s 1.25s
% Output : Proof 5.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 21 unt; 1 def)
% Number of atoms : 82 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 79 ( 32 ~; 24 |; 19 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-4 aty)
% Number of variables : 35 ( 3 sgn 19 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [W0] :
( ( isTerminating0(W0)
& aRewritingSystem0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
fof(f13_nnf,plain,
! [W0] :
( ! [W1] :
( ? [W2] : aNormalFormOfIn0(W2,W1,W0)
| ~ aElement0(W1) )
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [W0,W1] :
( aNormalFormOfIn0(sk12(W0,W1),W1,W0)
| ~ aElement0(W1)
| ~ isTerminating0(W0)
| ~ aRewritingSystem0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12])],[f13_nnf]) ).
cnf(c42,plain,
( aNormalFormOfIn0(sk12(X0,X1),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi37,axiom,
ifeq(aRewritingSystem0(X0),true,ifeq(isTerminating0(X0),true,ifeq(aElement0(X1),true,aNormalFormOfIn0(sk12(X0,X1),X1,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
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(c45,plain,
isTerminating0(xR),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi40,axiom,
isTerminating0(xR) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f21,hypothesis,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f21_nnf,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& sdtmndtasgtdt0(xu,xR,xw)
& aElement0(xw) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c60,plain,
aElement0(xw),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi55,axiom,
aElement0(xw) = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(h18,plain,
aNormalFormOfIn0(sk12(xR,xw),xw,xR) = true,
inference(hyper_resolution,[status(thm)],[hi37,hi38,hi40,hi55]) ).
fof(f22,conjecture,
? [W0] : aNormalFormOfIn0(W0,xw,xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f22_neg,negated_conjecture,
~ ? [W0] : aNormalFormOfIn0(W0,xw,xR),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f22_nnf,plain,
! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(nnf_transformation,[status(thm)],[f22_neg]) ).
fof(f22_sk,plain,
! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c63,plain,
~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi59,negated_conjecture,
ifeq(aNormalFormOfIn0(X0,xw,xR),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi59,h18]) ).
cnf(t2740,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,c63]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2740]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM018+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.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 : Fri Sep 25 07:54:55 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.99/1.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.99/1.25 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------