%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM020+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 : n003.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 01:03:31 PM UTC 2026
% Result : Theorem 17.14s 2.91s
% Output : Proof 17.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 46 unt; 3 def)
% Number of atoms : 281 ( 31 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 314 ( 120 ~; 113 |; 69 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-4 aty)
% Number of variables : 120 ( 1 sgn 54 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(f5_nnf,plain,
! [W0,W1,W2] :
( ( ( ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ? [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(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( ( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ( sdtmndtplgtdt0(sk0(W0,W1,W2),W1,W2)
& aReductOfIn0(sk0(W0,W1,W2),W0,W1)
& aElement0(sk0(W0,W1,W2)) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f5_nnf]) ).
cnf(c8,plain,
( ~ aReductOfIn0(X2,X0,X1)
| sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(aElement0(X0),true,ifeq(aRewritingSystem0(X1),true,ifeq(aElement0(X2),true,ifeq(aReductOfIn0(X2,X0,X1),true,sdtmndtplgtdt0(X0,X1,X2),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
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(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(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]) ).
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(h31,plain,
sdtmndtplgtdt0(xa,xR,xu) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi41,hi38,hi49,hi50]) ).
fof(f11,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isTerminating0(W0)
<=> ! [W1,W2] :
( ( aElement0(W2)
& aElement0(W1) )
=> ( sdtmndtplgtdt0(W1,W0,W2)
=> iLess0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermin) ).
fof(f11_nnf,plain,
! [W0] :
( ( ( ? [W1,W2] :
( ~ iLess0(W2,W1)
& sdtmndtplgtdt0(W1,W0,W2)
& aElement0(W2)
& aElement0(W1) )
| isTerminating0(W0) )
& ( ! [W1,W2] :
( iLess0(W2,W1)
| ~ sdtmndtplgtdt0(W1,W0,W2)
| ~ aElement0(W2)
| ~ aElement0(W1) )
| ~ isTerminating0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [W0,W1,W2] :
( ( ( ( ~ iLess0(sk10(W0),sk9(W0))
& sdtmndtplgtdt0(sk9(W0),W0,sk10(W0))
& aElement0(sk10(W0))
& aElement0(sk9(W0)) )
| isTerminating0(W0) )
& ( iLess0(W2,W1)
| ~ sdtmndtplgtdt0(W1,W0,W2)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ isTerminating0(W0) ) )
| ~ aRewritingSystem0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f11_nnf]) ).
cnf(c33,plain,
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi29,axiom,
ifeq(aRewritingSystem0(X0),true,ifeq(isTerminating0(X0),true,ifeq(aElement0(X1),true,ifeq(aElement0(X2),true,ifeq(sdtmndtplgtdt0(X1,X0,X2),true,iLess0(X2,X1),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
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]) ).
cnf(h56,plain,
iLess0(xu,xa) = true,
inference(hyper_resolution,[status(thm)],[hi29,hi38,hi40,hi41,hi49,h31]) ).
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(c39,plain,
( sdtmndtasgtdt0(X0,X1,X2)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi35,axiom,
ifeq(aElement0(X0),true,ifeq(aRewritingSystem0(X1),true,ifeq(aNormalFormOfIn0(X2,X0,X1),true,sdtmndtasgtdt0(X0,X1,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
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]) ).
fof(f22,hypothesis,
aNormalFormOfIn0(xd,xw,xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__818) ).
fof(f22_nnf,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c63,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi58,axiom,
aNormalFormOfIn0(xd,xw,xR) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(h49,plain,
sdtmndtasgtdt0(xw,xR,xd) = true,
inference(hyper_resolution,[status(thm)],[hi35,hi55,hi38,hi58]) ).
cnf(c38,plain,
( aElement0(X2)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi34,axiom,
ifeq(aElement0(X0),true,ifeq(aRewritingSystem0(X1),true,ifeq(aNormalFormOfIn0(X2,X0,X1),true,aElement0(X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h50,plain,
aElement0(xd) = true,
inference(hyper_resolution,[status(thm)],[hi34,hi55,hi38,hi58]) ).
fof(f8,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtasgtdt0(W2,W1,W3)
& sdtmndtasgtdt0(W0,W1,W2) )
=> sdtmndtasgtdt0(W0,W1,W3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRTrans) ).
fof(f8_nnf,plain,
! [W0,W1,W2,W3] :
( sdtmndtasgtdt0(W0,W1,W3)
| ~ sdtmndtasgtdt0(W2,W1,W3)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [W0,W1,W2,W3] :
( sdtmndtasgtdt0(W0,W1,W3)
| ~ sdtmndtasgtdt0(W2,W1,W3)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c14,plain,
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi10,axiom,
ifeq(aElement0(X0),true,ifeq(aRewritingSystem0(X1),true,ifeq(aElement0(X2),true,ifeq(aElement0(X3),true,ifeq(sdtmndtasgtdt0(X0,X1,X2),true,ifeq(sdtmndtasgtdt0(X2,X1,X3),true,sdtmndtasgtdt0(X0,X1,X3),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(c61,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi56,axiom,
sdtmndtasgtdt0(xu,xR,xw) = true,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(h88,plain,
sdtmndtasgtdt0(xu,xR,xd) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi49,hi38,hi55,h50,hi56,h49]) ).
fof(f17,hypothesis,
! [W0,W1,W2] :
( ( sdtmndtasgtdt0(W0,xR,W2)
& sdtmndtasgtdt0(W0,xR,W1)
& aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( iLess0(W0,xa)
=> ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& sdtmndtasgtdt0(W1,xR,W3)
& aElement0(W3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__715) ).
fof(f17_nnf,plain,
! [W0,W1,W2] :
( ? [W3] :
( sdtmndtasgtdt0(W2,xR,W3)
& sdtmndtasgtdt0(W1,xR,W3)
& aElement0(W3) )
| ~ iLess0(W0,xa)
| ~ sdtmndtasgtdt0(W0,xR,W2)
| ~ sdtmndtasgtdt0(W0,xR,W1)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [W0,W1,W2] :
( ( sdtmndtasgtdt0(W2,xR,sk13(W0,W1,W2))
& sdtmndtasgtdt0(W1,xR,sk13(W0,W1,W2))
& aElement0(sk13(W0,W1,W2)) )
| ~ iLess0(W0,xa)
| ~ sdtmndtasgtdt0(W0,xR,W2)
| ~ sdtmndtasgtdt0(W0,xR,W1)
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f17_nnf]) ).
cnf(c51,plain,
( sdtmndtasgtdt0(X2,xR,sk13(X0,X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi46,axiom,
ifeq(aElement0(X0),true,ifeq(aElement0(X1),true,ifeq(aElement0(X2),true,ifeq(sdtmndtasgtdt0(X0,xR,X1),true,ifeq(sdtmndtasgtdt0(X0,xR,X2),true,ifeq(iLess0(X0,xa),true,sdtmndtasgtdt0(X2,xR,sk13(X0,X1,X2)),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(c47,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi42,axiom,
aElement0(xb) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(c56,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi51,axiom,
sdtmndtasgtdt0(xu,xR,xb) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(h114,plain,
sdtmndtasgtdt0(xd,xR,sk13(xu,xb,xd)) = true,
inference(hyper_resolution,[status(thm)],[hi46,hi49,hi42,h50,hi51,h88,h56]) ).
cnf(c50,plain,
( sdtmndtasgtdt0(X1,xR,sk13(X0,X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi45,axiom,
ifeq(aElement0(X0),true,ifeq(aElement0(X1),true,ifeq(aElement0(X2),true,ifeq(sdtmndtasgtdt0(X0,xR,X1),true,ifeq(sdtmndtasgtdt0(X0,xR,X2),true,ifeq(iLess0(X0,xa),true,sdtmndtasgtdt0(X1,xR,sk13(X0,X1,X2)),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(h118,plain,
sdtmndtasgtdt0(xb,xR,sk13(xu,xb,xd)) = true,
inference(hyper_resolution,[status(thm)],[hi45,hi49,hi42,h50,hi51,h88,h56]) ).
cnf(c49,plain,
( aElement0(sk13(X0,X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi44,axiom,
ifeq(aElement0(X0),true,ifeq(aElement0(X1),true,ifeq(aElement0(X2),true,ifeq(sdtmndtasgtdt0(X0,xR,X1),true,ifeq(sdtmndtasgtdt0(X0,xR,X2),true,ifeq(iLess0(X0,xa),true,aElement0(sk13(X0,X1,X2)),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h123,plain,
aElement0(sk13(xu,xb,xd)) = true,
inference(hyper_resolution,[status(thm)],[hi44,hi49,hi42,h50,hi51,h88,h56]) ).
fof(f23,conjecture,
? [W0] :
( sdtmndtasgtdt0(xd,xR,W0)
& sdtmndtasgtdt0(xb,xR,W0)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f23_neg,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(xd,xR,W0)
& sdtmndtasgtdt0(xb,xR,W0)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f23_nnf,plain,
! [W0] :
( ~ sdtmndtasgtdt0(xd,xR,W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f23_neg]) ).
fof(f23_sk,plain,
! [W0] :
( ~ sdtmndtasgtdt0(xd,xR,W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c64,plain,
( ~ sdtmndtasgtdt0(xd,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi60,negated_conjecture,
ifeq(aElement0(X0),true,ifeq(sdtmndtasgtdt0(xb,xR,X0),true,ifeq(sdtmndtasgtdt0(xd,xR,X0),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi60,h123,h118,h114]) ).
cnf(t5469,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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,c64]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5469]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM020+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n003.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 : Fri Sep 25 07:50:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.14/2.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.14/2.91 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------