%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 01:04:19 PM UTC 2026
% Result : Theorem 1.63s 1.29s
% Output : CNFRefutation 1.63s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f66ERROR: Could not build tree for root c_2297ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0] :
( ( isTerminating0(X0)
& aRewritingSystem0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ? [X2] : aNormalFormOfIn0(X2,X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f22,axiom,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xv,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(f23,conjecture,
? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X1] : aReductOfIn0(X1,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f24,negated_conjecture,
~ ? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X1] : aReductOfIn0(X1,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f32,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ? [X1] :
( sdtmndtplgtdt0(X1,xR,xw)
& aReductOfIn0(X1,xv,xR)
& aElement0(X1) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ? [X0] :
( sdtmndtplgtdt0(X0,xR,xw)
& aReductOfIn0(X0,xu,xR)
& aElement0(X0) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(rectify,[],[f22]) ).
fof(f33,plain,
~ ? [X0] :
( aNormalFormOfIn0(X0,xw,xR)
| ( ~ ? [X2] : aReductOfIn0(X2,X0,xR)
& ( sdtmndtasgtdt0(xw,xR,X0)
| sdtmndtplgtdt0(xw,xR,X0)
| ? [X1] :
( sdtmndtplgtdt0(X1,xR,X0)
& aReductOfIn0(X1,xw,xR)
& aElement0(X1) )
| aReductOfIn0(X0,xw,xR)
| xw = X0 )
& aElement0(X0) ) ),
inference(rectify,[],[f24]) ).
fof(f52,plain,
! [X0] :
( ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0)
| ! [X1] :
( ~ aElement0(X1)
| ? [X2] : aNormalFormOfIn0(X2,X1,X0) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f53,plain,
! [X0] :
( ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0)
| ! [X1] :
( ~ aElement0(X1)
| ? [X2] : aNormalFormOfIn0(X2,X1,X0) ) ),
inference(flattening,[],[f52]) ).
fof(f58,plain,
! [X0] :
( ~ aNormalFormOfIn0(X0,xw,xR)
& ( ? [X2] : aReductOfIn0(X2,X0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,X0)
& ~ sdtmndtplgtdt0(xw,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xw,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xw,xR)
& xw != X0 )
| ~ aElement0(X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f92,plain,
! [X0] :
( ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0)
| ! [X1] :
( ~ aElement0(X1)
| aNormalFormOfIn0(sK20(X0,X1),X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X0,X1))],[f53]) ).
fof(f96,plain,
( isTerminating0(xR)
& ! [X5,X6] :
( ~ aElement0(X6)
| ~ aElement0(X5)
| ( ~ sdtmndtplgtdt0(X5,xR,X6)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X6)
| ~ aReductOfIn0(X7,X5,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X6,X5,xR) )
| iLess0(X6,X5) )
& isLocallyConfluent0(xR)
& ! [X0,X1,X2] :
( ~ aReductOfIn0(X2,X0,xR)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sP4(X3,X2)
& sdtmndtasgtdt0(X1,xR,X3)
& ( ( sdtmndtplgtdt0(X1,xR,X3)
& ( ? [X4] :
( sdtmndtplgtdt0(X4,xR,X3)
& aReductOfIn0(X4,X1,xR)
& aElement0(X4) )
| aReductOfIn0(X3,X1,xR) ) )
| X1 = X3 )
& aElement0(X3) ) ) ),
inference(rectify,[],[f66]) ).
fof(f97,plain,
( isTerminating0(xR)
& ! [X5,X6] :
( ~ aElement0(X6)
| ~ aElement0(X5)
| ( ~ sdtmndtplgtdt0(X5,xR,X6)
& ! [X7] :
( ~ sdtmndtplgtdt0(X7,xR,X6)
| ~ aReductOfIn0(X7,X5,xR)
| ~ aElement0(X7) )
& ~ aReductOfIn0(X6,X5,xR) )
| iLess0(X6,X5) )
& isLocallyConfluent0(xR)
& ! [X0,X1,X2] :
( ~ aReductOfIn0(X2,X0,xR)
| ~ aReductOfIn0(X1,X0,xR)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtmndtasgtdt0(X2,xR,sK22(X1,X2))
& sP4(sK22(X1,X2),X2)
& sdtmndtasgtdt0(X1,xR,sK22(X1,X2))
& ( ( sdtmndtplgtdt0(X1,xR,sK22(X1,X2))
& ( ( sdtmndtplgtdt0(sK23(X1,X2),xR,sK22(X1,X2))
& aReductOfIn0(sK23(X1,X2),X1,xR)
& aElement0(sK23(X1,X2)) )
| aReductOfIn0(sK22(X1,X2),X1,xR) ) )
| sK22(X1,X2) = X1 )
& aElement0(sK22(X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22,sK23]),skolemize(X3,sK22(X1,X2)),skolemize(X4,sK23(X1,X2))],[f96]) ).
fof(f109,plain,
( sdtmndtasgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(xv,xR,xw)
& ( ( sdtmndtplgtdt0(sK32,xR,xw)
& aReductOfIn0(sK32,xv,xR)
& aElement0(sK32) )
| aReductOfIn0(xw,xv,xR) ) )
| xv = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(xu,xR,xw)
& ( ( sdtmndtplgtdt0(sK31,xR,xw)
& aReductOfIn0(sK31,xu,xR)
& aElement0(sK31) )
| aReductOfIn0(xw,xu,xR) ) )
| xu = xw )
& aElement0(xw) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32]),skolemize(X0,sK31),skolemize(X1,sK32)],[f32]) ).
fof(f110,plain,
! [X0] :
( ~ aNormalFormOfIn0(X0,xw,xR)
& ( aReductOfIn0(sK33(X0),X0,xR)
| ( ~ sdtmndtasgtdt0(xw,xR,X0)
& ~ sdtmndtplgtdt0(xw,xR,X0)
& ! [X1] :
( ~ sdtmndtplgtdt0(X1,xR,X0)
| ~ aReductOfIn0(X1,xw,xR)
| ~ aElement0(X1) )
& ~ aReductOfIn0(X0,xw,xR)
& xw != X0 )
| ~ aElement0(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(X2,sK33(X0))],[f58]) ).
fof(f155,plain,
! [X0,X1] :
( ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0)
| ~ aElement0(X1)
| aNormalFormOfIn0(sK20(X0,X1),X1,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f156,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f161,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f97]) ).
fof(f231,plain,
aElement0(xw),
inference(cnf_transformation,[],[f109]) ).
fof(f232,plain,
! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[],[f110]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( aNormalFormOfIn0(sK20(X1,X0),X0,X1)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_94,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f156]) ).
tcf(c_111,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f161]) ).
tcf(c_159,plain,
aElement0(xw),
inference(cnf_transformation,[],[f231]) ).
tcf(c_175,negated_conjecture,
! [X0: $i] : ~ aNormalFormOfIn0(X0,xw,xR),
inference(cnf_transformation,[],[f232]) ).
tcf(c_2295,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0)
| ~ aElement0(X1)
| ( X1 != xw )
| ( X0 != xR )
| ( sK20(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_93,c_175]) ).
tcf(c_2296,plain,
( ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xw) ),
inference(unflattening,[status(thm)],[c_2295]) ).
tcf(c_2297,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2296,c_94,c_111,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM018+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 07:50:38 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 1.63/1.29 % SZS status Started for theBenchmark.p
% 1.63/1.29 % SZS status Theorem for theBenchmark.p
% 1.63/1.29
% 1.63/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.63/1.29
% 1.63/1.29 % ------ iProver source info
% 1.63/1.29
% 1.63/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.63/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.63/1.29 % git: non_committed_changes: false
% 1.63/1.29
% 1.63/1.29 % ------ Parsing...
% 1.63/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.63/1.29
% 1.63/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s%
% 1.63/1.29
% 1.63/1.29 % SZS status Theorem for theBenchmark.p
% 1.63/1.29
% 1.63/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.63/1.29
% 1.63/1.29
%------------------------------------------------------------------------------