%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG073+2 : 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 : n013.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 02:38:44 PM UTC 2026
% Result : Theorem 4.40s 1.29s
% Output : CNFRefutation 4.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 23 unt; 0 def)
% Number of atoms : 153 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 180 ( 84 ~; 79 |; 11 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSumSc) ).
fof(f11,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulSc) ).
fof(f21,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEASm) ).
fof(f28,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> ( ( sdtasdt0(X0,X0) = sdtasdt0(X1,X1)
& sdtlseqdt0(sz0z00,X1)
& sdtlseqdt0(sz0z00,X0) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSqrt) ).
fof(f52,axiom,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1892) ).
fof(f53,axiom,
( xP = sdtasdt0(xE,xH)
& aScalar0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1911) ).
fof(f54,axiom,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1930) ).
fof(f59,axiom,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2405) ).
fof(f62,axiom,
( sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
& sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2628) ).
fof(f63,axiom,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2654) ).
fof(f64,conjecture,
sdtpldt0(xR,xS) = sdtpldt0(xP,xP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f65,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f71,plain,
sdtpldt0(xP,xP) != sdtpldt0(xR,xS),
inference(flattening,[],[f65]) ).
fof(f78,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f79,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f80]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f96,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f95]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f28]) ).
fof(f109,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(flattening,[],[f108]) ).
fof(f141,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f142,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| aScalar0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f163,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f96]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,X0) != sdtasdt0(X1,X1)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f109]) ).
fof(f214,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f52]) ).
fof(f216,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f53]) ).
fof(f218,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f54]) ).
fof(f224,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(cnf_transformation,[],[f59]) ).
fof(f227,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
inference(cnf_transformation,[],[f62]) ).
fof(f228,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(cnf_transformation,[],[f62]) ).
fof(f229,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(cnf_transformation,[],[f63]) ).
fof(f230,plain,
sdtpldt0(xP,xP) != sdtpldt0(xR,xS),
inference(cnf_transformation,[],[f71]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f141]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ~ sdtlseqdt0(sz0z00,X1)
| ~ sdtlseqdt0(sz0z00,X0)
| ( sdtasdt0(X0,X0) != sdtasdt0(X1,X1) ) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_129,plain,
aScalar0(xR),
inference(cnf_transformation,[],[f214]) ).
tcf(c_131,plain,
aScalar0(xP),
inference(cnf_transformation,[],[f216]) ).
tcf(c_133,plain,
aScalar0(xS),
inference(cnf_transformation,[],[f218]) ).
tcf(c_140,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS))),
inference(cnf_transformation,[],[f224]) ).
tcf(c_143,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xR,xS)),
inference(cnf_transformation,[],[f228]) ).
tcf(c_144,plain,
sdtlseqdt0(sz0z00,sdtpldt0(xP,xP)),
inference(cnf_transformation,[],[f227]) ).
tcf(c_145,plain,
sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))),
inference(cnf_transformation,[],[f229]) ).
tcf(c_146,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(cnf_transformation,[],[f230]) ).
tcf(c_1176,negated_conjecture,
sdtpldt0(xR,xS) != sdtpldt0(xP,xP),
inference(subtyping,[status(esa)],[c_146]) ).
tcf(c_1232,plain,
! [X0_iProver_sdtpldt0_1: iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1: iProver_sdtpldt0_1] :
( ( X0_iProver_sdtpldt0_1 = X1_iProver_sdtpldt0_1 )
| ~ aScalar0(X1_iProver_sdtpldt0_1)
| ~ aScalar0(X0_iProver_sdtpldt0_1)
| ~ sdtlseqdt0(sz0z00,X1_iProver_sdtpldt0_1)
| ~ sdtlseqdt0(sz0z00,X0_iProver_sdtpldt0_1)
| ( sdtasdt0(X0_iProver_sdtpldt0_1,X0_iProver_sdtpldt0_1) != sdtasdt0(X1_iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1) ) ),
inference(subtyping,[status(esa)],[c_87]) ).
tcf(c_1240,plain,
! [X0_iProver_sdtpldt0_1: iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1: iProver_sdtpldt0_1] :
( ( X0_iProver_sdtpldt0_1 = X1_iProver_sdtpldt0_1 )
| ~ aScalar0(X1_iProver_sdtpldt0_1)
| ~ aScalar0(X0_iProver_sdtpldt0_1)
| ~ sdtlseqdt0(X1_iProver_sdtpldt0_1,X0_iProver_sdtpldt0_1)
| ~ sdtlseqdt0(X0_iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1) ),
inference(subtyping,[status(esa)],[c_79]) ).
tcf(c_1260,plain,
! [X0_iProver_sdtpldt0_1: iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1: iProver_sdtpldt0_1] :
( aScalar0(sdtasdt0(X0_iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1))
| ~ aScalar0(X1_iProver_sdtpldt0_1)
| ~ aScalar0(X0_iProver_sdtpldt0_1) ),
inference(subtyping,[status(esa)],[c_58]) ).
tcf(c_1261,plain,
! [X0_iProver_sdtpldt0_1: iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1: iProver_sdtpldt0_1] :
( aScalar0(sdtpldt0(X0_iProver_sdtpldt0_1,X1_iProver_sdtpldt0_1))
| ~ aScalar0(X1_iProver_sdtpldt0_1)
| ~ aScalar0(X0_iProver_sdtpldt0_1) ),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_2472,plain,
( ( sdtpldt0(xR,xS) = sdtpldt0(xP,xP) )
| ~ aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(sdtpldt0(xR,xS))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xP,xP))
| ~ sdtlseqdt0(sz0z00,sdtpldt0(xR,xS))
| ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) != sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) ) ),
inference(instantiation,[status(thm)],[c_1232]) ).
tcf(c_2567,plain,
( aScalar0(sdtpldt0(xP,xP))
| ~ aScalar0(xP) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_2581,plain,
( aScalar0(sdtpldt0(xR,xS))
| ~ aScalar0(xS)
| ~ aScalar0(xR) ),
inference(instantiation,[status(thm)],[c_1261]) ).
tcf(c_2791,plain,
( ( sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)) = sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)) )
| ~ aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)),sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ sdtlseqdt0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)),sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP))) ),
inference(instantiation,[status(thm)],[c_1240]) ).
tcf(c_3292,plain,
( aScalar0(sdtasdt0(sdtpldt0(xP,xP),sdtpldt0(xP,xP)))
| ~ aScalar0(sdtpldt0(xP,xP)) ),
inference(instantiation,[status(thm)],[c_1260]) ).
tcf(c_3657,plain,
( aScalar0(sdtasdt0(sdtpldt0(xR,xS),sdtpldt0(xR,xS)))
| ~ aScalar0(sdtpldt0(xR,xS)) ),
inference(instantiation,[status(thm)],[c_1260]) ).
tcf(c_3658,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3657,c_3292,c_2791,c_2581,c_2567,c_2472,c_1176,c_140,c_145,c_143,c_144,c_129,c_131,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG073+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 08:05:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 4.40/1.29 % SZS status Started for theBenchmark.p
% 4.40/1.29 % SZS status Theorem for theBenchmark.p
% 4.40/1.29
% 4.40/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.40/1.29
% 4.40/1.29 % ------ iProver source info
% 4.40/1.29
% 4.40/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 4.40/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.40/1.29 % git: non_committed_changes: false
% 4.40/1.29
% 4.40/1.29 % ------ Parsing...
% 4.40/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.40/1.29
% 4.40/1.29 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.40/1.29
% 4.40/1.29 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.40/1.29
% 4.40/1.29 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 4.40/1.29 % ------ Proving...
% 4.40/1.29 % ------ Problem Properties
% 4.40/1.29
% 4.40/1.29 %
% 4.40/1.29 % clauses 100
% 4.40/1.29 % conjectures 1
% 4.40/1.29 % EPR 25
% 4.40/1.29 % Horn 88
% 4.40/1.29 % unary 47
% 4.40/1.29 % binary 19
% 4.40/1.29 % lits 234
% 4.40/1.29 % lits eq 72
% 4.40/1.29 % fd_pure 0
% 4.40/1.29 % fd_pseudo 0
% 4.40/1.29 % fd_cond 1
% 4.40/1.29 % fd_pseudo_cond 5
% 4.40/1.29 % AC symbols 0
% 4.40/1.29
% 4.40/1.29 % ------ Input Options Time Limit: Unbounded
% 4.40/1.29
% 4.40/1.29
% 4.40/1.29 % ------
% 4.40/1.29 % Current options:
% 4.40/1.29 % ------
% 4.40/1.29
% 4.40/1.29
% 4.40/1.29 %
% 4.40/1.29
% 4.40/1.29 % ------ Proving...
% 4.40/1.29 %
% 4.40/1.29
% 4.40/1.29 % SZS status Theorem for theBenchmark.p
% 4.40/1.29
% 4.40/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.40/1.29
% 4.40/1.29
%------------------------------------------------------------------------------