%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM524+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n011.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 02:25:49 PM UTC 2026
% Result : Theorem 1.31s 1.74s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 28 unt; 0 def)
% Number of atoms : 172 ( 73 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 201 ( 94 ~; 86 |; 14 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 != sz00
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(f40,axiom,
( xp != sz00
& xm != sz00
& xn != sz00
& aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
fof(f42,axiom,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
fof(f45,axiom,
( xq = sdtsldt0(xn,xp)
& xn = sdtasdt0(xp,xq)
& aNaturalNumber0(xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
fof(f46,conjecture,
sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(negated_conjecture,[status(cth)],[f46]) ).
fof(f51,plain,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(flattening,[],[f47]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f55,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f54]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(flattening,[],[f63]) ).
fof(f71,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f72,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ! [X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| X1 = X2 ) ),
inference(flattening,[],[f71]) ).
fof(f143,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f55]) ).
fof(f148,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X0)
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f208,plain,
sz00 != xp,
inference(cnf_transformation,[],[f40]) ).
fof(f211,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f40]) ).
fof(f212,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f40]) ).
fof(f221,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f42]) ).
fof(f233,plain,
xn = sdtasdt0(xp,xq),
inference(cnf_transformation,[],[f45]) ).
fof(f234,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f45]) ).
fof(f235,plain,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 = sz00 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_118,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f212]) ).
tcf(c_119,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f211]) ).
tcf(c_122,plain,
sz00 != xp,
inference(cnf_transformation,[],[f208]) ).
tcf(c_130,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnf_transformation,[],[f221]) ).
tcf(c_141,plain,
aNaturalNumber0(xq),
inference(cnf_transformation,[],[f234]) ).
tcf(c_142,plain,
sdtasdt0(xp,xq) = xn,
inference(cnf_transformation,[],[f233]) ).
tcf(c_144,negated_conjecture,
sdtasdt0(xp,sdtasdt0(xq,xq)) != sdtasdt0(xm,xm),
inference(cnf_transformation,[],[f235]) ).
tcf(c_190,plain,
( aNaturalNumber0(xn)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm)],[c_142,c_53]) ).
tcf(c_204,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xq) = sdtasdt0(xq,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_141,c_58]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(xp,X0),X1) = sdtasdt0(xp,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_119,c_59]) ).
tcf(c_289,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( sdtasdt0(xm,xm) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( sdtasdt0(xp,X0) != sdtasdt0(xn,xn) ) ),
inference(superposition,[status(thm)],[c_130,c_68]) ).
tcf(c_354,plain,
aNaturalNumber0(xn),
inference(global_subsumption_just,[status(thm)],[c_190,c_141,c_119,c_190]) ).
tcf(c_419,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xp) = sdtasdt0(xp,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_119,c_58]) ).
tcf(c_426,plain,
sdtasdt0(xn,xq) = sdtasdt0(xq,xn),
inference(superposition,[status(thm)],[c_354,c_204]) ).
tcf(c_574,plain,
! [X0: $i] :
( ( sz00 = xp )
| ( sdtasdt0(xm,xm) = X0 )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( sdtasdt0(xp,X0) != sdtasdt0(xn,xn) ) ),
inference(superposition,[status(thm)],[c_130,c_68]) ).
tcf(c_587,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(xp,xq),X0) = sdtasdt0(xp,sdtasdt0(xq,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_141,c_250]) ).
tcf(c_716,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( sdtasdt0(xp,X0) != sdtasdt0(xn,xn) )
| ( sdtasdt0(xm,xm) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_289,c_119,c_122,c_289]) ).
tcf(c_717,plain,
! [X0: $i] :
( ( sdtasdt0(xm,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( sdtasdt0(xp,X0) != sdtasdt0(xn,xn) ) ),
inference(renaming,[status(thm)],[c_716]) ).
tcf(c_947,plain,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(superposition,[status(thm)],[c_118,c_419]) ).
tcf(c_1158,plain,
( aNaturalNumber0(sdtasdt0(xn,xq))
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm)],[c_426,c_53]) ).
tcf(c_1277,plain,
! [X0: $i] :
( ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( sdtasdt0(xp,X0) != sdtasdt0(xn,xn) )
| ( sdtasdt0(xm,xm) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_574,c_717]) ).
tcf(c_1278,plain,
! [X0: $i] :
( ( sdtasdt0(xm,xm) = X0 )
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( sdtasdt0(xp,X0) != sdtasdt0(xn,xn) ) ),
inference(renaming,[status(thm)],[c_1277]) ).
tcf(c_1650,plain,
! [X0: $i] :
( ( sdtasdt0(xp,sdtasdt0(xq,X0)) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_587,c_142]) ).
tcf(c_1656,plain,
sdtasdt0(xp,sdtasdt0(xq,xn)) = sdtasdt0(xn,xn),
inference(superposition,[status(thm)],[c_354,c_1650]) ).
tcf(c_1659,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) = sdtasdt0(xn,xq),
inference(superposition,[status(thm)],[c_141,c_1650]) ).
tcf(c_1661,plain,
sdtasdt0(xn,xq) != sdtasdt0(xm,xm),
inference(demodulation,[status(thm)],[c_144,c_1659]) ).
tcf(c_2318,plain,
( ( sdtasdt0(xm,xm) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ( sdtasdt0(xn,xn) != sdtasdt0(xm,xp) ) ),
inference(superposition,[status(thm)],[c_947,c_1278]) ).
tcf(c_6824,plain,
sdtasdt0(xp,sdtasdt0(xn,xq)) = sdtasdt0(xn,xn),
inference(light_normalisation,[status(thm)],[c_1656,c_426]) ).
tcf(c_6835,plain,
( ( sdtasdt0(xn,xq) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xq)) ),
inference(superposition,[status(thm)],[c_6824,c_717]) ).
tcf(c_8815,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(global_subsumption_just,[status(thm)],[c_2318,c_141,c_119,c_190,c_1158,c_1661,c_6835]) ).
tcf(c_8817,plain,
~ aNaturalNumber0(xm),
inference(superposition,[status(thm)],[c_53,c_8815]) ).
tcf(c_8818,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_118,c_8817]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM524+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n011.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 04:26:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 1.31/1.74 % SZS status Started for theBenchmark.p
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74
% 1.31/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.31/1.74
% 1.31/1.74 % ------ iProver source info
% 1.31/1.74
% 1.31/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.31/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.31/1.74 % git: non_committed_changes: false
% 1.31/1.74
% 1.31/1.74 % ------ Parsing...
% 1.31/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.31/1.74 % ------ Proving...
% 1.31/1.74 % ------ Problem Properties
% 1.31/1.74
% 1.31/1.74 %
% 1.31/1.74 % clauses 96
% 1.31/1.74 % conjectures 1
% 1.31/1.74 % EPR 28
% 1.31/1.74 % Horn 60
% 1.31/1.74 % unary 22
% 1.31/1.74 % binary 10
% 1.31/1.74 % lits 390
% 1.31/1.74 % lits eq 133
% 1.31/1.74 % fd_pure 0
% 1.31/1.74 % fd_pseudo 0
% 1.31/1.74 % fd_cond 23
% 1.31/1.74 % fd_pseudo_cond 15
% 1.31/1.74 % AC symbols 0
% 1.31/1.74
% 1.31/1.74 % ------ Input Options Time Limit: Unbounded
% 1.31/1.74
% 1.31/1.74
% 1.31/1.74 % ------
% 1.31/1.74 % Current options:
% 1.31/1.74 % ------
% 1.31/1.74
% 1.31/1.74
% 1.31/1.74 %
% 1.31/1.74
% 1.31/1.74 % ------ Proving...
% 1.31/1.74 %
% 1.31/1.74
% 1.31/1.74 % SZS status Theorem for theBenchmark.p
% 1.31/1.74
% 1.31/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.31/1.74
% 1.31/1.74
%------------------------------------------------------------------------------