%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM478+2 : 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 : n007.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 02:25:10 PM UTC 2026
% Result : Theorem 4.39s 1.31s
% Output : CNFRefutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 21 unt; 0 def)
% Number of atoms : 88 ( 39 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 36 ~; 30 |; 12 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
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(f36,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1524) ).
fof(f38,axiom,
aNaturalNumber0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1553) ).
fof(f39,conjecture,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40,negated_conjecture,
~ ( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
=> ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl)
| sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f53,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(flattening,[],[f53]) ).
fof(f55,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(f56,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(flattening,[],[f55]) ).
fof(f100,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl)
& sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(ennf_transformation,[],[f40]) ).
fof(f101,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl))
& sdtasdt0(xn,sdtsldt0(xm,xl)) != sdtsldt0(sdtasdt0(xn,xm),xl)
& sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) ),
inference(flattening,[],[f100]) ).
fof(f122,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[],[f54]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f169,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f36]) ).
fof(f170,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f36]) ).
fof(f175,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f38]) ).
fof(f176,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f101]) ).
fof(f177,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f101]) ).
fof(f179,plain,
sdtasdt0(xn,xm) != sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(cnf_transformation,[],[f101]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f122]) ).
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,[],[f123]) ).
tcf(c_104,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f170]) ).
tcf(c_105,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f169]) ).
tcf(c_110,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f175]) ).
tcf(c_111,negated_conjecture,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) != sdtasdt0(xn,xm),
inference(cnf_transformation,[],[f179]) ).
tcf(c_113,negated_conjecture,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnf_transformation,[],[f177]) ).
tcf(c_114,negated_conjecture,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(cnf_transformation,[],[f176]) ).
tcf(c_152,plain,
! [X0: $i] :
( ( sdtasdt0(X0,xn) = sdtasdt0(xn,X0) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_110,c_58]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(xl,X0),X1) = sdtasdt0(xl,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_104,c_59]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtasdt0(xn,X0),X1) = sdtasdt0(xn,sdtasdt0(X0,X1)) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_110,c_59]) ).
tcf(c_221,plain,
sdtasdt0(xl,xn) = sdtasdt0(xn,xl),
inference(superposition,[status(thm)],[c_104,c_152]) ).
tcf(c_222,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(superposition,[status(thm)],[c_105,c_152]) ).
tcf(c_225,plain,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm)],[c_111,c_222]) ).
tcf(c_347,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(xn,xl),X0) = sdtasdt0(xn,sdtasdt0(xl,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_104,c_182]) ).
tcf(c_421,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(xl,xn),X0) = sdtasdt0(xl,sdtasdt0(xn,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(superposition,[status(thm)],[c_110,c_180]) ).
tcf(c_894,plain,
! [X0: $i] :
( ( sdtasdt0(sdtasdt0(xl,xn),X0) = sdtasdt0(xn,sdtasdt0(xl,X0)) )
| ~ aNaturalNumber0(X0) ),
inference(light_normalisation,[status(thm)],[c_347,c_221]) ).
tcf(c_904,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xn,sdtasdt0(xl,sdtsldt0(xm,xl))),
inference(superposition,[status(thm)],[c_113,c_894]) ).
tcf(c_1121,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))),
inference(superposition,[status(thm)],[c_113,c_421]) ).
tcf(c_3646,plain,
sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xm,xn),
inference(light_normalisation,[status(thm)],[c_904,c_114,c_222]) ).
tcf(c_4424,plain,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) = sdtasdt0(xm,xn),
inference(light_normalisation,[status(thm)],[c_1121,c_3646]) ).
tcf(c_4425,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4424,c_225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM478+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n007.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 04:08:52 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.44 % Proving...
% 4.39/1.31 % SZS status Started for theBenchmark.p
% 4.39/1.31 % SZS status Theorem for theBenchmark.p
% 4.39/1.31
% 4.39/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.39/1.31
% 4.39/1.31 % ------ iProver source info
% 4.39/1.31
% 4.39/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 4.39/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.39/1.31 % git: non_committed_changes: false
% 4.39/1.31
% 4.39/1.31 % ------ Parsing...
% 4.39/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.39/1.31 % ------ Proving...
% 4.39/1.31 % ------ Problem Properties
% 4.39/1.31
% 4.39/1.31 %
% 4.39/1.31 % clauses 66
% 4.39/1.31 % conjectures 4
% 4.39/1.31 % EPR 17
% 4.39/1.31 % Horn 50
% 4.39/1.31 % unary 14
% 4.39/1.31 % binary 8
% 4.39/1.31 % lits 244
% 4.39/1.31 % lits eq 65
% 4.39/1.31 % fd_pure 0
% 4.39/1.31 % fd_pseudo 0
% 4.39/1.31 % fd_cond 7
% 4.39/1.31 % fd_pseudo_cond 13
% 4.39/1.31 % AC symbols 0
% 4.39/1.31
% 4.39/1.31 % ------ Input Options Time Limit: Unbounded
% 4.39/1.31
% 4.39/1.31
% 4.39/1.31 % ------
% 4.39/1.31 % Current options:
% 4.39/1.31 % ------
% 4.39/1.31
% 4.39/1.31
% 4.39/1.31 %
% 4.39/1.31
% 4.39/1.31 % ------ Proving...
% 4.39/1.31 %
% 4.39/1.31
% 4.39/1.31 % SZS status Theorem for theBenchmark.p
% 4.39/1.31
% 4.39/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.39/1.31
% 4.39/1.31
%------------------------------------------------------------------------------