%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG103+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 : n015.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 02:38:57 PM UTC 2026
% Result : Theorem 46.04s 9.63s
% Output : CNFRefutation 46.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 17 unt; 0 def)
% Number of atoms : 111 ( 83 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 123 ( 62 ~; 53 |; 7 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 39 ( 0 sgn 39 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1905) ).
fof(f40,axiom,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1956) ).
fof(f41,axiom,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1979) ).
fof(f42,conjecture,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f52,plain,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(flattening,[],[f43]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(flattening,[],[f71]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f229,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f237,plain,
xx = sdtasdt0(xc,xu),
inference(cnf_transformation,[],[f40]) ).
fof(f238,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f239,plain,
xy = sdtasdt0(xc,xv),
inference(cnf_transformation,[],[f41]) ).
fof(f240,plain,
aElement0(xv),
inference(cnf_transformation,[],[f41]) ).
fof(f241,plain,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) = sdtasdt0(X0,sdtpldt0(X1,X2)) )
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_138,plain,
aElement0(xc),
inference(cnf_transformation,[],[f229]) ).
tcf(c_146,plain,
aElement0(xu),
inference(cnf_transformation,[],[f238]) ).
tcf(c_147,plain,
sdtasdt0(xc,xu) = xx,
inference(cnf_transformation,[],[f237]) ).
tcf(c_148,plain,
aElement0(xv),
inference(cnf_transformation,[],[f240]) ).
tcf(c_149,plain,
sdtasdt0(xc,xv) = xy,
inference(cnf_transformation,[],[f239]) ).
tcf(c_150,negated_conjecture,
sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(xx,xy),
inference(cnf_transformation,[],[f241]) ).
tcf(c_2556,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3366,plain,
! [X0: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy) )
| ( sdtpldt0(xx,xy) != X0 )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 ) ),
inference(instantiation,[status(thm)],[c_2556]) ).
tcf(c_3379,plain,
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy) )
| ( sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_3366]) ).
tcf(c_3380,plain,
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy) )
| ( sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)) ) ),
inference(equality_resolution_simp,[status(thm)],[c_3379]) ).
tcf(c_3417,plain,
! [X0: $i] :
( ( sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ( sdtpldt0(xx,xy) != X0 )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 ) ),
inference(instantiation,[status(thm)],[c_2556]) ).
tcf(c_3452,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = X1 )
| ( X1 != X0 )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 ) ),
inference(instantiation,[status(thm)],[c_2556]) ).
tcf(c_3495,plain,
! [X0: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = X0 )
| ( X0 != sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_3452]) ).
tcf(c_3496,plain,
! [X0: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = X0 )
| ( X0 != sdtasdt0(xc,sdtpldt0(xu,xv)) ) ),
inference(equality_resolution_simp,[status(thm)],[c_3495]) ).
tcf(c_3538,plain,
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) )
| ( sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_3496]) ).
tcf(c_3954,plain,
( ( sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) = sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ~ aElement0(xv)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_4413,plain,
! [X0: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy) )
| ( sdtpldt0(xx,xy) != X0 )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 ) ),
inference(instantiation,[status(thm)],[c_2556]) ).
tcf(c_4414,plain,
! [X0: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 )
| ( sdtpldt0(xx,xy) != X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_4413,c_150,c_3380,c_3417]) ).
tcf(c_4415,plain,
! [X0: $i] :
( ( sdtpldt0(xx,xy) != X0 )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 ) ),
inference(renaming,[status(thm)],[c_4414]) ).
tcf(c_4751,plain,
( ( sdtpldt0(xx,xy) != sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) ) ),
inference(instantiation,[status(thm)],[c_4415]) ).
tcf(c_5249,plain,
( ( sdtpldt0(xx,xy) = sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) )
| ( xy != sdtasdt0(xc,xv) )
| ( xx != sdtasdt0(xc,xu) ) ),
inference(instantiation,[status(thm)],[c_2559]) ).
tcf(c_5250,plain,
( ( xx != sdtasdt0(xc,xu) )
| ( xy != sdtasdt0(xc,xv) ) ),
inference(global_subsumption_just,[status(thm)],[c_5249,c_148,c_146,c_138,c_3538,c_3954,c_4751,c_5249]) ).
tcf(c_5251,plain,
( ( xy != sdtasdt0(xc,xv) )
| ( xx != sdtasdt0(xc,xu) ) ),
inference(renaming,[status(thm)],[c_5250]) ).
tcf(c_7399,plain,
! [X0: $i,X1: $i] :
( ( xy = X0 )
| ( xy != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2556]) ).
tcf(c_7801,plain,
! [X0: $i] :
( ( xy = X0 )
| ( xy != xy )
| ( X0 != xy ) ),
inference(instantiation,[status(thm)],[c_7399]) ).
tcf(c_7802,plain,
! [X0: $i] :
( ( xy = X0 )
| ( X0 != xy ) ),
inference(equality_resolution_simp,[status(thm)],[c_7801]) ).
tcf(c_8479,plain,
( ( xy = sdtasdt0(xc,xv) )
| ( sdtasdt0(xc,xv) != xy ) ),
inference(instantiation,[status(thm)],[c_7802]) ).
tcf(c_9850,plain,
! [X0: $i,X1: $i] :
( ( xx = X0 )
| ( xx != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_2556]) ).
tcf(c_10630,plain,
! [X0: $i] :
( ( xx = X0 )
| ( xx != xx )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_9850]) ).
tcf(c_10631,plain,
! [X0: $i] :
( ( xx = X0 )
| ( X0 != xx ) ),
inference(equality_resolution_simp,[status(thm)],[c_10630]) ).
tcf(c_11777,plain,
( ( xx = sdtasdt0(xc,xu) )
| ( sdtasdt0(xc,xu) != xx ) ),
inference(instantiation,[status(thm)],[c_10631]) ).
tcf(c_11778,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_11777,c_8479,c_5251,c_147,c_149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG103+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/0.43 % Computer : n015.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Thu Sep 24 08:18:10 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 0.21/0.51
% 0.21/0.51 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.51
% 0.21/0.51 % Detected problem language: tptp
% 0.21/0.53 % Proving...
% 46.04/9.63 % SZS status Started for theBenchmark.p
% 46.04/9.63 % SZS status Theorem for theBenchmark.p
% 46.04/9.63
% 46.04/9.63 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 46.04/9.63
% 46.04/9.63 % ------ iProver source info
% 46.04/9.63
% 46.04/9.63 % git: date: 2026-07-19 20:42:38 +0200
% 46.04/9.63 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 46.04/9.63 % git: non_committed_changes: false
% 46.04/9.63
% 46.04/9.63 % ------ Parsing...
% 46.04/9.63 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 46.04/9.63
% 46.04/9.63 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 2 0s sf_e pe_s pe_e %
% 46.04/9.63
% 46.04/9.63 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 46.04/9.63
% 46.04/9.63 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 % ------ Problem Properties
% 46.04/9.63
% 46.04/9.63 %
% 46.04/9.63 % clauses 98
% 46.04/9.63 % conjectures 1
% 46.04/9.63 % EPR 19
% 46.04/9.63 % Horn 74
% 46.04/9.63 % unary 16
% 46.04/9.63 % binary 14
% 46.04/9.63 % lits 334
% 46.04/9.63 % lits eq 47
% 46.04/9.63 % fd_pure 0
% 46.04/9.63 % fd_pseudo 0
% 46.04/9.63 % fd_cond 3
% 46.04/9.63 % fd_pseudo_cond 11
% 46.04/9.63 % AC symbols 0
% 46.04/9.63
% 46.04/9.63 % ------ Input Options Time Limit: Unbounded
% 46.04/9.63
% 46.04/9.63
% 46.04/9.63 % ------
% 46.04/9.63 % Current options:
% 46.04/9.63 % ------
% 46.04/9.63
% 46.04/9.63
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % ------ Proving...
% 46.04/9.63 %
% 46.04/9.63
% 46.04/9.63 % SZS status Theorem for theBenchmark.p
% 46.04/9.63
% 46.04/9.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 46.04/9.64
% 46.04/9.64
%------------------------------------------------------------------------------