%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG103+1 : 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 : n016.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 10.79s 2.26s
% Output : CNFRefutation 10.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 60 ( 19 unt; 0 def)
% Number of atoms : 149 ( 86 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 170 ( 81 ~; 77 |; 9 &)
% ( 0 <=>; 3 =>; 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 : 61 ( 0 sgn 61 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> aElement0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f7,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aElement0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f38,axiom,
aElement0(xc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1905) ).
fof(f40,axiom,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1956) ).
fof(f41,axiom,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1979) ).
fof(f42,conjecture,
sdtpldt0(xx,xy) = sdtasdt0(xc,sdtpldt0(xu,xv)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f43,negated_conjecture,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f51,plain,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(flattening,[],[f43]) ).
fof(f57,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(flattening,[],[f59]) ).
fof(f70,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(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(flattening,[],[f70]) ).
fof(f142,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| aElement0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f58]) ).
fof(f143,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aElement0(X0)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f154,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,[],[f71]) ).
fof(f227,plain,
aElement0(xc),
inference(cnf_transformation,[],[f38]) ).
fof(f231,plain,
xx = sdtasdt0(xc,xu),
inference(cnf_transformation,[],[f40]) ).
fof(f232,plain,
aElement0(xu),
inference(cnf_transformation,[],[f40]) ).
fof(f233,plain,
xy = sdtasdt0(xc,xv),
inference(cnf_transformation,[],[f41]) ).
fof(f234,plain,
aElement0(xv),
inference(cnf_transformation,[],[f41]) ).
fof(f235,plain,
sdtpldt0(xx,xy) != sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0) )
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f143]) ).
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,[],[f154]) ).
tcf(c_138,plain,
aElement0(xc),
inference(cnf_transformation,[],[f227]) ).
tcf(c_142,plain,
aElement0(xu),
inference(cnf_transformation,[],[f232]) ).
tcf(c_143,plain,
sdtasdt0(xc,xu) = xx,
inference(cnf_transformation,[],[f231]) ).
tcf(c_144,plain,
aElement0(xv),
inference(cnf_transformation,[],[f234]) ).
tcf(c_145,plain,
sdtasdt0(xc,xv) = xy,
inference(cnf_transformation,[],[f233]) ).
tcf(c_146,negated_conjecture,
sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(xx,xy),
inference(cnf_transformation,[],[f235]) ).
tcf(c_3800,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_3802,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_3805,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5286,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_3802]) ).
tcf(c_5288,plain,
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy) )
| ( sdtpldt0(xx,xy) != sdtpldt0(xy,xx) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(xy,xx) ) ),
inference(instantiation,[status(thm)],[c_5286]) ).
tcf(c_5317,plain,
( ( sdtpldt0(xx,xy) = sdtpldt0(xy,xx) )
| ~ aElement0(xy)
| ~ aElement0(xx) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_5432,plain,
! [X0: $i,X1: $i] :
( ( X1 = sdtpldt0(xy,xx) )
| ( X1 != X0 )
| ( sdtpldt0(xy,xx) != X0 ) ),
inference(instantiation,[status(thm)],[c_3802]) ).
tcf(c_5642,plain,
( ( sdtpldt0(xy,xx) = sdtpldt0(xx,xy) )
| ~ aElement0(xy)
| ~ aElement0(xx) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_5692,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(xy,xx) = X1 )
| ( X1 != X0 )
| ( sdtpldt0(xy,xx) != X0 ) ),
inference(instantiation,[status(thm)],[c_3802]) ).
tcf(c_5919,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(xx,xy) )
| ( X1 != xy )
| ( X0 != xx ) ),
inference(instantiation,[status(thm)],[c_3805]) ).
tcf(c_6549,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(xy,xx) = X2 )
| ( X2 != sdtpldt0(X0,X1) )
| ( sdtpldt0(xy,xx) != sdtpldt0(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_5692]) ).
tcf(c_6750,plain,
! [X0: $i] :
( ( sdtpldt0(sdtasdt0(xc,xu),X0) = sdtpldt0(xx,xy) )
| ( X0 != xy )
| ( sdtasdt0(xc,xu) != xx ) ),
inference(instantiation,[status(thm)],[c_5919]) ).
tcf(c_7209,plain,
( aElement0(xx)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(superposition,[status(thm)],[c_143,c_53]) ).
tcf(c_7210,plain,
( aElement0(xy)
| ~ aElement0(xv)
| ~ aElement0(xc) ),
inference(superposition,[status(thm)],[c_145,c_53]) ).
tcf(c_7543,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = X1 )
| ( X1 != X0 )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 ) ),
inference(instantiation,[status(thm)],[c_3802]) ).
tcf(c_7596,plain,
! [X0: $i] :
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xy,xx) )
| ( sdtpldt0(xy,xx) != X0 )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != X0 ) ),
inference(instantiation,[status(thm)],[c_5432]) ).
tcf(c_7833,plain,
( ( sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) = sdtpldt0(xx,xy) )
| ( sdtasdt0(xc,xv) != xy )
| ( sdtasdt0(xc,xu) != xx ) ),
inference(instantiation,[status(thm)],[c_6750]) ).
tcf(c_9622,plain,
sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtasdt0(xc,sdtpldt0(xu,xv)),
inference(instantiation,[status(thm)],[c_3800]) ).
tcf(c_11421,plain,
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xy,xx) )
| ( sdtpldt0(xy,xx) != sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_7596]) ).
tcf(c_11580,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_7543]) ).
tcf(c_12828,plain,
! [X0: $i] :
( ( sdtpldt0(xy,xx) = X0 )
| ( X0 != sdtpldt0(xx,xy) )
| ( sdtpldt0(xy,xx) != sdtpldt0(xx,xy) ) ),
inference(instantiation,[status(thm)],[c_6549]) ).
tcf(c_16815,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(xy,xx) = sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ( sdtpldt0(xy,xx) != sdtpldt0(X0,X1) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_6549]) ).
tcf(c_19119,plain,
( ( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ( sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) != sdtasdt0(xc,sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_11580]) ).
tcf(c_19319,plain,
( ( sdtpldt0(xy,xx) = sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) )
| ( sdtpldt0(xy,xx) != sdtpldt0(xx,xy) )
| ( sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) != sdtpldt0(xx,xy) ) ),
inference(instantiation,[status(thm)],[c_12828]) ).
tcf(c_26894,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_35219,plain,
( ( sdtpldt0(xy,xx) = sdtasdt0(xc,sdtpldt0(xu,xv)) )
| ( sdtpldt0(xy,xx) != sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) )
| ( sdtasdt0(xc,sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xc,xu),sdtasdt0(xc,xv)) ) ),
inference(instantiation,[status(thm)],[c_16815]) ).
tcf(c_35220,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_35219,c_26894,c_19319,c_19119,c_11421,c_9622,c_7833,c_7209,c_7210,c_5642,c_5317,c_5288,c_146,c_143,c_145,c_138,c_142,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG103+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 08:19:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.40 % Proving...
% 10.79/2.26 % SZS status Started for theBenchmark.p
% 10.79/2.26 % SZS status Theorem for theBenchmark.p
% 10.79/2.26
% 10.79/2.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.79/2.26
% 10.79/2.26 % ------ iProver source info
% 10.79/2.26
% 10.79/2.26 % git: date: 2026-07-19 20:42:38 +0200
% 10.79/2.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.79/2.26 % git: non_committed_changes: false
% 10.79/2.26
% 10.79/2.26 % ------ Parsing...
% 10.79/2.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.79/2.26
% 10.79/2.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 10.79/2.26
% 10.79/2.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.79/2.26
% 10.79/2.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.79/2.26 % ------ Proving...
% 10.79/2.26 % ------ Problem Properties
% 10.79/2.26
% 10.79/2.26 %
% 10.79/2.26 % clauses 93
% 10.79/2.26 % conjectures 1
% 10.79/2.26 % EPR 16
% 10.79/2.26 % Horn 70
% 10.79/2.26 % unary 12
% 10.79/2.26 % binary 14
% 10.79/2.26 % lits 328
% 10.79/2.26 % lits eq 45
% 10.79/2.26 % fd_pure 0
% 10.79/2.26 % fd_pseudo 0
% 10.79/2.26 % fd_cond 3
% 10.79/2.26 % fd_pseudo_cond 11
% 10.79/2.26 % AC symbols 0
% 10.79/2.26
% 10.79/2.26 % ------ Input Options Time Limit: Unbounded
% 10.79/2.26
% 10.79/2.26
% 10.79/2.26 % ------
% 10.79/2.26 % Current options:
% 10.79/2.26 % ------
% 10.79/2.26
% 10.79/2.26
% 10.79/2.26 %
% 10.79/2.26
% 10.79/2.26 % ------ Proving...
% 10.79/2.26 %
% 10.79/2.26
% 10.79/2.26 % SZS status Theorem for theBenchmark.p
% 10.79/2.26
% 10.79/2.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.79/2.26
% 10.79/2.26
%------------------------------------------------------------------------------