%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG045+1 : 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 : n005.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 02:38:18 PM UTC 2026
% Result : Theorem 3.98s 1.34s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 78 ( 44 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 81 ( 38 ~; 34 |; 8 &)
% ( 0 <=>; 1 =>; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 27 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistr) ).
fof(f16,axiom,
( aScalar0(xv)
& aScalar0(xu)
& aScalar0(xy)
& aScalar0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__674) ).
fof(f17,axiom,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__733) ).
fof(f18,conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f19,negated_conjecture,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(flattening,[],[f19]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| ( sdtasdt0(sdtpldt0(X0,X1),X2) = sdtpldt0(sdtasdt0(X0,X2),sdtasdt0(X1,X2))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
inference(flattening,[],[f22]) ).
fof(f30,plain,
aScalar0(xv),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
aScalar0(xu),
inference(cnf_transformation,[],[f16]) ).
fof(f32,plain,
aScalar0(xy),
inference(cnf_transformation,[],[f16]) ).
fof(f33,plain,
aScalar0(xx),
inference(cnf_transformation,[],[f16]) ).
fof(f34,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))),
inference(cnf_transformation,[],[f17]) ).
fof(f35,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0)
| sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,plain,
aScalar0(xx),
inference(cnf_transformation,[],[f33]) ).
tcf(c_50,plain,
aScalar0(xy),
inference(cnf_transformation,[],[f32]) ).
tcf(c_51,plain,
aScalar0(xu),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
aScalar0(xv),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) = sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,negated_conjecture,
sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) = sdtasdt0(X0,sdtpldt0(X1,X2)) )
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_211,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_529,plain,
! [X0: $i] :
( ( sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) = sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != X0 )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) != X0 ) ),
inference(instantiation,[status(thm)],[c_213]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = X1 )
| ( X1 != X0 )
| ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != X0 ) ),
inference(instantiation,[status(thm)],[c_213]) ).
tcf(c_602,plain,
! [X0: $i] :
( ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = X0 )
| ( X0 != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_568]) ).
tcf(c_603,plain,
sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)),
inference(instantiation,[status(thm)],[c_211]) ).
tcf(c_703,plain,
( ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) )
| ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) )
| ( sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) != sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_602]) ).
tcf(c_985,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) = sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) )
| ( sdtasdt0(sdtpldt0(xx,xy),sdtpldt0(xu,xv)) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) != sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) ) ),
inference(instantiation,[status(thm)],[c_529]) ).
tcf(c_1319,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)),sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv))) = sdtpldt0(sdtasdt0(xx,sdtpldt0(xu,xv)),sdtasdt0(xy,sdtpldt0(xu,xv))) )
| ( sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) != sdtasdt0(xy,sdtpldt0(xu,xv)) )
| ( sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) != sdtasdt0(xx,sdtpldt0(xu,xv)) ) ),
inference(instantiation,[status(thm)],[c_215]) ).
tcf(c_1975,plain,
( ( sdtpldt0(sdtasdt0(xx,xu),sdtasdt0(xx,xv)) = sdtasdt0(xx,sdtpldt0(xu,xv)) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xx) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_3415,plain,
( ( sdtpldt0(sdtasdt0(xy,xu),sdtasdt0(xy,xv)) = sdtasdt0(xy,sdtpldt0(xu,xv)) )
| ~ aScalar0(xv)
| ~ aScalar0(xu)
| ~ aScalar0(xy) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_3416,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3415,c_1975,c_1319,c_985,c_703,c_603,c_54,c_53,c_49,c_50,c_51,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG045+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 07:56:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.42 Running first-order theorem proving
% 0.14/0.42 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
% 0.14/0.43
% 0.14/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.43
% 0.14/0.43 % Detected problem language: tptp
% 0.14/0.44 % Proving...
% 3.98/1.34 % SZS status Started for theBenchmark.p
% 3.98/1.34 % SZS status Theorem for theBenchmark.p
% 3.98/1.34
% 3.98/1.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.98/1.34
% 3.98/1.34 % ------ iProver source info
% 3.98/1.34
% 3.98/1.34 % git: date: 2026-07-19 20:42:38 +0200
% 3.98/1.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.98/1.34 % git: non_committed_changes: false
% 3.98/1.34
% 3.98/1.34 % ------ Parsing...
% 3.98/1.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.98/1.34
% 3.98/1.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.98/1.34
% 3.98/1.34 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.98/1.34
% 3.98/1.34 % ------ Preprocessing... sf_s rm: 4 0s sf_e sf_s rm: 0 0s sf_e
% 3.98/1.34 % ------ Proving...
% 3.98/1.34 % ------ Problem Properties
% 3.98/1.34
% 3.98/1.34 %
% 3.98/1.34 % clauses 17
% 3.98/1.34 % conjectures 1
% 3.98/1.34 % EPR 7
% 3.98/1.34 % Horn 15
% 3.98/1.34 % unary 6
% 3.98/1.34 % binary 3
% 3.98/1.34 % lits 42
% 3.98/1.34 % lits eq 8
% 3.98/1.34 % fd_pure 0
% 3.98/1.34 % fd_pseudo 0
% 3.98/1.34 % fd_cond 0
% 3.98/1.34 % fd_pseudo_cond 0
% 3.98/1.34 % AC symbols 0
% 3.98/1.34
% 3.98/1.34 % ------ Schedule dynamic 5 is on
% 3.98/1.34
% 3.98/1.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.98/1.34
% 3.98/1.34
% 3.98/1.34 % ------
% 3.98/1.34 % Current options:
% 3.98/1.34 % ------
% 3.98/1.34
% 3.98/1.34
% 3.98/1.34 %
% 3.98/1.34
% 3.98/1.34 % ------ Proving...
% 3.98/1.34 %
% 3.98/1.34
% 3.98/1.34 % SZS status Theorem for theBenchmark.p
% 3.98/1.34
% 3.98/1.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.98/1.34
% 3.98/1.34
%------------------------------------------------------------------------------