%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN074+1 : TPTP v9.3.1. Released v2.0.0.
% 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 03:39:06 PM UTC 2026
% Result : Theorem 1.83s 1.29s
% Output : CNFRefutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 6 unt; 0 def)
% Number of atoms : 150 ( 95 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 173 ( 70 ~; 80 |; 16 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 71 !; 18 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X0,X1] :
! [X2,X3] :
( big_f(X2,X3)
<=> ( X3 = X1
& X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel51_1) ).
fof(f2,conjecture,
? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel51) ).
fof(f3,negated_conjecture,
~ ? [X0] :
! [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<=> X1 = X0 ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
! [X0] :
? [X1] :
( ? [X2] :
! [X3] :
( big_f(X1,X3)
<=> X3 = X2 )
<~> X1 = X0 ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0,X1] :
! [X2,X3] :
( ( ~ big_f(X2,X3)
| ( X3 = X1
& X2 = X0 ) )
& ( X1 != X3
| X0 != X2
| big_f(X2,X3) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f6,plain,
? [X0,X1] :
! [X2,X3] :
( ( ~ big_f(X2,X3)
| ( X3 = X1
& X2 = X0 ) )
& ( X1 != X3
| X0 != X2
| big_f(X2,X3) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X2,X3] :
( ( ~ big_f(X2,X3)
| ( sK1 = X3
& sK0 = X2 ) )
& ( sK1 != X3
| sK0 != X2
| big_f(X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
fof(f8,plain,
! [X0] :
? [X1] :
( ( ? [X2] :
! [X3] :
( ( ~ big_f(X1,X3)
| X3 = X2 )
& ( X2 != X3
| big_f(X1,X3) ) )
| X1 = X0 )
& ( ! [X2] :
? [X3] :
( ( big_f(X1,X3)
| X3 = X2 )
& ( ~ big_f(X1,X3)
| X2 != X3 ) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f9,plain,
! [X0] :
? [X1] :
( ( ? [X4] :
! [X5] :
( ( ~ big_f(X1,X5)
| X4 = X5 )
& ( X4 != X5
| big_f(X1,X5) ) )
| X1 = X0 )
& ( ! [X2] :
? [X3] :
( ( big_f(X1,X3)
| X3 = X2 )
& ( ~ big_f(X1,X3)
| X2 != X3 ) )
| X0 != X1 ) ),
inference(rectify,[],[f8]) ).
fof(f10,plain,
! [X0] :
( ( ! [X5] :
( ( ~ big_f(sK2(X0),X5)
| sK4(X0) = X5 )
& ( sK4(X0) != X5
| big_f(sK2(X0),X5) ) )
| sK2(X0) = X0 )
& ( ! [X2] :
( ( big_f(sK2(X0),sK3(X0,X2))
| sK3(X0,X2) = X2 )
& ( ~ big_f(sK2(X0),sK3(X0,X2))
| sK3(X0,X2) != X2 ) )
| sK2(X0) != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X1,sK2(X0)),skolemize(X3,sK3(X0,X2)),skolemize(X4,sK4(X0))],[f9]) ).
fof(f11,plain,
! [X2,X3] :
( ~ big_f(X2,X3)
| sK1 = X3 ),
inference(cnf_transformation,[],[f7]) ).
fof(f12,plain,
! [X2,X3] :
( ~ big_f(X2,X3)
| sK0 = X2 ),
inference(cnf_transformation,[],[f7]) ).
fof(f13,plain,
! [X2,X3] :
( sK1 != X3
| sK0 != X2
| big_f(X2,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X0,X5] :
( sK4(X0) != X5
| big_f(sK2(X0),X5)
| sK2(X0) = X0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X2,X0] :
( big_f(sK2(X0),sK3(X0,X2))
| sK3(X0,X2) = X2
| sK2(X0) != X0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
! [X2,X0] :
( ~ big_f(sK2(X0),sK3(X0,X2))
| sK3(X0,X2) != X2
| sK2(X0) != X0 ),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X3] :
( sK1 != X3
| big_f(sK0,X3) ),
inference(equality_resolution,[],[f13]) ).
fof(f19,plain,
big_f(sK0,sK1),
inference(equality_resolution,[],[f18]) ).
fof(f20,plain,
! [X0] :
( big_f(sK2(X0),sK4(X0))
| sK2(X0) = X0 ),
inference(equality_resolution,[],[f15]) ).
tcf(c_49,plain,
big_f(sK0,sK1),
inference(cnf_transformation,[],[f19]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK0 )
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( X1 = sK1 )
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(sK2(X0),sK3(X0,X1))
| ( sK2(X0) != X0 )
| ( sK3(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK2(X0),sK3(X0,X1))
| ( sK3(X0,X1) = X1 )
| ( sK2(X0) != X0 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( big_f(sK2(X0),sK4(X0))
| ( sK2(X0) = X0 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = sK0 )
| ( sK2(X0) = X0 )
| ( sK4(X0) != X2 )
| ( sK2(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_207,plain,
! [X0: $i] :
( ( sK2(X0) = sK0 )
| ( sK2(X0) = X0 ) ),
inference(unflattening,[status(thm)],[c_206]) ).
tcf(c_208,plain,
sK2(sK0) = sK0,
inference(instantiation,[status(thm)],[c_207]) ).
tcf(c_297,negated_conjecture,
! [X0: $i] :
( big_f(sK2(X0),sK4(X0))
| ( sK2(X0) = X0 ) ),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_298,negated_conjecture,
! [X0: $i,X1: $i] :
( big_f(sK2(X0),sK3(X0,X1))
| ( sK3(X0,X1) = X1 )
| ( sK2(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_299,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ big_f(sK2(X0),sK3(X0,X1))
| ( sK2(X0) != X0 )
| ( sK3(X0,X1) != X1 ) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( big_f(X0,X2)
| ~ big_f(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_430,plain,
! [X0: $i] :
( ( sK2(X0) = sK0 )
| ( sK2(X0) = X0 ) ),
inference(superposition,[status(thm)],[c_297,c_50]) ).
tcf(c_447,plain,
! [X0: $i] :
( ( sK2(X0) = sK0 )
| ( X0 != sK0 ) ),
inference(equality_factoring,[status(thm)],[c_430]) ).
tcf(c_474,plain,
sK2(sK0) = sK0,
inference(equality_resolution,[status(thm)],[c_447]) ).
tcf(c_514,plain,
! [X0: $i] :
( big_f(sK2(sK0),sK3(sK0,X0))
| ( sK3(sK0,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_474,c_298]) ).
tcf(c_517,plain,
! [X0: $i] :
( big_f(sK0,sK3(sK0,X0))
| ( sK3(sK0,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_514,c_474]) ).
tcf(c_521,plain,
! [X0: $i,X1: $i] :
( big_f(X0,X1)
| ~ big_f(sK0,sK1)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(instantiation,[status(thm)],[c_303]) ).
tcf(c_532,plain,
! [X0: $i] :
( ( sK3(sK0,X0) = sK1 )
| ( sK3(sK0,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_517,c_51]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i] :
( big_f(X1,sK3(X0,sK1))
| ~ big_f(sK0,sK1)
| ( X1 != sK0 )
| ( sK3(X0,sK1) != sK1 ) ),
inference(instantiation,[status(thm)],[c_521]) ).
tcf(c_567,plain,
! [X0: $i] :
( ( sK3(sK0,X0) = sK1 )
| ( X0 != sK1 ) ),
inference(equality_factoring,[status(thm)],[c_532]) ).
tcf(c_810,plain,
! [X0: $i] :
( big_f(sK2(X0),sK3(X0,sK1))
| ~ big_f(sK0,sK1)
| ( sK2(X0) != sK0 )
| ( sK3(X0,sK1) != sK1 ) ),
inference(instantiation,[status(thm)],[c_541]) ).
tcf(c_811,plain,
! [X0: $i] :
( ~ big_f(sK2(X0),sK3(X0,sK1))
| ( sK2(X0) != X0 )
| ( sK3(X0,sK1) != sK1 ) ),
inference(instantiation,[status(thm)],[c_299]) ).
tcf(c_812,plain,
( big_f(sK2(sK0),sK3(sK0,sK1))
| ~ big_f(sK0,sK1)
| ( sK2(sK0) != sK0 )
| ( sK3(sK0,sK1) != sK1 ) ),
inference(instantiation,[status(thm)],[c_810]) ).
tcf(c_813,plain,
( ~ big_f(sK2(sK0),sK3(sK0,sK1))
| ( sK2(sK0) != sK0 )
| ( sK3(sK0,sK1) != sK1 ) ),
inference(instantiation,[status(thm)],[c_811]) ).
tcf(c_851,plain,
sK3(sK0,sK1) = sK1,
inference(equality_resolution,[status(thm)],[c_567]) ).
tcf(c_852,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_851,c_813,c_812,c_208,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN074+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 00:07:43 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.83/1.29 % SZS status Started for theBenchmark.p
% 1.83/1.29 % SZS status Theorem for theBenchmark.p
% 1.83/1.29
% 1.83/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.83/1.29
% 1.83/1.29 % ------ iProver source info
% 1.83/1.29
% 1.83/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.83/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.83/1.29 % git: non_committed_changes: false
% 1.83/1.29
% 1.83/1.29 % ------ Parsing...
% 1.83/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.83/1.29
% 1.83/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.83/1.29
% 1.83/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.83/1.29
% 1.83/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.83/1.29 % ------ Proving...
% 1.83/1.29 % ------ Problem Properties
% 1.83/1.29
% 1.83/1.29 %
% 1.83/1.29 % clauses 7
% 1.83/1.29 % conjectures 4
% 1.83/1.29 % EPR 3
% 1.83/1.29 % Horn 4
% 1.83/1.29 % unary 1
% 1.83/1.29 % binary 3
% 1.83/1.29 % lits 16
% 1.83/1.29 % lits eq 9
% 1.83/1.29 % fd_pure 0
% 1.83/1.29 % fd_pseudo 0
% 1.83/1.29 % fd_cond 2
% 1.83/1.29 % fd_pseudo_cond 0
% 1.83/1.29 % AC symbols 0
% 1.83/1.29
% 1.83/1.29 % ------ Schedule dynamic 5 is on
% 1.83/1.29
% 1.83/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.83/1.29
% 1.83/1.29
% 1.83/1.29 % ------
% 1.83/1.29 % Current options:
% 1.83/1.29 % ------
% 1.83/1.29
% 1.83/1.29
% 1.83/1.29 %
% 1.83/1.29
% 1.83/1.29 % ------ Proving...
% 1.83/1.29 %
% 1.83/1.29
% 1.83/1.29 % SZS status Theorem for theBenchmark.p
% 1.83/1.29
% 1.83/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.83/1.29
% 1.83/1.29
%------------------------------------------------------------------------------