%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 02:05:40 PM UTC 2026
% Result : Unsatisfiable 1.04s 0.98s
% Output : CNFRefutation 1.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 26 unt; 4 def)
% Number of atoms : 110 ( 41 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 57 ( 31 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
fof(f4,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
fof(f7,axiom,
! [X0,X1] : big_V(X0,X1) = implies(implies(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',big_V_definition) ).
fof(f8,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = big_V(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f10,axiom,
! [X0,X1] :
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',partial_order_definition1) ).
fof(f11,plain,
! [X0,X1] :
( truth = implies(X0,X1)
| ~ ordered(X0,X1) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( ordered(X0,X1)
| implies(X0,X1) != truth ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL001-1.ax',partial_order_definition2) ).
fof(f13,plain,
! [X0,X1] :
( ordered(X0,X1)
| truth != implies(X0,X1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( ordered(implies(X0,X2),implies(X1,X2))
| ~ ordered(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1) ).
fof(f17,axiom,
! [X2,X0,X1] :
( ordered(X1,implies(X0,X2))
| ~ ordered(X0,implies(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_3_2) ).
fof(f23,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mv_4) ).
fof(f24,plain,
truth != big_V(implies(x,y),implies(y,x)),
inference(reorient_equations,[],[f23]) ).
fof(f30,plain,
truth != implies(implies(implies(x,y),implies(y,x)),implies(y,x)),
inference(definition_unfolding,[],[f24,f8]) ).
tcf(c_66,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( ( implies(X0,X1) = truth )
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ordered(X0,X1)
| ( implies(X0,X1) != truth ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordered(implies(X0,X2),implies(X1,X2))
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( ordered(X1,implies(X0,X2))
| ~ ordered(X0,implies(X1,X2)) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_80,negated_conjecture,
implies(implies(implies(x,y),implies(y,x)),implies(y,x)) != truth,
inference(cnf_transformation,[],[f30]) ).
tcf(c_285,definition,
iPr_def_10 = implies(x,y),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_286,definition,
iPr_def_11 = implies(y,x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_287,definition,
iPr_def_12 = implies(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_288,definition,
iPr_def_13 = implies(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_289,negated_conjecture,
iPr_def_13 != truth,
inference(demodulation,[status(thm)],[c_80,c_286,c_285,c_287,c_288]) ).
tcf(c_290,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_292,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_298,plain,
truth = truth,
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_559,plain,
! [X0: $i] :
( ordered(truth,X0)
| ( X0 != truth ) ),
inference(superposition,[status(thm)],[c_66,c_71]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i] :
( ordered(X1,implies(X0,X1))
| ~ ordered(truth,X0) ),
inference(superposition,[status(thm)],[c_66,c_72]) ).
tcf(c_631,plain,
! [X0: $i] :
( ordered(iPr_def_12,implies(X0,iPr_def_11))
| ~ ordered(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_287,c_72]) ).
tcf(c_679,plain,
! [X0: $i] :
( ( iPr_def_13 = truth )
| ( iPr_def_13 != X0 )
| ( truth != X0 ) ),
inference(instantiation,[status(thm)],[c_292]) ).
tcf(c_684,plain,
( ( iPr_def_13 = truth )
| ( iPr_def_13 != implies(iPr_def_12,iPr_def_11) )
| ( truth != implies(iPr_def_12,iPr_def_11) ) ),
inference(instantiation,[status(thm)],[c_679]) ).
tcf(c_687,plain,
! [X0: $i] :
( ( truth = implies(iPr_def_12,iPr_def_11) )
| ( truth != X0 )
| ( implies(iPr_def_12,iPr_def_11) != X0 ) ),
inference(instantiation,[status(thm)],[c_292]) ).
tcf(c_688,plain,
( ( truth = implies(iPr_def_12,iPr_def_11) )
| ( truth != truth )
| ( implies(iPr_def_12,iPr_def_11) != truth ) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_751,plain,
( ( implies(iPr_def_12,iPr_def_11) = truth )
| ~ ordered(iPr_def_12,iPr_def_11) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_900,plain,
ordered(truth,truth),
inference(equality_resolution,[status(thm)],[c_559]) ).
tcf(c_1456,plain,
! [X0: $i] :
( ordered(X0,X0)
| ~ ordered(truth,truth) ),
inference(superposition,[status(thm)],[c_66,c_629]) ).
tcf(c_1470,plain,
! [X0: $i] : ordered(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_1456,c_900]) ).
tcf(c_1496,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(superposition,[status(thm)],[c_1470,c_70]) ).
tcf(c_1497,plain,
! [X0: $i,X1: $i] : ordered(X0,implies(implies(X0,X1),X1)),
inference(superposition,[status(thm)],[c_1470,c_75]) ).
tcf(c_1611,plain,
! [X0: $i,X1: $i] : ordered(X0,implies(implies(X1,X0),X0)),
inference(superposition,[status(thm)],[c_68,c_1497]) ).
tcf(c_2032,plain,
! [X0: $i] : ordered(X0,implies(X0,X0)),
inference(superposition,[status(thm)],[c_66,c_1611]) ).
tcf(c_2048,plain,
! [X0: $i] : ordered(X0,truth),
inference(light_normalisation,[status(thm)],[c_2032,c_1496]) ).
tcf(c_3427,plain,
( ordered(iPr_def_12,iPr_def_11)
| ~ ordered(iPr_def_10,truth) ),
inference(superposition,[status(thm)],[c_66,c_631]) ).
tcf(c_3436,plain,
ordered(iPr_def_12,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_3427,c_2048]) ).
tcf(c_3444,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3436,c_751,c_688,c_684,c_289,c_288,c_298]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL109-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.05/0.30 % Computer : n012.cluster.edu
% 0.05/0.30 % Model : x86_64 x86_64
% 0.05/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.30 % Memory : 8046.5625MB
% 0.05/0.30 % OS : Linux 6.8.0-71-generic
% 0.05/0.30 % CPULimit : 300
% 0.05/0.30 % WCLimit : 300
% 0.05/0.30 % DateTime : Wed Sep 23 21:57:32 UTC 2026
% 0.05/0.30 % CPUTime :
% 0.05/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.32 Running first-order theorem proving
% 0.07/0.32 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
% 0.07/0.33
% 0.07/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.33
% 0.07/0.33 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 1.04/0.98 % SZS status Started for theBenchmark.p
% 1.04/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 1.04/0.98
% 1.04/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.04/0.98
% 1.04/0.98 % ------ iProver source info
% 1.04/0.98
% 1.04/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 1.04/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.04/0.98 % git: non_committed_changes: false
% 1.04/0.98
% 1.04/0.98 % ------ Parsing...% successful
% 1.04/0.98
% 1.04/0.98
% 1.04/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.04/0.98
% 1.04/0.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.04/0.98
% 1.04/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.04/0.98
% 1.04/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.04/0.98 % ------ Proving...
% 1.04/0.98 % ------ Problem Properties
% 1.04/0.98
% 1.04/0.98 %
% 1.04/0.98 % clauses 18
% 1.04/0.98 % conjectures 1
% 1.04/0.98 % EPR 1
% 1.04/0.98 % Horn 18
% 1.04/0.98 % unary 13
% 1.04/0.98 % binary 5
% 1.04/0.98 % lits 23
% 1.04/0.98 % lits eq 15
% 1.04/0.98 % fd_pure 0
% 1.04/0.98 % fd_pseudo 0
% 1.04/0.98 % fd_cond 0
% 1.04/0.98 % fd_pseudo_cond 0
% 1.04/0.98 % AC symbols 0
% 1.04/0.98
% 1.04/0.98 % ------ Schedule dynamic 5 is on
% 1.04/0.98
% 1.04/0.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.04/0.98
% 1.04/0.98
% 1.04/0.98 % ------
% 1.04/0.98 % Current options:
% 1.04/0.98 % ------
% 1.04/0.98
% 1.04/0.98
% 1.04/0.98 %
% 1.04/0.98
% 1.04/0.98 % ------ Proving...
% 1.04/0.98 %
% 1.04/0.98
% 1.04/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 1.04/0.98
% 1.04/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.04/0.98
% 1.04/0.98
%------------------------------------------------------------------------------