%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:05:46 PM UTC 2026
% Result : Unsatisfiable 2.99s 0.98s
% Output : CNFRefutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 37 unt; 0 def)
% Number of atoms : 102 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 68 ( 31 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_1) ).
fof(f2,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_2) ).
fof(f3,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL001-0.ax',wajsberg_3) ).
fof(f10,axiom,
! [X0,X1] :
( implies(X0,X1) = truth
| ~ ordered(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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,negated_conjecture,
( ordered(y,implies(x,z))
| ordered(x,implies(y,z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antecedent) ).
fof(f15,negated_conjecture,
( ~ ordered(y,implies(x,z))
| ~ ordered(x,implies(y,z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_wajsberg_theorem) ).
tcf(c_59,negated_conjecture,
( ordered(y,implies(x,z))
| ordered(x,implies(y,z)) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_60,negated_conjecture,
( ~ ordered(y,implies(x,z))
| ~ ordered(x,implies(y,z)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ordered(X0,X1)
| ( implies(X0,X1) != truth ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ( implies(X0,X1) = truth )
| ~ ordered(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
! [X0: $i] : implies(truth,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_134,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_140,plain,
truth = truth,
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_305,plain,
! [X0: $i] :
( ordered(truth,X0)
| ( X0 != truth ) ),
inference(superposition,[status(thm)],[c_65,c_61]) ).
tcf(c_318,plain,
( ordered(x,implies(y,z))
| ( implies(y,implies(x,z)) = truth ) ),
inference(superposition,[status(thm)],[c_59,c_62]) ).
tcf(c_327,plain,
( ( implies(y,implies(x,z)) = truth )
| ( implies(x,implies(y,z)) = truth ) ),
inference(superposition,[status(thm)],[c_318,c_62]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] : implies(implies(truth,X0),implies(implies(X0,X1),X1)) = truth,
inference(superposition,[status(thm)],[c_65,c_64]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i,X2: $i] : ordered(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(superposition,[status(thm)],[c_64,c_61]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] : implies(X0,implies(implies(X0,X1),X1)) = truth,
inference(light_normalisation,[status(thm)],[c_350,c_65]) ).
tcf(c_372,plain,
( ordered(y,implies(x,z))
| ( implies(y,implies(x,z)) != truth ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_416,plain,
implies(y,implies(x,z)) = implies(y,implies(x,z)),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_417,plain,
! [X0: $i,X1: $i] :
( ( implies(y,implies(x,z)) = X1 )
| ( X1 != X0 )
| ( implies(y,implies(x,z)) != X0 ) ),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i] : ordered(X0,implies(implies(X0,X1),X1)),
inference(superposition,[status(thm)],[c_360,c_61]) ).
tcf(c_455,plain,
! [X0: $i] : implies(implies(truth,X0),X0) = truth,
inference(superposition,[status(thm)],[c_360,c_65]) ).
tcf(c_460,plain,
! [X0: $i] : implies(X0,X0) = truth,
inference(light_normalisation,[status(thm)],[c_455,c_65]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] : ordered(X0,implies(implies(X1,X0),X0)),
inference(superposition,[status(thm)],[c_63,c_454]) ).
tcf(c_572,plain,
! [X0: $i] : ordered(X0,implies(X0,X0)),
inference(superposition,[status(thm)],[c_65,c_528]) ).
tcf(c_578,plain,
! [X0: $i] : ordered(X0,truth),
inference(light_normalisation,[status(thm)],[c_572,c_460]) ).
tcf(c_582,plain,
! [X0: $i] : implies(X0,truth) = truth,
inference(superposition,[status(thm)],[c_578,c_62]) ).
tcf(c_589,plain,
! [X0: $i] :
( ( implies(x,implies(y,z)) = truth )
| ( implies(truth,implies(implies(implies(x,z),X0),implies(y,X0))) = truth ) ),
inference(superposition,[status(thm)],[c_327,c_64]) ).
tcf(c_622,plain,
! [X0: $i] :
( ( implies(y,implies(x,z)) = X0 )
| ( X0 != implies(y,implies(x,z)) )
| ( implies(y,implies(x,z)) != implies(y,implies(x,z)) ) ),
inference(instantiation,[status(thm)],[c_417]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( truth = implies(X0,X1) )
| ( truth != X2 )
| ( implies(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_136]) ).
tcf(c_645,plain,
! [X0: $i] :
( ( implies(x,implies(y,z)) = truth )
| ( implies(implies(implies(x,z),X0),implies(y,X0)) = truth ) ),
inference(demodulation,[status(thm)],[c_589,c_65]) ).
tcf(c_724,plain,
! [X0: $i,X1: $i,X2: $i] : ordered(truth,implies(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2))),
inference(superposition,[status(thm)],[c_360,c_355]) ).
tcf(c_801,plain,
( ( implies(y,implies(x,z)) = implies(truth,implies(y,implies(x,z))) )
| ( implies(y,implies(x,z)) != implies(y,implies(x,z)) )
| ( implies(truth,implies(y,implies(x,z))) != implies(y,implies(x,z)) ) ),
inference(instantiation,[status(thm)],[c_622]) ).
tcf(c_802,plain,
implies(truth,implies(y,implies(x,z))) = implies(y,implies(x,z)),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_826,plain,
! [X0: $i,X1: $i] : implies(truth,implies(implies(truth,X0),implies(X1,X0))) = truth,
inference(superposition,[status(thm)],[c_582,c_64]) ).
tcf(c_846,plain,
! [X0: $i,X1: $i] : implies(truth,implies(X0,implies(X1,X0))) = truth,
inference(light_normalisation,[status(thm)],[c_826,c_65]) ).
tcf(c_1191,plain,
! [X0: $i] :
( ( implies(y,implies(x,z)) = X0 )
| ( X0 != implies(truth,implies(y,implies(x,z))) )
| ( implies(y,implies(x,z)) != implies(truth,implies(y,implies(x,z))) ) ),
inference(instantiation,[status(thm)],[c_417]) ).
tcf(c_1193,plain,
( ( implies(y,implies(x,z)) = truth )
| ( truth != implies(truth,implies(y,implies(x,z))) )
| ( implies(y,implies(x,z)) != implies(truth,implies(y,implies(x,z))) ) ),
inference(instantiation,[status(thm)],[c_1191]) ).
tcf(c_1376,plain,
! [X0: $i,X1: $i] : implies(X0,implies(X1,X0)) = truth,
inference(demodulation,[status(thm)],[c_846,c_65]) ).
tcf(c_1396,plain,
! [X0: $i,X1: $i,X2: $i] : implies(truth,implies(implies(implies(X0,X1),X2),implies(X1,X2))) = truth,
inference(superposition,[status(thm)],[c_1376,c_64]) ).
tcf(c_2107,plain,
! [X0: $i] :
( ( truth = implies(truth,implies(y,implies(x,z))) )
| ( truth != X0 )
| ( implies(truth,implies(y,implies(x,z))) != X0 ) ),
inference(instantiation,[status(thm)],[c_623]) ).
tcf(c_2108,plain,
( ( truth = implies(truth,implies(y,implies(x,z))) )
| ( truth != truth )
| ( implies(truth,implies(y,implies(x,z))) != truth ) ),
inference(instantiation,[status(thm)],[c_2107]) ).
tcf(c_3236,plain,
( ordered(truth,implies(truth,implies(x,implies(y,z))))
| ( implies(x,implies(y,z)) = truth ) ),
inference(superposition,[status(thm)],[c_645,c_724]) ).
tcf(c_4058,plain,
( ( implies(truth,implies(y,implies(x,z))) = truth )
| ~ ordered(truth,implies(y,implies(x,z))) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_4312,plain,
( ordered(truth,implies(x,implies(y,z)))
| ( implies(x,implies(y,z)) = truth ) ),
inference(demodulation,[status(thm)],[c_3236,c_65]) ).
tcf(c_4315,plain,
ordered(truth,implies(x,implies(y,z))),
inference(forward_subsumption_resolution,[status(thm)],[c_4312,c_305]) ).
tcf(c_4316,plain,
implies(truth,implies(x,implies(y,z))) = truth,
inference(superposition,[status(thm)],[c_4315,c_62]) ).
tcf(c_5016,plain,
implies(x,implies(y,z)) = truth,
inference(demodulation,[status(thm)],[c_4316,c_65]) ).
tcf(c_5039,plain,
! [X0: $i] : implies(truth,implies(implies(implies(y,z),X0),implies(x,X0))) = truth,
inference(superposition,[status(thm)],[c_5016,c_64]) ).
tcf(c_5041,plain,
ordered(x,implies(y,z)),
inference(superposition,[status(thm)],[c_5016,c_61]) ).
tcf(c_5619,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(implies(X0,X1),X2),implies(X1,X2)) = truth,
inference(demodulation,[status(thm)],[c_1396,c_65]) ).
tcf(c_5675,plain,
! [X0: $i,X1: $i,X2: $i] : ordered(implies(implies(X0,X1),X2),implies(X1,X2)),
inference(superposition,[status(thm)],[c_5619,c_61]) ).
tcf(c_5819,plain,
! [X0: $i,X1: $i,X2: $i] : ordered(implies(implies(implies(X0,X1),X1),X2),implies(X0,X2)),
inference(superposition,[status(thm)],[c_63,c_5675]) ).
tcf(c_10798,plain,
! [X0: $i] : implies(implies(implies(y,z),X0),implies(x,X0)) = truth,
inference(demodulation,[status(thm)],[c_5039,c_65]) ).
tcf(c_10908,plain,
ordered(truth,implies(y,implies(x,z))),
inference(superposition,[status(thm)],[c_10798,c_5819]) ).
tcf(c_10930,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10908,c_5041,c_4058,c_2108,c_1193,c_802,c_801,c_416,c_372,c_140,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Wed Sep 23 22:04:21 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 0.07/0.33
% 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...
% 2.99/0.98 % SZS status Started for theBenchmark.p
% 2.99/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 2.99/0.98
% 2.99/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.99/0.98
% 2.99/0.98 % ------ iProver source info
% 2.99/0.98
% 2.99/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 2.99/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.99/0.98 % git: non_committed_changes: false
% 2.99/0.98
% 2.99/0.98 % ------ Parsing...% successful
% 2.99/0.98
% 2.99/0.98
% 2.99/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.99/0.98
% 2.99/0.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.99/0.98
% 2.99/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.99/0.98
% 2.99/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.99/0.98 % ------ Proving...
% 2.99/0.98 % ------ Problem Properties
% 2.99/0.98
% 2.99/0.98 %
% 2.99/0.98 % clauses 7
% 2.99/0.98 % conjectures 2
% 2.99/0.98 % EPR 0
% 2.99/0.98 % Horn 6
% 2.99/0.98 % unary 3
% 2.99/0.98 % binary 4
% 2.99/0.98 % lits 11
% 2.99/0.98 % lits eq 5
% 2.99/0.98 % fd_pure 0
% 2.99/0.98 % fd_pseudo 0
% 2.99/0.98 % fd_cond 0
% 2.99/0.98 % fd_pseudo_cond 0
% 2.99/0.98 % AC symbols 0
% 2.99/0.98
% 2.99/0.98 % ------ Schedule dynamic 5 is on
% 2.99/0.98
% 2.99/0.98 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.99/0.98
% 2.99/0.98
% 2.99/0.98 % ------
% 2.99/0.98 % Current options:
% 2.99/0.98 % ------
% 2.99/0.98
% 2.99/0.98
% 2.99/0.98 %
% 2.99/0.98
% 2.99/0.98 % ------ Proving...
% 2.99/0.98 %
% 2.99/0.98
% 2.99/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 2.99/0.98
% 2.99/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.99/0.98
% 2.99/0.98
%------------------------------------------------------------------------------