%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 01:58:05 PM UTC 2026
% Result : Unsatisfiable 61.44s 8.81s
% Output : CNFRefutation 61.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 67 unt; 0 def)
% Number of atoms : 67 ( 66 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 173 ( 0 sgn 173 !; 0 ?; 155 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : join(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
fof(f3,axiom,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
fof(f4,axiom,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
fof(f6,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
fof(f7,axiom,
! [X2,X0,X1] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
fof(f8,axiom,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
fof(f9,axiom,
! [X2,X0,X1] : join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)) = meet(join(meet(join(X0,X1),X2),X1),join(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity_dual) ).
fof(f10,negated_conjecture,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
tcf(c_60,plain,
! [X0: $i] : join(X0,X0) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : meet(X0,join(X0,X1)) = X0,
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : join(X0,meet(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : meet(X0,X1) = meet(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(meet(join(X0,X1),X2),X1),join(X2,X0)) = join(meet(join(meet(X0,X1),X2),X1),meet(X2,X0)),
inference(cnf_transformation,[],[f9]) ).
tcf(c_68,negated_conjecture,
meet(join(a,b),join(a,c)) != join(a,meet(b,c)),
inference(cnf_transformation,[],[f10]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),join(X2,meet(join(X1,X2),X0))) = join(meet(X0,X1),meet(X2,join(meet(X1,X2),X0))),
inference(theory_normalisation,[status(thm)],[c_67,c_66,c_64,c_65,c_63]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(X1,X2)) = meet(X1,meet(X0,X2)),
inference(superposition,[status(thm)],[c_65,c_63]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_66,c_64]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] : join(X0,meet(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_63,c_62]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] : meet(X0,join(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_64,c_61]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),join(X2,meet(join(X0,X2),X1))) = join(meet(X1,X0),meet(X2,join(meet(X0,X2),X1))),
inference(superposition,[status(thm)],[c_64,c_78]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),join(meet(X0,X1),meet(X2,join(meet(X1,X2),X0)))) = join(X0,X1),
inference(superposition,[status(thm)],[c_78,c_62]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,join(meet(X0,X1),meet(X2,join(meet(X1,X2),X0))))) = join(X0,X1),
inference(theory_normalisation,[status(thm)],[c_187,c_65,c_63,c_66,c_64]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(join(X0,X1),X2)) = meet(X0,X2),
inference(superposition,[status(thm)],[c_61,c_65]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(X0,meet(X1,X2))) = meet(X0,X1),
inference(superposition,[status(thm)],[c_65,c_62]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(X1,meet(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_65,c_159]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : join(X0,join(X0,X1)) = join(X0,X1),
inference(superposition,[status(thm)],[c_60,c_66]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(meet(X0,X1),X2)) = join(X0,X2),
inference(superposition,[status(thm)],[c_62,c_66]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(meet(X1,X0),X2)) = join(X0,X2),
inference(superposition,[status(thm)],[c_159,c_66]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(X1,meet(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_63,c_229]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(meet(X0,X1),X2),meet(X1,join(meet(X2,X1),meet(X0,X1)))) = meet(join(meet(X0,X1),X2),X1),
inference(superposition,[status(thm)],[c_229,c_78]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,meet(X1,X2)),meet(X1,join(meet(X2,X1),meet(X0,X1)))) = meet(X1,join(meet(X0,X1),X2)),
inference(theory_normalisation,[status(thm)],[c_361,c_65,c_63,c_66,c_64]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(join(X1,X2),join(meet(X1,join(X1,X2)),X0))) = meet(join(X0,X1),join(join(X1,X2),meet(join(X1,X2),X0))),
inference(superposition,[status(thm)],[c_248,c_78]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(join(X1,X2),join(meet(X1,join(X1,X2)),X0))) = meet(join(X0,X1),join(X1,join(X2,meet(join(X1,X2),X0)))),
inference(theory_normalisation,[status(thm)],[c_427,c_65,c_63,c_66,c_64]) ).
tcf(c_645,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(X0,meet(X2,X1))) = meet(X0,X1),
inference(superposition,[status(thm)],[c_149,c_159]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(join(X0,X1),X2),meet(X0,X2)) = meet(join(X0,X1),X2),
inference(superposition,[status(thm)],[c_224,c_159]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),meet(X0,X2)) = join(X0,X1),
inference(superposition,[status(thm)],[c_224,c_350]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,meet(X0,X2))) = join(X0,X1),
inference(theory_normalisation,[status(thm)],[c_752,c_65,c_63,c_66,c_64]) ).
tcf(c_758,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(join(X0,X2),X1)) = meet(join(X0,X2),X1),
inference(theory_normalisation,[status(thm)],[c_746,c_65,c_63,c_66,c_64]) ).
tcf(c_828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : join(X0,join(X1,join(meet(X0,X2),X3))) = join(X0,join(X1,X3)),
inference(superposition,[status(thm)],[c_150,c_249]) ).
tcf(c_953,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(meet(X0,X1),X2),join(X1,X2)) = join(meet(X0,X1),X2),
inference(superposition,[status(thm)],[c_250,c_161]) ).
tcf(c_968,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),join(meet(X2,X0),X1)) = join(meet(X2,X0),X1),
inference(theory_normalisation,[status(thm)],[c_953,c_65,c_63,c_66,c_64]) ).
tcf(c_5581,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,join(X1,X2)),meet(X0,X1)) = meet(X0,join(X1,X2)),
inference(superposition,[status(thm)],[c_61,c_645]) ).
tcf(c_5650,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,X1),meet(X0,join(X1,X2))) = meet(X0,join(X1,X2)),
inference(theory_normalisation,[status(thm)],[c_5581,c_65,c_63,c_66,c_64]) ).
tcf(c_8182,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,meet(X2,join(meet(X1,X2),X0)))) = join(X0,X1),
inference(demodulation,[status(thm)],[c_195,c_828]) ).
tcf(c_8232,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,meet(join(X1,X2),join(X1,X0)))) = join(X0,X1),
inference(superposition,[status(thm)],[c_61,c_8182]) ).
tcf(c_16172,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(join(X0,X1),join(X0,X2))) = meet(join(X0,X1),join(X0,X2)),
inference(superposition,[status(thm)],[c_61,c_758]) ).
tcf(c_21145,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(meet(X1,X0),meet(X2,X0))) = join(meet(X1,X0),meet(X2,X0)),
inference(superposition,[status(thm)],[c_159,c_968]) ).
tcf(c_22415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : join(meet(X0,X1),join(X2,meet(X0,join(X1,X3)))) = join(X2,meet(X0,join(X1,X3))),
inference(superposition,[status(thm)],[c_5650,c_150]) ).
tcf(c_31262,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(join(X1,X2),join(X1,X0))) = join(X0,X1),
inference(demodulation,[status(thm)],[c_8232,c_16172]) ).
tcf(c_31268,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(join(X1,X0),join(X1,X2))) = join(X0,X1),
inference(superposition,[status(thm)],[c_63,c_31262]) ).
tcf(c_32429,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(join(X0,X1),join(X1,X2))) = join(X0,X1),
inference(superposition,[status(thm)],[c_64,c_31268]) ).
tcf(c_34442,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(join(X1,X0),join(X1,X2))) = join(X1,X0),
inference(superposition,[status(thm)],[c_64,c_32429]) ).
tcf(c_35322,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(join(X0,X1),X0),meet(X2,join(meet(X0,X2),join(X0,X1)))) = meet(join(X0,join(X0,X1)),join(X0,X2)),
inference(superposition,[status(thm)],[c_34442,c_174]) ).
tcf(c_35447,plain,
! [X0: $i,X1: $i,X2: $i] : join(meet(X0,join(X0,X1)),meet(X2,join(X0,join(X1,meet(X0,X2))))) = meet(join(X0,join(X0,X1)),join(X0,X2)),
inference(theory_normalisation,[status(thm)],[c_35322,c_65,c_63,c_66,c_64]) ).
tcf(c_35448,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),join(X0,X2)) = join(X0,meet(X2,join(X0,X1))),
inference(light_normalisation,[status(thm)],[c_35447,c_61,c_248,c_754]) ).
tcf(c_35479,plain,
join(a,meet(c,join(a,b))) != join(a,meet(b,c)),
inference(demodulation,[status(thm)],[c_68,c_35448]) ).
tcf(c_57342,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(meet(X1,X0),X2)) = join(meet(X2,X0),meet(X1,X0)),
inference(demodulation,[status(thm)],[c_367,c_64,c_150,c_226,c_21145]) ).
tcf(c_57349,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),join(X2,meet(join(X1,X2),X0))) = join(meet(X0,X1),join(meet(X0,X2),meet(X1,X2))),
inference(demodulation,[status(thm)],[c_78,c_57342]) ).
tcf(c_57432,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),join(X1,X2)) = join(meet(X2,join(X0,X1)),X1),
inference(superposition,[status(thm)],[c_161,c_57342]) ).
tcf(c_57602,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),join(X1,X2)) = join(X1,meet(X2,join(X0,X1))),
inference(theory_normalisation,[status(thm)],[c_57432,c_65,c_63,c_66,c_64]) ).
tcf(c_77160,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,meet(X1,join(X0,X2))) = join(X0,meet(X1,X2)),
inference(demodulation,[status(thm)],[c_432,c_61,c_63,c_64,c_250,c_754,c_22415,c_57342,c_57349,c_57602]) ).
tcf(c_77161,plain,
join(a,meet(b,c)) != join(a,meet(c,b)),
inference(demodulation,[status(thm)],[c_35479,c_77160]) ).
tcf(c_77162,plain,
$false,
inference(theory_normalisation,[status(thm)],[c_77161,c_65,c_63,c_66,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n026.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 : Wed Sep 23 20:02:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 Running UEQ theorem proving
% 0.11/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 61.44/8.81 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 61.44/8.81 % SZS status Started for theBenchmark.p
% 61.44/8.81 % SZS status Unsatisfiable for theBenchmark.p
% 61.44/8.81
% 61.44/8.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 61.44/8.81
% 61.44/8.81 % ------ iProver source info
% 61.44/8.81
% 61.44/8.81 % git: date: 2026-07-19 20:42:38 +0200
% 61.44/8.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 61.44/8.81 % git: non_committed_changes: false
% 61.44/8.81
% 61.44/8.81 % ------ Parsing...% successful
% 61.44/8.81
% 61.44/8.81
% 61.44/8.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 61.44/8.81
% 61.44/8.81 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 61.44/8.81
% 61.44/8.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 61.44/8.81
% 61.44/8.81 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 61.44/8.81 % ------ Proving...
% 61.44/8.81 % ------ Problem Properties
% 61.44/8.81
% 61.44/8.81 %
% 61.44/8.81 % clauses 10
% 61.44/8.81 % conjectures 1
% 61.44/8.81 % EPR 0
% 61.44/8.81 % Horn 10
% 61.44/8.81 % unary 10
% 61.44/8.81 % binary 0
% 61.44/8.81 % lits 10
% 61.44/8.81 % lits eq 10
% 61.44/8.81 % fd_pure 0
% 61.44/8.81 % fd_pseudo 0
% 61.44/8.81 % fd_cond 0
% 61.44/8.81 % fd_pseudo_cond 0
% 61.44/8.81 % AC symbols 2
% 61.44/8.81
% 61.44/8.81 % ------ Input Options Time Limit: Unbounded
% 61.44/8.81
% 61.44/8.81
% 61.44/8.81 % ------
% 61.44/8.81 % Current options:
% 61.44/8.81 % ------
% 61.44/8.81
% 61.44/8.81
% 61.44/8.81 %
% 61.44/8.81
% 61.44/8.81 % ------ Proving...
% 61.44/8.81 %
% 61.44/8.81
% 61.44/8.81 % SZS status Unsatisfiable for theBenchmark.p
% 61.44/8.81
% 61.44/8.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.44/8.81
% 61.44/8.81
%------------------------------------------------------------------------------