%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX199-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 03:32:48 PM UTC 2026
% Result : Unsatisfiable 104.51s 31.01s
% Output : CNFRefutation 104.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 55 ( 49 unt; 0 def)
% Number of atoms : 61 ( 60 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 17 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 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 : 14 ( 14 usr; 4 con; 0-5 aty)
% Number of variables : 133 ( 0 sgn 133 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : aux(X0,X1,X2,X3,btrue) = cons(X0,merge(X1,cons(X2,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
fof(f3,axiom,
! [X0] : leqNat(z,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(f4,plain,
! [X0] : btrue = leqNat(z,X0),
inference(reorient_equations,[],[f3]) ).
fof(f7,axiom,
! [X0,X1] : leqNat(s(X0),s(X1)) = leqNat(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
fof(f8,axiom,
! [X0] : merge(nil,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f9,axiom,
! [X0,X1] : merge(cons(X0,X1),nil) = cons(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
fof(f10,plain,
! [X0,X1] : cons(X0,X1) = merge(cons(X0,X1),nil),
inference(reorient_equations,[],[f9]) ).
fof(f11,axiom,
! [X2,X3,X0,X1] : merge(cons(X0,X1),cons(X2,X3)) = aux(X0,X1,X2,X3,leqNat(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f12,axiom,
! [X0] : impl(btrue,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
fof(f15,axiom,
! [X2,X0,X1] : prop_merge_comm(X0,X1,X2) = impl(eq(merge(X0,X1),merge(X1,X0)),impl(eq(merge(X0,X2),merge(X2,X0)),eq(merge(X1,X2),merge(X2,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
fof(f23,axiom,
! [X0] : eq2(s(X0),z) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(f24,plain,
! [X0] : bfalse = eq2(s(X0),z),
inference(reorient_equations,[],[f23]) ).
fof(f25,axiom,
! [X0] : eq(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_016) ).
fof(f26,plain,
! [X0] : btrue = eq(X0,X0),
inference(reorient_equations,[],[f25]) ).
fof(f27,axiom,
! [X0] : eq2(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
fof(f28,plain,
! [X0] : btrue = eq2(X0,X0),
inference(reorient_equations,[],[f27]) ).
fof(f29,axiom,
! [X0] : eq3(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
fof(f30,plain,
! [X0] : btrue = eq3(X0,X0),
inference(reorient_equations,[],[f29]) ).
fof(f31,axiom,
! [X2,X3,X0,X1] :
( eq(cons(X0,X2),cons(X1,X3)) = bfalse
| eq2(X0,X1) != bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( bfalse = eq(cons(X0,X2),cons(X1,X3))
| bfalse != eq2(X0,X1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,axiom,
! [X2,X3,X0,X1] :
( eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3)
| eq2(X0,X1) != btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3)
| btrue != eq2(X0,X1) ),
inference(reorient_equations,[],[f33]) ).
fof(f39,negated_conjecture,
! [X2,X0,X1] : eq3(prop_merge_comm(X0,X1,X2),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f40,plain,
! [X2,X0,X1] : btrue != eq3(prop_merge_comm(X0,X1,X2),bfalse),
inference(reorient_equations,[],[f39]) ).
fof(f41,plain,
! [X2,X0,X1] : btrue != eq3(impl(eq(merge(X0,X1),merge(X1,X0)),impl(eq(merge(X0,X2),merge(X2,X0)),eq(merge(X1,X2),merge(X2,X1)))),bfalse),
inference(definition_unfolding,[],[f40,f15]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : cons(X0,merge(X1,cons(X2,X3))) = aux(X0,X1,X2,X3,btrue),
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
! [X0: $i] : leqNat(z,X0) = btrue,
inference(cnf_transformation,[],[f4]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : leqNat(s(X0),s(X1)) = leqNat(X0,X1),
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,plain,
! [X0: $i] : merge(nil,X0) = X0,
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : merge(cons(X0,X1),nil) = cons(X0,X1),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : aux(X0,X1,X2,X3,leqNat(X0,X2)) = merge(cons(X0,X1),cons(X2,X3)),
inference(cnf_transformation,[],[f11]) ).
tcf(c_81,plain,
! [X0: $i] : impl(btrue,X0) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_87,plain,
! [X0: $i] : eq2(s(X0),z) = bfalse,
inference(cnf_transformation,[],[f24]) ).
tcf(c_88,plain,
! [X0: $i] : eq(X0,X0) = btrue,
inference(cnf_transformation,[],[f26]) ).
tcf(c_89,plain,
! [X0: $i] : eq2(X0,X0) = btrue,
inference(cnf_transformation,[],[f28]) ).
tcf(c_90,plain,
! [X0: $i] : eq3(X0,X0) = btrue,
inference(cnf_transformation,[],[f30]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( eq(cons(X0,X2),cons(X1,X3)) = bfalse )
| ( eq2(X0,X1) != bfalse ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( eq(cons(X0,X2),cons(X1,X3)) = eq(X2,X3) )
| ( eq2(X0,X1) != btrue ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_95,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] : eq3(impl(eq(merge(X0,X1),merge(X1,X0)),impl(eq(merge(X0,X2),merge(X2,X0)),eq(merge(X1,X2),merge(X2,X1)))),bfalse) != btrue,
inference(cnf_transformation,[],[f41]) ).
tcf(c_683,plain,
! [X0: $i,X1: $i,X2: $i] : merge(cons(z,X0),cons(X1,X2)) = aux(z,X0,X1,X2,btrue),
inference(superposition,[status(thm)],[c_75,c_80]) ).
tcf(c_685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : aux(s(X0),X1,s(X2),X3,leqNat(X0,X2)) = merge(cons(s(X0),X1),cons(s(X2),X3)),
inference(superposition,[status(thm)],[c_77,c_80]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i,X2: $i] : eq(cons(s(X0),X1),cons(z,X2)) = bfalse,
inference(superposition,[status(thm)],[c_87,c_91]) ).
tcf(c_1094,plain,
! [X0: $i,X1: $i,X2: $i] : eq(cons(X0,X1),cons(X0,X2)) = eq(X1,X2),
inference(superposition,[status(thm)],[c_89,c_92]) ).
tcf(c_1488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : eq(cons(s(X0),X1),aux(z,X2,X3,X4,btrue)) = bfalse,
inference(superposition,[status(thm)],[c_73,c_692]) ).
tcf(c_1494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : eq(aux(X0,X1,X2,X3,btrue),cons(X0,X4)) = eq(merge(X1,cons(X2,X3)),X4),
inference(superposition,[status(thm)],[c_73,c_1094]) ).
tcf(c_6975,plain,
! [X0: $i,X1: $i,X2: $i] : merge(cons(s(z),X0),cons(s(X1),X2)) = aux(s(z),X0,s(X1),X2,btrue),
inference(superposition,[status(thm)],[c_75,c_685]) ).
tcf(c_8371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : eq(aux(X0,X1,X2,X3,btrue),aux(X0,X4,X5,X6,btrue)) = eq(merge(X1,cons(X2,X3)),merge(X4,cons(X5,X6))),
inference(superposition,[status(thm)],[c_73,c_1494]) ).
tcf(c_9692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : eq3(impl(eq(merge(X0,cons(s(z),X1)),merge(cons(s(z),X1),X0)),impl(eq(merge(X0,cons(s(X2),X3)),merge(cons(s(X2),X3),X0)),eq(aux(s(z),X1,s(X2),X3,btrue),merge(cons(s(X2),X3),cons(s(z),X1))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_6975,c_95]) ).
tcf(c_14771,plain,
! [X0: $i,X1: $i,X2: $i] : eq3(impl(eq(merge(X0,cons(s(z),X1)),merge(cons(s(z),X1),X0)),impl(eq(merge(X0,cons(s(z),X2)),merge(cons(s(z),X2),X0)),eq(aux(s(z),X1,s(z),X2,btrue),aux(s(z),X2,s(z),X1,btrue)))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_6975,c_9692]) ).
tcf(c_14782,plain,
! [X0: $i,X1: $i,X2: $i] : eq3(impl(eq(merge(X0,cons(s(z),X1)),merge(cons(s(z),X1),X0)),impl(eq(merge(X0,cons(s(z),X2)),merge(cons(s(z),X2),X0)),eq(merge(X1,cons(s(z),X2)),merge(X2,cons(s(z),X1))))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_14771,c_8371]) ).
tcf(c_19941,plain,
! [X0: $i,X1: $i] : eq3(impl(eq(merge(nil,cons(s(z),X0)),merge(cons(s(z),X0),nil)),impl(eq(merge(nil,cons(s(z),X1)),cons(s(z),X1)),eq(merge(X0,cons(s(z),X1)),merge(X1,cons(s(z),X0))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_79,c_14782]) ).
tcf(c_19959,plain,
! [X0: $i,X1: $i] : eq3(eq(merge(X0,cons(s(z),X1)),merge(X1,cons(s(z),X0))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_19941,c_78,c_79,c_81,c_88,c_1094]) ).
tcf(c_20036,plain,
! [X0: $i] : eq3(eq(cons(s(z),X0),merge(X0,cons(s(z),nil))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_78,c_19959]) ).
tcf(c_20184,plain,
! [X0: $i] : eq3(eq(cons(s(z),cons(z,X0)),aux(z,X0,s(z),nil,btrue)),bfalse) != btrue,
inference(superposition,[status(thm)],[c_683,c_20036]) ).
tcf(c_20187,plain,
$false,
inference(ground_joinability,[status(thm)],[c_20184,c_90,c_1488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX199-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 23:36:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 104.51/31.01 % SZS status Started for theBenchmark.p
% 104.51/31.01 % SZS status Unsatisfiable for theBenchmark.p
% 104.51/31.01
% 104.51/31.01 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 104.51/31.01
% 104.51/31.01 % ------ iProver source info
% 104.51/31.01
% 104.51/31.01 % git: date: 2026-07-19 20:42:38 +0200
% 104.51/31.01 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 104.51/31.01 % git: non_committed_changes: false
% 104.51/31.01
% 104.51/31.01 % ------ Parsing...% successful
% 104.51/31.01
% 104.51/31.01
% 104.51/31.01 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 104.51/31.01
% 104.51/31.01 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 104.51/31.01
% 104.51/31.01 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 104.51/31.01
% 104.51/31.01 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 104.51/31.01 % ------ Proving...
% 104.51/31.01 % ------ Problem Properties
% 104.51/31.01
% 104.51/31.01 %
% 104.51/31.01 % clauses 23
% 104.51/31.01 % conjectures 1
% 104.51/31.01 % EPR 0
% 104.51/31.01 % Horn 23
% 104.51/31.01 % unary 21
% 104.51/31.01 % binary 2
% 104.51/31.01 % lits 25
% 104.51/31.01 % lits eq 25
% 104.51/31.01 % fd_pure 0
% 104.51/31.01 % fd_pseudo 0
% 104.51/31.01 % fd_cond 0
% 104.51/31.01 % fd_pseudo_cond 0
% 104.51/31.01 % AC symbols 0
% 104.51/31.01
% 104.51/31.01 % ------ Input Options Time Limit: Unbounded
% 104.51/31.01
% 104.51/31.01
% 104.51/31.01 % ------
% 104.51/31.01 % Current options:
% 104.51/31.01 % ------
% 104.51/31.01
% 104.51/31.01
% 104.51/31.01 %
% 104.51/31.01
% 104.51/31.01 % ------ Proving...
% 104.51/31.01 %
% 104.51/31.01
% 104.51/31.01 % SZS status Unsatisfiable for theBenchmark.p
% 104.51/31.01
% 104.51/31.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 104.51/31.01
% 104.51/31.01
%------------------------------------------------------------------------------