%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX222-1 : 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 : n005.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 03:32:53 PM UTC 2026
% Result : Unsatisfiable 0.90s 1.08s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X3,X0,X1] : aux(X0,X1,X2,just(X3)) = eq(X3,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
fof(f3,axiom,
notb(btrue) = bfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
fof(f4,plain,
bfalse = notb(btrue),
inference(reorient_equations,[],[f3]) ).
fof(f9,axiom,
! [X0,X1] : index(cons(X0,X1),zero) = just(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
fof(f11,axiom,
! [X0] : andb(btrue,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
fof(f18,axiom,
! [X0] : nf(lam(X0)) = nf(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
fof(f19,axiom,
! [X0] : nf(var(X0)) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_013) ).
fof(f20,plain,
! [X0] : btrue = nf(var(X0)),
inference(reorient_equations,[],[f19]) ).
fof(f22,axiom,
! [X2,X3,X0,X1] : tc(X0,lam(X1),arr(X2,X3)) = tc(cons(X2,X0),X1,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
fof(f29,axiom,
! [X2,X0,X1] : tc(X0,var(X1),X2) = aux(X0,X2,X1,index(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_019) ).
fof(f30,axiom,
! [X0] : sat_synth_nf_k(X0) = notb(andb(nf(X0),tc(nil,X0,arr(a,arr(b,b))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_020) ).
fof(f90,axiom,
! [X0] : eq(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
fof(f91,plain,
! [X0] : btrue = eq(X0,X0),
inference(reorient_equations,[],[f90]) ).
fof(f96,axiom,
! [X0] : eq4(X0,X0) = btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_054) ).
fof(f97,plain,
! [X0] : btrue = eq4(X0,X0),
inference(reorient_equations,[],[f96]) ).
fof(f98,negated_conjecture,
! [X0] : eq4(sat_synth_nf_k(X0),bfalse) != btrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f99,plain,
! [X0] : btrue != eq4(sat_synth_nf_k(X0),bfalse),
inference(reorient_equations,[],[f98]) ).
fof(f100,plain,
! [X0] : btrue != eq4(notb(andb(nf(X0),tc(nil,X0,arr(a,arr(b,b))))),bfalse),
inference(definition_unfolding,[],[f99,f30]) ).
tcf(c_105,negated_conjecture,
! [X0: $i] : eq4(notb(andb(nf(X0),tc(nil,X0,arr(a,arr(b,b))))),bfalse) != btrue,
inference(cnf_transformation,[],[f100]) ).
tcf(c_107,plain,
! [X0: $i] : eq(X0,X0) = btrue,
inference(cnf_transformation,[],[f91]) ).
tcf(c_111,plain,
! [X0: $i] : eq4(X0,X0) = btrue,
inference(cnf_transformation,[],[f97]) ).
tcf(c_128,plain,
notb(btrue) = bfalse,
inference(cnf_transformation,[],[f4]) ).
tcf(c_134,plain,
! [X0: $i] : andb(btrue,X0) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_135,plain,
! [X0: $i] : nf(var(X0)) = btrue,
inference(cnf_transformation,[],[f20]) ).
tcf(c_136,plain,
! [X0: $i] : nf(lam(X0)) = nf(X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] : aux(X0,X1,X2,index(X0,X2)) = tc(X0,var(X2),X1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : aux(X0,X1,X2,just(X3)) = eq(X3,X1),
inference(cnf_transformation,[],[f2]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : tc(X0,lam(X1),arr(X2,X3)) = tc(cons(X2,X0),X1,X3),
inference(cnf_transformation,[],[f22]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : index(cons(X0,X1),zero) = just(X0),
inference(cnf_transformation,[],[f9]) ).
tcf(c_765,plain,
! [X0: $i] : eq4(notb(andb(nf(X0),tc(nil,lam(X0),arr(a,arr(b,b))))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_136,c_105]) ).
tcf(c_771,plain,
! [X0: $i] : eq4(notb(andb(nf(X0),tc(cons(a,nil),X0,arr(b,b)))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_765,c_153]) ).
tcf(c_774,plain,
! [X0: $i] : eq4(notb(andb(nf(X0),tc(cons(a,nil),lam(X0),arr(b,b)))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_136,c_771]) ).
tcf(c_785,plain,
! [X0: $i] : eq4(notb(andb(nf(X0),tc(cons(b,cons(a,nil)),X0,b))),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_774,c_153]) ).
tcf(c_786,plain,
! [X0: $i] : eq4(notb(andb(btrue,tc(cons(b,cons(a,nil)),var(X0),b))),bfalse) != btrue,
inference(superposition,[status(thm)],[c_135,c_785]) ).
tcf(c_938,plain,
! [X0: $i,X1: $i,X2: $i] : aux(cons(X0,X1),X2,zero,just(X0)) = tc(cons(X0,X1),var(zero),X2),
inference(superposition,[status(thm)],[c_154,c_148]) ).
tcf(c_1011,plain,
! [X0: $i] : eq4(notb(tc(cons(b,cons(a,nil)),var(X0),b)),bfalse) != btrue,
inference(demodulation,[status(thm)],[c_786,c_134]) ).
tcf(c_2772,plain,
! [X0: $i,X1: $i,X2: $i] : tc(cons(X0,X1),var(zero),X2) = eq(X0,X2),
inference(demodulation,[status(thm)],[c_938,c_152]) ).
tcf(c_2778,plain,
eq4(notb(eq(b,b)),bfalse) != btrue,
inference(superposition,[status(thm)],[c_2772,c_1011]) ).
tcf(c_2779,plain,
$false,
inference(ground_joinability,[status(thm)],[c_2778,c_128,c_107,c_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX222-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 23:43:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 0.90/1.08 % SZS status Started for theBenchmark.p
% 0.90/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 0.90/1.08
% 0.90/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.90/1.08
% 0.90/1.08 % ------ iProver source info
% 0.90/1.08
% 0.90/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 0.90/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.90/1.08 % git: non_committed_changes: false
% 0.90/1.08
% 0.90/1.08 % ------ Parsing...% successful
% 0.90/1.08
% 0.90/1.08
% 0.90/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.90/1.08
% 0.90/1.08 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.90/1.08
% 0.90/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.90/1.08
% 0.90/1.08 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.90/1.08 % ------ Proving...
% 0.90/1.08 % ------ Problem Properties
% 0.90/1.08
% 0.90/1.08 %
% 0.90/1.08 % clauses 53
% 0.90/1.08 % conjectures 1
% 0.90/1.08 % EPR 0
% 0.90/1.08 % Horn 53
% 0.90/1.08 % unary 48
% 0.90/1.08 % binary 3
% 0.90/1.08 % lits 60
% 0.90/1.08 % lits eq 60
% 0.90/1.08 % fd_pure 0
% 0.90/1.08 % fd_pseudo 0
% 0.90/1.08 % fd_cond 0
% 0.90/1.08 % fd_pseudo_cond 0
% 0.90/1.08 % AC symbols 0
% 0.90/1.08
% 0.90/1.08 % ------ Schedule dynamic 5 is on
% 0.90/1.08
% 0.90/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.90/1.08
% 0.90/1.08
% 0.90/1.08 % ------
% 0.90/1.08 % Current options:
% 0.90/1.08 % ------
% 0.90/1.08
% 0.90/1.08
% 0.90/1.08 %
% 0.90/1.08
% 0.90/1.08 % ------ Proving...
% 0.90/1.08 %
% 0.90/1.08
% 0.90/1.08 % SZS status Unsatisfiable for theBenchmark.p
% 0.90/1.08
% 0.90/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.90/1.08
% 0.90/1.08
%------------------------------------------------------------------------------