%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 01:02:45 PM UTC 2026
% Result : Unsatisfiable 2.89s 1.32s
% Output : CNFRefutation 2.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 11 unt; 0 def)
% Number of atoms : 11 ( 10 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 9 ( 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',q_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
fof(f4,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p_combinator) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(w,X0),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[c_56,c_54,c_55]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(w,apply(apply(q,X0),X1)),X2) = apply(apply(X1,apply(X0,X2)),X2),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(q,X0)),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[status(thm)],[c_54,c_55]) ).
tcf(c_141,plain,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[c_68,c_138]) ).
tcf(c_156,plain,
$false,
inference(ground_joinability,[status(thm)],[c_141,c_54,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 07:26:51 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.45 Running UEQ theorem proving
% 0.10/0.45 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46
% 0.10/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.46
% 0.10/0.46 % Detected problem language: tptp
% 0.19/0.48 % Proving...
% 2.89/1.32 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.89/1.32 % SZS status Started for theBenchmark.p
% 2.89/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 2.89/1.32
% 2.89/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.89/1.32
% 2.89/1.32 % ------ iProver source info
% 2.89/1.32
% 2.89/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 2.89/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.89/1.32 % git: non_committed_changes: false
% 2.89/1.32
% 2.89/1.32 % ------ Parsing...% successful
% 2.89/1.32
% 2.89/1.32
% 2.89/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.89/1.32
% 2.89/1.32 % ------ Preprocessing... sup_sim: 1 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.89/1.32
% 2.89/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.89/1.32
% 2.89/1.32 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.89/1.32 % ------ Proving...
% 2.89/1.32 % ------ Problem Properties
% 2.89/1.32
% 2.89/1.32 %
% 2.89/1.32 % clauses 4
% 2.89/1.32 % conjectures 0
% 2.89/1.32 % EPR 0
% 2.89/1.32 % Horn 4
% 2.89/1.32 % unary 4
% 2.89/1.32 % binary 0
% 2.89/1.32 % lits 4
% 2.89/1.32 % lits eq 4
% 2.89/1.32 % fd_pure 0
% 2.89/1.32 % fd_pseudo 0
% 2.89/1.32 % fd_cond 0
% 2.89/1.32 % fd_pseudo_cond 0
% 2.89/1.32 % AC symbols 0
% 2.89/1.32
% 2.89/1.32 % ------ Input Options Time Limit: Unbounded
% 2.89/1.32
% 2.89/1.32
% 2.89/1.32 % ------
% 2.89/1.32 % Current options:
% 2.89/1.32 % ------
% 2.89/1.32
% 2.89/1.32
% 2.89/1.32 %
% 2.89/1.32
% 2.89/1.32 % ------ Proving...
% 2.89/1.32 %
% 2.89/1.32
% 2.89/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 2.89/1.32
% 2.89/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.89/1.32
% 2.89/1.32
%------------------------------------------------------------------------------