%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL004-1 : 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 : 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 01:02:31 PM UTC 2026
% Result : Unsatisfiable 7.96s 11.67s
% Output : CNFRefutation 7.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(apply(X0,f(X0)),g(X0)) != apply(g(X0),apply(apply(f(X0),f(X0)),g(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_combinator) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] : apply(g(X0),apply(apply(f(X0),f(X0)),g(X0))) != apply(apply(X0,f(X0)),g(X0)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[status(thm)],[c_52,c_53]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(X0,X2),X2),
inference(superposition,[status(thm)],[c_103,c_52]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,apply(s,k)),X0),X1) = apply(X0,X1),
inference(superposition,[status(thm)],[c_103,c_52]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,apply(s,apply(s,k))),X0),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[status(thm)],[c_118,c_52]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,apply(s,apply(k,X0))),X1),X2) = apply(X0,apply(X2,apply(X1,X2))),
inference(superposition,[status(thm)],[c_95,c_52]) ).
tcf(c_819,plain,
! [X0: $i,X1: $i] : apply(apply(apply(apply(s,s),apply(s,k)),X0),X1) = apply(apply(X0,X1),X1),
inference(superposition,[status(thm)],[c_52,c_117]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),X0)),X1) = apply(X1,X1),
inference(superposition,[status(thm)],[c_117,c_118]) ).
tcf(c_1289,plain,
! [X0: $i] : apply(apply(apply(s,apply(s,apply(s,k))),apply(f(X0),f(X0))),g(X0)) != apply(apply(X0,f(X0)),g(X0)),
inference(superposition,[status(thm)],[c_132,c_54]) ).
tcf(c_2616,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(apply(apply(s,s),apply(s,k)),X0),X2),
inference(superposition,[status(thm)],[c_819,c_117]) ).
tcf(c_4500,plain,
! [X0: $i,X1: $i,X2: $i] : apply(X0,apply(apply(apply(s,apply(s,apply(s,k))),X1),X2)) = apply(apply(apply(s,apply(s,apply(k,X0))),X1),X2),
inference(superposition,[status(thm)],[c_132,c_154]) ).
tcf(c_9336,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(apply(s,apply(s,apply(s,k))),apply(apply(s,k),X0)),f(X1))),g(X1)) != apply(apply(X1,f(X1)),g(X1)),
inference(superposition,[status(thm)],[c_884,c_1289]) ).
tcf(c_9870,plain,
! [X0: $i] : apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,apply(s,apply(s,apply(s,k)))))),f(X0)),g(X0)) != apply(apply(X0,f(X0)),g(X0)),
inference(demodulation,[status(thm)],[c_9336,c_2616,c_4500]) ).
tcf(c_9892,plain,
$false,
inference(equality_resolution,[status(thm)],[c_9870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/10.38 % Computer : n026.cluster.edu
% 0.08/10.38 % Model : x86_64 x86_64
% 0.08/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.38 % Memory : 8046.5625MB
% 0.08/10.38 % OS : Linux 6.8.0-71-generic
% 0.08/10.38 % CPULimit : 300
% 0.08/10.38 % WCLimit : 300
% 0.08/10.38 % DateTime : Fri Sep 25 07:12:35 UTC 2026
% 0.08/10.38 % CPUTime :
% 0.08/10.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/10.42 Running UEQ theorem proving
% 0.13/10.42 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
% 0.13/10.43
% 0.13/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.13/10.43
% 0.13/10.43 % Detected problem language: tptp
% 0.13/10.44 % Proving...
% 7.96/11.67 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 7.96/11.67 % SZS status Started for theBenchmark.p
% 7.96/11.67 % SZS status Unsatisfiable for theBenchmark.p
% 7.96/11.67
% 7.96/11.67 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.96/11.67
% 7.96/11.67 % ------ iProver source info
% 7.96/11.67
% 7.96/11.67 % git: date: 2026-07-19 20:42:38 +0200
% 7.96/11.67 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.96/11.67 % git: non_committed_changes: false
% 7.96/11.67
% 7.96/11.67 % ------ Parsing...% successful
% 7.96/11.67
% 7.96/11.67
% 7.96/11.67 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.96/11.67
% 7.96/11.67 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.96/11.67
% 7.96/11.67 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.96/11.67
% 7.96/11.67 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.96/11.67 % ------ Proving...
% 7.96/11.67 % ------ Problem Properties
% 7.96/11.67
% 7.96/11.67 %
% 7.96/11.67 % clauses 3
% 7.96/11.67 % conjectures 1
% 7.96/11.67 % EPR 0
% 7.96/11.67 % Horn 3
% 7.96/11.67 % unary 3
% 7.96/11.67 % binary 0
% 7.96/11.67 % lits 3
% 7.96/11.67 % lits eq 3
% 7.96/11.67 % fd_pure 0
% 7.96/11.67 % fd_pseudo 0
% 7.96/11.67 % fd_cond 0
% 7.96/11.67 % fd_pseudo_cond 0
% 7.96/11.67 % AC symbols 0
% 7.96/11.67
% 7.96/11.67 % ------ Input Options Time Limit: Unbounded
% 7.96/11.67
% 7.96/11.67
% 7.96/11.67 % ------
% 7.96/11.67 % Current options:
% 7.96/11.67 % ------
% 7.96/11.67
% 7.96/11.67
% 7.96/11.67 %
% 7.96/11.67
% 7.96/11.67 % ------ Proving...
% 7.96/11.67 %
% 7.96/11.67
% 7.96/11.67 % SZS status Unsatisfiable for theBenchmark.p
% 7.96/11.67
% 7.96/11.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.96/11.67
% 7.96/11.67
%------------------------------------------------------------------------------