%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL004-3 : 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 : n007.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 2.98s 1.52s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 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; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?; 5 :)
% 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,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
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,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,plain,
apply(y,apply(apply(x,x),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[c_54,c_52,c_53]) ).
tcf(c_64,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 07:07:38 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.50 Running UEQ theorem proving
% 0.19/0.50 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
% 0.25/0.52
% 0.25/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.25/0.52
% 0.25/0.52 % Detected problem language: tptp
% 0.25/0.54 % Proving...
% 2.98/1.52 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.98/1.52 % SZS status Started for theBenchmark.p
% 2.98/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 2.98/1.52
% 2.98/1.52 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.98/1.52
% 2.98/1.52 % ------ iProver source info
% 2.98/1.52
% 2.98/1.52 % git: date: 2026-07-19 20:42:38 +0200
% 2.98/1.52 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.98/1.52 % git: non_committed_changes: false
% 2.98/1.52
% 2.98/1.52 % ------ Parsing...% successful
% 2.98/1.52
% 2.98/1.52
% 2.98/1.52 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.98/1.52
% 2.98/1.52 % ------ Preprocessing...%
% 2.98/1.52
% 2.98/1.52 % SZS status Unsatisfiable for theBenchmark.p
% 2.98/1.52
% 2.98/1.52 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.98/1.52
% 2.98/1.52
%------------------------------------------------------------------------------