%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 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 01:02:46 PM UTC 2026
% Result : Unsatisfiable 3.90s 6.51s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 19 unt; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 2 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn 17 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f7,axiom,
! [X0] : apply(eq,pair(X0,X0)) = projection1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality) ).
fof(f8,plain,
! [X0] : projection1 = apply(eq,pair(X0,X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( apply(eq,pair(X0,X1)) = projection2
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
fof(f10,plain,
! [X0,X1] :
( projection2 = apply(eq,pair(X0,X1))
| X0 = X1 ),
inference(reorient_equations,[],[f9]) ).
fof(f12,axiom,
projection1 != projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_projections) ).
fof(f14,axiom,
apply(k,projection2) = k_projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_projection2) ).
fof(f15,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_referential) ).
tcf(c_62,negated_conjecture,
! [X0: $i,X1: $i] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i] : apply(eq,pair(X0,X0)) = projection1,
inference(cnf_transformation,[],[f8]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( apply(eq,pair(X0,X1)) = projection2 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
projection1 != projection2,
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,plain,
apply(k,projection2) = k_projection2,
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,plain,
apply(eq,pair(apply(k,s),apply(k,projection2))) = s,
inference(cnf_transformation,[],[f15]) ).
tcf(c_114,plain,
apply(eq,pair(apply(k,s),k_projection2)) = s,
inference(light_normalisation,[status(thm)],[c_74,c_73]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i] : apply(apply(k,X0),X1) = X0,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_473,plain,
! [X0: $i] : apply(k_projection2,X0) = projection2,
inference(superposition,[status(thm)],[c_73,c_128]) ).
tcf(c_789,plain,
( ( projection2 = s )
| ( apply(k,s) = k_projection2 ) ),
inference(superposition,[status(thm)],[c_69,c_114]) ).
tcf(c_1180,plain,
! [X0: $i] :
( ( projection2 = s )
| ( apply(k_projection2,X0) = s ) ),
inference(superposition,[status(thm)],[c_789,c_128]) ).
tcf(c_1188,plain,
projection2 = s,
inference(light_normalisation,[status(thm)],[c_1180,c_473]) ).
tcf(c_1189,plain,
apply(eq,pair(apply(k,projection2),k_projection2)) = projection2,
inference(demodulation,[status(thm)],[c_114,c_1188]) ).
tcf(c_1190,plain,
apply(eq,pair(k_projection2,k_projection2)) = projection2,
inference(light_normalisation,[status(thm)],[c_1189,c_73]) ).
tcf(c_1191,plain,
projection1 = projection2,
inference(demodulation,[status(thm)],[c_1190,c_68]) ).
tcf(c_1192,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1191,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.59 % Computer : n005.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.60 % CPULimit : 300
% 0.11/5.60 % WCLimit : 300
% 0.11/5.60 % DateTime : Fri Sep 25 07:29:09 UTC 2026
% 0.15/5.60 % CPUTime :
% 0.15/5.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.64 Running first-order theorem proving
% 0.15/5.64 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
% 0.15/5.65
% 0.15/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.65
% 0.15/5.65 % Detected problem language: tptp
% 0.15/5.66 % Proving...
% 3.90/6.51 % SZS status Started for theBenchmark.p
% 3.90/6.51 % SZS status Unsatisfiable for theBenchmark.p
% 3.90/6.51
% 3.90/6.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.90/6.51
% 3.90/6.51 % ------ iProver source info
% 3.90/6.51
% 3.90/6.51 % git: date: 2026-07-19 20:42:38 +0200
% 3.90/6.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.90/6.51 % git: non_committed_changes: false
% 3.90/6.51
% 3.90/6.51 % ------ Parsing...% successful
% 3.90/6.51
% 3.90/6.51
% 3.90/6.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.90/6.51
% 3.90/6.51 % ------ Preprocessing... sup_sim: 2 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.90/6.51
% 3.90/6.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.90/6.51
% 3.90/6.51 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.90/6.51 % ------ Proving...
% 3.90/6.51 % ------ Problem Properties
% 3.90/6.51
% 3.90/6.51 %
% 3.90/6.51 % clauses 13
% 3.90/6.51 % conjectures 2
% 3.90/6.51 % EPR 1
% 3.90/6.51 % Horn 12
% 3.90/6.51 % unary 11
% 3.90/6.51 % binary 2
% 3.90/6.51 % lits 15
% 3.90/6.51 % lits eq 15
% 3.90/6.51 % fd_pure 0
% 3.90/6.51 % fd_pseudo 0
% 3.90/6.51 % fd_cond 0
% 3.90/6.51 % fd_pseudo_cond 2
% 3.90/6.51 % AC symbols 0
% 3.90/6.51
% 3.90/6.51 % ------ Schedule dynamic 5 is on
% 3.90/6.51
% 3.90/6.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.90/6.51
% 3.90/6.51
% 3.90/6.51 % ------
% 3.90/6.51 % Current options:
% 3.90/6.51 % ------
% 3.90/6.51
% 3.90/6.51
% 3.90/6.51 %
% 3.90/6.51
% 3.90/6.51 % ------ Proving...
% 3.90/6.51 %
% 3.90/6.51
% 3.90/6.51 % SZS status Unsatisfiable for theBenchmark.p
% 3.90/6.51
% 3.90/6.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.90/6.52
% 3.90/6.52
%------------------------------------------------------------------------------